performance evaluation of transit routes duong_tran... · 2019. 2. 6. · practical framework to...

PERFORMANCE EVALUATION OF TRANSIT

ROUTES

*****************************************************

Khac Duong Tran

Bachelor of Road and Highway Engineering

Master of Automobile and Urban Road Engineering

Submitted in fulfilment of the requirements for the degree of

Doctor of Philosophy

School of Civil Engineering and Built Environment

Science and Engineering Faculty

Queensland University of Technology

2019

Performance evaluation of transit routes

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Keywords

Transit System Performance/ Operation

Transit Route Performance/ Operation

Transit Performance Indicators

Technical Efficiency

Service Effectiveness

Operational Effectiveness

Efficiency Evaluation/ Measurement

Data Envelopment Analysis

Bootstrap Technique

Smartcard Data

Automatic Fare Collection


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Abstract

Transit agencies aim to allocate limited resources properly and maximise ridership.

Measuring the performance of individual transit routes within a transit system plays a critical

role in identifying operational issues and increasing transit ridership. However, evaluating the

performance of a transit route is a complex procedure because multiple objectives and

multiple input and output variables exist. Transit agencies thus need an appropriate method

to evaluate the efficiency of the transit routes’ performance and identify the key factors

influencing overall efficiency. The Data Envelopment Analysis (DEA) approach has been

utilised widely for comparing the performance of different transit systems or different transit

routes as production units. However, due to the simple transit data collected through manual

survey, the application of DEA models for measuring the performance of transit routes is fairly

limited. Addressing the aforementioned needs, this study aims to develop a scientific and

practical framework to evaluate the spatial and temporal performance of individual transit

routes that compose a transit network, and investigate sources of inefficiency.

To achieve this research aim, four major objectives are raised including to (1) develop

a conceptual framework to measure the operational effectiveness of individual bus routes

within a bus network, (2) measure the temporal and spatial performance of several key bus

routes within a bus network using the proposed framework, (3) investigate the external

sources of inefficiency by using the truncated regression model, and (4) provide general

recommendations to transit agencies based on the research findings for performance

improvement of bus routes of the case study. A network DEA model is adopted for efficiency

analysis, and the double bootstrap model is selected for sensitivity analysis of DEA efficiency

scores obtained to external factors (demographic and socio-economic characteristics).

Smart-card data from Brisbane, Australia is used to extract relevant inputs and outputs for

DEA models, and the ArcGIS spatial information tool is employed to collect external factors

within the service areas of individual bus routes. Those sources of data provide the spatial

and temporal performance of individual transit routes in detail. Therefore, this research helps

to fill the gaps of preceding studies, which use monthly or annual data to evaluate the average

efficiency and effectiveness of transit routes.

Using detailed data to evaluate the spatial and temporal performance of transit routes

enables the transit agency to rank performance, and then identify both internal and external

sources of inefficiency (bus schedule, vehicle type, socioeconomic and demographic

characteristics etc.). Furthermore, the proposed approach will assist decision makers to

optimally allocate limited resources across their transit system. At the route level, this

approach allows the transit agencies to reallocate the resources across different components


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of a transit route appropriately (vehicle capacity, stops facility, bus lanes, bus frequency,

information systems etc.).


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Table of Contents

Keywords .................................................................................................................. ii

Abstract ................................................................................................................... iii

Table of Contents ..................................................................................................... v

List of Figures .......................................................................................................... ix

List of Tables .......................................................................................................... xii

List of Abbreviations................................................................................................ xv

Statement of Original Authorship .......................................................................... xvii

Acknowledgements .............................................................................................. xviii

1 Introduction ........................................................................................................ 1

Research Background ................................................................................ 1

Research Problem and Purpose ................................................................. 5

Research Aim ............................................................................................. 6

Research Hypothesis .................................................................................. 6

Research Questions ................................................................................... 7

Research Objectives ................................................................................... 7

Research Scope ......................................................................................... 7

Scientific and Practical Significance ............................................................ 8

Study Outline .............................................................................................. 8

Publications ........................................................................................... 10

2 Literature Review ............................................................................................. 11

Transit policy making ................................................................................ 11

The Performance Measurement of Bus System ........................................ 13

Application of DEA for Bus Performance Evaluation ................................. 15

2.3.1 Transit Performance Concepts ............................................................ 15

2.3.2 Technical Efficiency Assessment for Transit System Performance ...... 16

2.3.3 Two Dimensions Assessment for Transit System Performance ........... 17

2.3.4 Assessment for Transit Route Performance ........................................ 19


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2.3.5 Summary of findings ............................................................................. 20

Research Gaps ......................................................................................... 28

3 Methodology .................................................................................................... 29

Introduction ................................................................................................ 29

Efficiency Measurement Concepts ............................................................ 31

3.2.1 Production function............................................................................... 31

3.2.2 Input-Oriented Measure ....................................................................... 31

3.2.3 Output-Oriented Measure ..................................................................... 33

Data Envelopment Analysis (DEA) ............................................................ 33

3.3.1 CCR- DEA Model ................................................................................. 34

3.3.2 BCC-DEA model .................................................................................. 37

3.3.3 Network DEA model ............................................................................. 38

3.3.4 The need of using DEA model .............................................................. 42

Sensitivity analysis in DEA ........................................................................ 43

3.4.1 Sensitivity analysis of DEA efficiency scores ........................................ 43

3.4.2 The bootstrap approach ....................................................................... 44

Transit Productiveness Indexes ................................................................. 45

Discussion ................................................................................................. 46

4 Framework for Bus Route Performance Measurement ..................................... 48

Introduction ................................................................................................ 48

The Study Goals Needed To Be Achieved................................................. 48

Develop the Framework for Bus Route Performance Measurement .......... 49

Inputs and Outputs Selection for Bus Routes ............................................ 50

4.4.1 Some crucial recommendations for input and output variables selection,

and the combination of inputs and outputs in DEA ...................................................... 50

4.4.2 Selection of inputs and outputs ............................................................ 52

External Variables (EVs) Selection ............................................................ 56

Discussion ................................................................................................. 57

5 Data Collection ................................................................................................. 58


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Introduction ............................................................................................... 58

Internal Variables ...................................................................................... 58

External Variables..................................................................................... 62

Summary .................................................................................................. 66

6 Data Analysis for Individual Bus Route of the Case Study ............................... 68

Introduction ............................................................................................... 68

Data Analysis for Bus Route 111 .............................................................. 68

6.2.1 DEA-based performance evaluation of route 111 ................................ 69

6.2.2 Comparison between DEA efficiency score and basic transit

productiveness indexes .............................................................................................. 75

DEA-based Performance Analysis of Individual Routes ............................ 78

6.3.1 High frequency bus routes ................................................................... 79

6.3.2 Low frequency bus routes for long service period ................................ 82

6.3.3 Low frequency bus routes for short service period ............................... 86

Summary of Findings ................................................................................ 89

7 Empirical Analysis for Bus System in the Case Study ...................................... 91

Introduction ............................................................................................... 91

Efficiency Analysis of Key Bus Routes for Separate Node ........................ 91

Efficiency Analysis of Key Bus Routes Using Network model ................... 99

Ranking the Performance of 52 Bus Routes ........................................... 105

7.4.1 Technical efficiency measure for bus routes (Model 1) ...................... 106

7.4.2 Service effectiveness measure (Model 2) .......................................... 113

7.4.3 Network performance measurement .................................................. 119

Identification of External Sources of Inefficiency and Recommendations 126

Summary of Findings .............................................................................. 133

8 Conclusion and Recommendations................................................................ 135

Summary of Research Findings .............................................................. 135

Research Contributions .......................................................................... 139

Practical Implications .............................................................................. 141


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Limitations ............................................................................................... 143

Recommendation for Future Research .................................................... 144

References .......................................................................................................... 146

SPATIAL EFFICIENCY SCORES OF INDIVIDUAL BUS ROUTES

151

DISCUSSION ON SLACKS ........................................................ 158

EXAMPLES FOR DETAILED SAMPLE CALCULATION USING THE

DEA MODELS 159


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List of Figures

Figure 1-1: Multiple objectives related to transit stakeholders of a transit route

(Source: Sheth et al. (2007)) ............................................................................................... 2

Figure 1-2: Framework for a transit network performance concept model (adapted

from Fielding et al. (1985)) .................................................................................................. 3

Figure 1-3: Research outline .................................................................................... 9

Figure 3-1: The outlines of research methodology ................................................. 30

Figure 3-2: Input-oriented technical and allocative efficiencies (Source: Coelli,

Prasada Rao et al. (1998)) ................................................................................................ 32

Figure 3-3: Output-oriented technical and allocative efficiencies (Source: Coelli,

Prasada Rao et al. (1998) ................................................................................................. 33

Figure 3-4: Production frontier of (a) CCR and (b) BCC models ............................. 37

Figure 3-5: The aggregated technology (Source: Färe et al. (2000)) ...................... 39

Figure 3-6: The network technology (Source: Färe et al. (2000)) ........................... 40

Figure 4-1: Framework for a transit route performance evaluation ......................... 50

Figure 4-2: The operational framework for a bus route performance evaluation ..... 54

Figure 5-1: Brisbane, Australia high frequency bus network map (Source:

http://translink.com.au) ...................................................................................................... 59

Figure 5-2: Flowchart for extracting transit route performance indicators ............... 61

Figure 5-3: An example of a bus route service area ............................................... 63

Figure 5-4: An example of pieces of land (POL) within the service corridor of bus route

.......................................................................................................................................... 64

Figure 6-1: Bus route 111 map (Source: Google map) ........................................... 70

Figure 6-2: The DEA efficiency score of the case 1, 2, and 3 for inbound direction 72

Figure 6-3: The DEA efficiency score of the case 1, 2, and 3 for outbound direction

.......................................................................................................................................... 73

Figure 6-4: The CRS-DEA efficiency score of the inbound, outbound, and combined

directions ........................................................................................................................... 74


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Figure 6-5: The VRS-DEA efficiency score of the inbound, outbound, and combined

directions ............................................................................................................................ 74

Figure 6-6: Transit work load factor and Passenger transmission efficiency of 111. 77

Figure 6-7: Correlation of Transit work load factor and DEA efficiency scores in case

1 ......................................................................................................................................... 77

Figure 6-8: Correlation of Transit passenger transmission efficiency and DEA

efficiency scores in case 2.................................................................................................. 77





Figure 6-11: CRS-DEA efficiency score of route 100 (follows pattern 1) ................. 80





Figure 6-16: CRS-DEA efficiency score of route 124 .............................................. 83












Figure 7-1: The VRS-DEA efficiency score of bus routes in model 1 ...................... 93


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Figure 7-2: The VRS-DEA efficiency score of bus routes in model 2 ...................... 94

Figure 7-3: The network technology of bus route performance ............................ 100

Figure 7-4: DEA efficiency scores of network and separate nodes (the morning peak

hour) ................................................................................................................................ 101

Figure 7-5: Efficiency score of the network and aggregate model (the morning peak

hour) ................................................................................................................................ 105

Figure 7-6: Efficiency score variations of bus routes in model 1 for different periods of

time, following the gradual decrease of a day’s efficiency scores .................................... 112

Figure 7-7: Efficiency score variations of bus routes in model 2 for different periods of

time, following the gradual decrease of a day’s efficiency scores .................................... 118

Figure 7-8: Efficiency score variations of bus routes in network model for different

periods of time, following the gradual decrease of a day’s efficiency scores .................... 124

Figure 7-9: Efficiency score variations of bus routes in models 1 and 2 for a day

following the gradual decrease of model 2 efficiency scores............................................ 125

Figure 8-1: Policy implications of transit routes performance analysis .................. 142


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List of Tables

Table 2-1: Quality of service measures for fixed-route transit ................................. 14

Table 2-2: An overview of the application of DEA in measuring the transit performance

........................................................................................................................................... 24

Table 4-1: An overview of inputs and outputs selection for bus route performance

evaluation ........................................................................................................................... 51

Table 4-2: Selection of inputs and outputs for bus route performance measurement

........................................................................................................................................... 55

Table 5-1: Statistical description of the inputs and outputs of the 52 bus routes for a

morning and an afternoon peak hour, and an off-peak hour of 21 August 2013 .................. 62

Table 5-2: a) Statistical description; and b) Correlation analysis results of EVs of 52

bus routes of the case study in Brisbane, Australia ............................................................ 66

Table 6-1: Statistical description of the inputs and outputs of route 111 for inbound

direction ............................................................................................................................. 70

Table 6-2: Statistical description of the inputs and outputs of route 111 for outbound

direction ............................................................................................................................. 71

Table 6-3: Inputs and outputs using for DEA models in cases 1, 2, 3, and 4 ........... 71

Table 6-4: Efficiency scores and scale efficiency of route 111 (combined directions)

........................................................................................................................................... 75

Table 6-5: Typical patterns describing the changes of efficiency scores of bus routes

during a day ....................................................................................................................... 89

Table 7-1: The summary statistics of efficiency scores obtained through DEA for

models 1 and 2 ................................................................................................................... 92

Table 7-2: Inputs and outputs of a) route 175 and its benchmarks in model 1; and b)

route 220 and its benchmarks in model 2 during the morning peak hour ............................ 95

Table 7-3: Slacks for inefficient routes in model 1 during the morning peak hour .... 96

Table 7-4: Slacks for some inefficient routes in model 2 during the morning peak hour

........................................................................................................................................... 98

Table 7-5: Input slacks for the most inefficient routes in the NDEA model during the

morning peak hour ........................................................................................................... 102


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Table 7-6: Output slacks for the most inefficient routes in the NDEA model during the

morning peak hour .......................................................................................................... 102

Table 7-7: Efficiency analysis of routes 100 and 353 for the morning peak hour using

the NDEA model .............................................................................................................. 104

Table 7-8: Efficiency scores of 52 bus routes in model 1 from hour 7 to hour 13 .. 107

Table 7-9: Efficiency scores of 52 bus routes in model 1 from hour 14 to hour 19 108

Table 7-10: Efficiency scores of 52 bus routes in model 1 for different periods of time

and a day ........................................................................................................................ 109

Table 7-11: Ranking of 52 bus routes in model 1 for a day (21 Aug 2013) ........... 110

Table 7-12: Correlation analysis results of efficiency scores of different periods of time

........................................................................................................................................ 111

Table 7-13: Efficiency scores of 52 bus routes in model 2 from hour 7 to hour 13 114

Table 7-14: Efficiency scores of 52 bus routes in model 2 from hour 14 to hour 19

........................................................................................................................................ 115

Table 7-15: Efficiency scores of 52 bus routes in model 2 for different periods of time

and a day ........................................................................................................................ 116

Table 7-16: Ranking of 52 bus routes in model 2 for a working day (21 Aug 2013)

........................................................................................................................................ 117


........................................................................................................................................ 118

Table 7-18: Network efficiency scores of 52 bus routes from hour 7 to hour 13 ... 120

Table 7-19: Network efficiency scores of 52 bus routes from hour 14 to hour 19 . 121

Table 7-20: Network efficiency scores of 52 bus routes for different periods of time

and a day ........................................................................................................................ 122

Table 7-21: Ranking of 52 bus routes in network model for a working day (21 Aug

2013) ............................................................................................................................... 123


........................................................................................................................................ 123

Table 7-23: Efficiency scores statistics of some routes for models 1 and 2 .......... 126


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Table 7-24: a) Original and bias-corrected efficiency scores; and b) Truncated

Regression ....................................................................................................................... 129

Table 7-25: Recommendations for performance improvement of inefficient bus routes

......................................................................................................................................... 131

Table 7-26: Reduction of service duration for inefficient bus routes in model 1 (the

morning peak hour) .......................................................................................................... 132

Table 7-27: Reduction of space-km for inefficient bus routes in model 2 (the morning

peak hour) ........................................................................................................................ 133


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List of Abbreviations

ABS: Australian Bureau of Statistics

AFC: Automated Fare Collection

BCC: Banker, Charnes, Cooper

CCR: Charnes, Cooper, Rhodes

CA: Comparative Analysis

CO: Car Ownership

CRS: Constant Returns to Scale

DEA: Data Envelopment Analysis

DMUs: Decision Making Units

EVs: External Variables

FDH: Free Disposal Hull

GIS: Geographic Information System

ID: Identification

MSL: Maximum Schedule Load

NDEA: Network Data Envelopment Analysis

OLS: Ordinary Least Square

OTP: On-Time Performance

PT: Public Transit

PR: Transit Provider

PA: Passenger

POP: Population

POD: Population Density

POL: Piece of Land

QOS: Quality of Service

SFA: Stochastic Frontier Analysis


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SEQ: South East Queensland

SK: Seat Kilometres

SH: Seat Hours

SA1: Statistical Areas Level 1

TE: Technical Efficiency

VRS: Variable Returns to Scale


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Statement of Original Authorship

The work contained in this thesis has not been previously submitted to meet

requirements for an award at this or any higher education institution. To the best of my

knowledge and belief, the thesis contains no material previously published or written by

another person except where due reference is made.

Signature: Khac Duong Tran

Date: January 2019

QUT Verified Signature


Khac Duong Tran Page xviii

Acknowledgements

I would like to acknowledge my principle supervisor, Dr Ahish Bhaskar, and my

associate supervisors, Associate Professor Jonathan Bunker and Dr Boon Lee, for their kind

support and guidance throughout my PhD project. I greatly appreciate their inspiring

supervision, constructive criticism, and encouragement during my PhD journey.

I wish to thank TransLink Division of the Queensland Department of Transport and

Main Roads, which has supplied the smart-card data of the transit system in South East

Queensland (SEQ), Australia. I would also like to express my gratitude to Prof. Edward Chung

and the Smart Transport Research Centre (STRC) staff, especially Dr Le Minh Kieu, for their

useful comments and friendly feedback on this research in the STRC seminars. Furthermore,

I would like to thank my friends at QUT for their support and friendly advice. They have made

my life at QUT meaningful and enjoyable.

Professional editor, Diane Kolomeitz, provided copyediting and proofreading services,

according to the guidelines laid out in the university-endorsed national ‘Guidelines for editing

research theses’.

I would especially like to acknowledge Vietnam International Education Development

(VIED) and Queensland University of Technology (QUT) for providing me with a PhD

scholarship, which has definitely motivated me a lot throughout my study time at QUT. This

research would not be possible without their finance support. I would also like to take this

opportunity to acknowledge the University of Transport and Communications (UTC),

Vietnam, my employer, for their support during the time in which I have performed my PhD

project abroad.

Finally, I would like to express my deepest gratitude to my family for their

unconditional love, emotional support, and encouragement. I am especially grateful to my

wife, Mrs Thanh Van Pham, and my children, who have always given me emotional

encouragement during difficult times. Without their love and trust, I would have not been able

to complete this dissertation.

Introduction

Khac Duong Tran Page 1

1 Introduction

Research Background

The rapid growth of population and the high level of dependence on private motor

vehicles are challenges that many urban areas worldwide are facing. This leads to the rapid

growth of private car use in urban areas and puts higher pressure on the urban transport

system. The increasing use of private motor vehicles has adverse impacts on the quality of

life of residents, such as excessive congestion, traffic noise and air pollution (Greene and

Wegener 1997). It is, thus, important to seek out effective solutions to reduce the use of

private cars and minimise their adverse effects on the urban environment. These solutions

include the improvement of city planning and infrastructure to reduce congestion; the

development of a new generation of private motor vehicles with less detrimental emissions;

establishment of travel behaviour change programs intended for active transport; and

provision of alternatives to private car use (Loukopoulos 2007). Public transport is considered

as a sustainable transport mode in urban areas and could be a viable alternative to private

motor vehicles (Holmgren 2007).

South East Queensland (SEQ), Australia, has experienced a rapid growth of

population. Between 2006 and 2016, SEQ witnessed a population increase of 24% (ABS

2016), which is forecasted to reach 4.2 million in 2031. This leads to increasing travel demand

within this region from just over 9 million daily trips in 2006 to an estimated 15 million daily

trips by 2031 (Government 2011). This region also witnesses a high level of dependence on

private motor vehicles, with the mode share of private cars being 83% compared to only 7%

mode share of public transport in 2006. Thus, Connecting SEQ 2031 (Government 2011),

the Queensland Government’s long-term transport plan to develop a sustainable transport

system in SEQ, has established a target to increase the mode share of transit in SEQ to 14%

in 2031, with a major shift from private car use.

To increase transit ridership effectively, transit agencies need to continuously

optimise their performance and improve the quality of service (QOS). Measuring the

performance of individual routes within a transit system plays a critical role in identifying

improvement needs in system design, operation and control; and in seeking means to

increase ridership.

However, evaluating the performance of individual transit lines/routes is complex

because multiple objectives, and multiple input and output variables, exist (Benn 1995, Sheth,

Triantis et al. 2007, Barnum, Tandon et al. 2008). As shown in Figure 1-1, there are multiple

Introduction


transit stakeholders relevant to bus operations including provider, user, and community.

Multiple quality (e.g., comfort) and quantity (e.g., revenue) objectives also apply to bus

operations on a given route. For example, bus operators strive to minimise the operational

cost (fuel, maintenance, staffs, vehicles), the negative impacts on environment and

community (emission, accidents), and maximise ridership. Subsequently, bus users strive to

maximise the span of service, the on-time performance, and service frequency (Benn 1995,

Barnum, Tandon et al. 2008). Each objective relates to some performance indicators and

relevant variables. For instance, ridership depends on population density, average residents’

income, parking space near bus stops, private car ownership, travel time, stop arrival

reliability, total kilometres traversed and service duration over a day. Furthermore, some

objectives are in conflict with others, such as the operational cost borne by the

provider versus service frequency and span of service offered to the user. Figure 1-1

presents the typical relationship between the ridership, the operational costs and key transit

performance indicators as well as relevant variables.

Figure 1-1: Multiple objectives related to transit stakeholders of a transit route (Source: Sheth et al.

(2007))

The complexity of transit performance led to the development of a framework by

Fielding et al. (1985) for transit system performance measurement. This framework, made

PT stakeholders Objectives

Minimise the operational costs

PT Provider

PT User

Community

Maximise the ridership

Maximise the revenue

Minimise the travel time

Maximise the on-time performance

Maximise the duration of service

Maximise the service frequency

Maximise the comfort

Minimise the emission

Minimise the number of accidents

Minimise the congestion

Minimise the resource degradation

Maximise the service coverage

PT Performance indicators

and relevant variables

Length of PT route

Number of stops

Number of intersections

Number of priority lanes

Service duration a day

Service frequency (headway)

Travel time

Dwell time at stops

Stop arrival reliability

Vehicle-km

Seat-km

Vehicle passenger loading

Stop Accessibility

Stop parking space availability

Linked stops

Population density

Private car ownership

Corridor congestions

PT vehicle size

Average corridor speed

Average resident's income

Introduction


up of three dimensions, comprises technical efficiency, operational effectiveness (also

termed cost effectiveness), and service effectiveness. Figure 1-2 illustrates the relationship

between the three performance measures and presents a sample list of variables related to

various inputs and outputs.

• Technical efficiency represents the process through which service inputs are

transformed into outputs. This means that a transit agency invests capital in

vehicles, fuel, information systems, employees, maintenance, and other costs

(inputs). This investment produces a certain service for a community such as

vehicle-km, seat-km, and seat-hours (outputs). An agency is considered efficient

if it can reduce the inputs to produce a fixed amount of outputs, or increase the

outputs while using similar or fewer inputs.

• Operational effectiveness indicates the relationship between service inputs and

consumed service. A transit agency spends money to offer its service, and a

number of passengers (per day or week) consume its service. The transit agency

will achieve higher cost effectiveness, if it increases ridership without increasing

the total cost of producing the service.

• Service effectiveness examines the relationship between produced outputs and

consumed service or how well a service offered by operators is consumed by a

community (Georgiadis, Politis et al. 2014). This means that not all of the services

offered (measured by vehicle-km, seat-km, and/or seat-hours) would be used by

a community. If it attracts more passengers without increasing service, or reduces

service but still serves a similar number of passengers, it will be more effective.

Figure 1-2: Framework for a transit network performance concept model (adapted from Fielding et al.

(1985))

Introduction


The framework of Fielding et al. (1985) allows one to compare the performance of

different transit systems for a particular performance concept (such as vehicle efficiency, fuel

efficiency, and operating safety) by using single ratios of service output and service input.

This approach cannot provide a single overall measure for transit performance evaluation.

This issue is addressed by using Data Envelopment Analysis (DEA), which is a non-

parametric approach to evaluate the efficiency of different production units or decision making

units (DMUs) accounting for multiple inputs and outputs (Sheth, Triantis et al. 2007, Barnum,

Tandon et al. 2008, Lao and Liu 2009, Georgiadis, Politis et al. 2014). However, different

transit performance concepts (technical efficiency, service effectiveness, and operational

effectiveness) are treated separately in those studies, leading to different efficiency

measures. Furthermore, these studies failed to adequately measure the temporal and spatial

performance of transit routes due to their limited data, collected from manual survey. For

instance, travel time is estimated on the basis of the standard of bus operating speed, which

depends upon the distribution of transit routes in the urban or suburban area, or schedule

reliability is estimated on the basis of traffic congestion (Sheth, Triantis et al. 2007).

Additionally, the influence of external factors (such as private car ownership, population

density, individual income, and employment distribution) on bus routes’ operation was not

examined sufficiently because of the lack of detailed data within the service areas of a single

bus route. Hence, it is worth developing a comprehensive approach for evaluating the

performance of transit routes within a network using a rich data source, considering the

influence of external factors.

Recently, the availability of smartcard-based automated fare collection systems (AFC)

in the transit sector has provided a valuable opportunity for better understanding the transit

operation in detail (Trépanier, Morency et al. 2009). This research, therefore, focuses on the

performance measurement of individual transit routes within a network, using AFC data. The

City of Brisbane, Australia, is opted as the case study, where the transit services are provided

by the Translink Division of the Queensland Department of Transport and Main Roads. As

bus transport has the most significant transit mode share in Brisbane (TransLink 2017), this

study selects the bus network in this region for empirical analysis.

The study findings provide transit agencies with a comprehensive approach for transit

route performance analysis. The knowledge gained helps to identify the most efficient routes

(the benchmarks), the most inefficient routes, and sources of inefficiency; and then effectively

assists policy makers in developing more practical and appropriate policies. The performance

improvement of inefficient routes will lead to the performance improvement of the whole

transit system (Barnum, Tandon et al. 2008).

Introduction


This chapter is organised as follows: Section 1.2 introduces the research problem and

purpose. The research aims and hypotheses are presented in section 1.3 and 1.4

respectively. Thereafter, the research questions are stated in section 1.5. Section 1.6

introduces the research objectives. The research scope is mentioned in section 1.7, which is

followed by the research significance in section 1.8. Section 1.9 represents the study outline.

Finally, the list of publications from this thesis is provided in section 1.10.

Research Problem and Purpose

If a given transit agency, such as Translink in Queensland, Australia, aims to improve

its transit system performance (for example a bus system) as efficiently and economically as

possible, it needs to investigate the performance of individual routes (the basic unit for

delivering services) within this network and identify the sources of inefficiencies that should

support the policy makers and network planners. However, as shown in Figure 1-1, evaluating

bus route performance is complex, as multiple bus indicators and variables exist.

This problem has raised questions:

• How can multiple objectives and performance indicators of bus routes be taken

into consideration when comparing the operation of different bus routes?

• Can a single composite score be generated that fairly and objectively aggregates

the various objectives of a bus route, to compare the operation of different bus

routes?

• How can the influences of external factors on bus routes’ performance be

investigated?

Answers to such questions would definitely be useful to transit agencies and policy

makers, to optimise current transit system performance.

Researchers have used both parametric (ordinary least squares (OLS) and stochastic

frontier analysis (SFA)) and non-parametric (free disposal hull (FDH) (Tulkens 1993), Data

Envelopment Analysis (DEA) (Ray 2004, Cooper, Seiford et al. 2007)) approaches for transit

performance evaluation. DEA is a non-parametric method based on linear programming and

optimisation. It measures the relative efficiencies of DMUs using multi-inputs and multi-

outputs. Most studies, thus, have developed DEA-based approaches to measure the

performance of transit agencies, as well as individual transit lines/routes within a transit

system (Chu, Fielding et al. 1992, Viton 1997, Viton 1998, Sheth, Triantis et al. 2007,

Georgiadis, Politis et al. 2014). However, most studies have treated transit agencies as DMUs

(macro level), while a limited number of studies have treated transit routes as DMUs (micro

Introduction


level) although this work, as above indicated, is of importance for short-term planning such

as network redesign (Sheth, Triantis et al. 2007, Barnum, Tandon et al. 2008, Lao and Liu

2009, Georgiadis, Politis et al. 2014, Rohácová 2015).

Regarding transit routes’ performance evaluation, particular performance concepts

such as technical efficiency, service effectiveness, and operational effectiveness are

measured separately. Thus, they cannot provide an overall and single measure for the whole

production process of transit routes. Furthermore, population information (regarded as an

external factor) is used as an input for efficiency analysis in those studies. For instance, Lao

and Liu (2009) use number of retirees within the service areas of a bus route as an input to

measure spatial effectiveness of bus routes; and Sheth et al. (2007) use population density

factor as an input of user node for estimating the efficiency scores of bus routes. Therefore,

the impact of a wide range of external factors (socioeconomic and demographic

characteristics) on transit route performance was not examined adequately.

With the availability of AFC data in the case study of Brisbane, and the socio-

economic and demographic data drawn from Australia Bureau of Statistics (ABS), this

research will develop a network DEA-based approach to compare and rank the performance

of several key bus routes within the Brisbane bus network. The approach developed helps to

provide insights into the performance of transit routes and identify internal factors related to

the inefficiency. Furthermore, the influence of a wide range of external factors (such as private

car ownership, population density, individual income, and route characteristics) on bus route

operation is examined in the second stage, using a truncated regression model. This provides

insights into the external reasons behind the poor performance of some routes.

Research Aim

This research aims to develop a scientific and practical framework to evaluate the

spatial and temporal performance of individual transit routes composing a transit network,

and investigate the sources of operational inefficiency of transit routes.

Research Hypothesis

The performance efficiency of transit routes within a network can be estimated using

a non-parametric approach, which accounts for the influences of external factors within the

service areas.

Introduction


Research Questions

Based on the aforementioned research aim and hypothesis, the following research

questions are identified:

1. Which models can be the best tools to measure the efficiency of bus routes?

2. Which inputs and outputs are used for the selected model to estimate the

efficiency scores of bus routes?

3. Which external factors potentially have most impact on the performance of bus

routes?

4. How can the sensitivity of external variables to efficiency scores of bus routes be

tested?

5. How can the robustness of the results be tested?

Research Objectives

The following research objectives have been set to achieve the research aim:

1. Build up a framework to measure the operational effectiveness of key bus routes

within a bus network.

2. Measure the temporal and spatial performance of key bus routes within the

Brisbane bus network using the proposed framework in objective 1.

3. Examine the influence of external variables on the efficiency scores estimated in

objective 2.

4. Provide recommendations to transit agencies and policy makers to improve bus

route performance considering the knowledge generated through the case study

conducted.

Research Scope

In an urban area, the transit system includes various modes such as bus, ferry, and

rail. An operator may employ one or more modes. While this study examines the performance

of individual urban bus routes within a transit agency, the framework developed in this

research is applicable to other modes (rail and ferry).

The case study performed in the research focuses on the weekdays and normal

running conditions only. Consideration of non-recurrent congestion due to incidents and

unplanned events are beyond the scope of the research.

Introduction


As abovementioned, the aim of this study is to provide insights into bus routes’

operation by using AFC data. Hence, the proposed approach is worth applying for AFC-based

transit networks.

Scientific and Practical Significance

▪ This research develops a comprehensive framework for performance evaluation

of bus routes, and investigates sources of inefficiencies using the AFC data.

▪ Transit agencies can apply the approach presented in this research to identify bus

routes that have the best performance (regarded as benchmark), fairly good

performance, and the worst performance. Sources of inefficiency related to

internal factors can also be identified.

▪ Findings from the current research will identify sources of inefficiency related to

external factors (socioeconomic and demographic characteristics of bus service

areas). This assists regulators in developing appropriate policies to enhance the

transit mode share.

▪ The application of the proposed approach assists transit agencies to optimally

allocate limited resources across their bus network. They can retain efficient bus

routes while reducing the operation of some inefficient bus routes to the extent

possible. At the route level, this approach allows transit agencies to reallocate the

resources across different components of bus route appropriately (vehicle

capacity, stops facility, bus lanes, bus frequency, information systems).

Study Outline

The remainder of this thesis is organised as follows:

Chapter 2 reviews key approaches for the performance measurement of bus systems

and transit policy making for the performance improvement of bus systems, and the

application of a non-parametric approach (DEA) for bus performance measurement.

Chapter 3 presents the basic DEA models and network DEA model, sensitivity

analysis in DEA, and several transit productiveness indexes.

Chapter 4 discusses and develops the framework for the performance measurement

of bus routes using network DEA models, with the selection of appropriate variables.

Chapter 5 introduces the case study site and the relevant data used for developing

and testing the proposed approach.

Introduction


Chapter 6 investigates the temporal performance of several bus routes of the case

study using DEA models. It enhances substantial understandings of each bus route

performance.

Chapter 7 compares the temporal and spatial performance of sample bus routes

using network DEA models. Sensitivity analysis is conducted for DEA-based efficiency scores

to investigate the influences of external factors on the efficiency level of bus routes.

Chapter 8 discusses the research findings, contributions, practical implications, and

limitations. Finally, future research directions are provided.

An outline of the present research is expressed in Figure 1-3, which consists of five

research questions (Q1, Q2, Q3, Q4, and Q5) and four research objectives (Obj 1, Obj 2, Obj

3, and Obj 4).

Figure 1-3: Research outline

Chapter 1: Introduction

Chapter 2: Literature Review

Chapter 3: Methodology

CCR-DEA and

BCC-DEA models

Network DEA models Sensitivity analysis in

DEA models

Chapter 4: Framework for bus route performance

evaluation and relevant variables

Chapter 5: Data collection

Internal variables External variables

Chapter 6: Data analysis for

individual bus routes of the case study

Chapter 7: Data analysis for

bus system of the case study

Chapter 8: Conclusions and recommendations

and future research directions

Obj 1

Obj 2 Obj 3

Obj 4

Q1

Q2, Q3

Q4

Q5

Introduction


Publications

Conference papers

1. Tran, Khac-Duong, Bhaskar, Ashish, Bunker, Jonathan M., & Lee, Boon

L. (2016) Data envelopment analysis (DEA) based transit route temporal

performance assessment: A pilot study. In 38th Australasian Transport Research

Forum (ATRF 2016), 16-18 November 2016, Melbourne, Vic.

2. Tran, Khac-Duong, Bhaskar, Ashish, Bunker, Jonathan M., & Lee, Boon

L. (2017) Data Envelopment Analysis (DEA) based transit routes performance

evaluation. In Transportation Research Board 96th Annual Meeting (TRB 2017),

8-12 January 2017, Washington D.C.

https://eprints.qut.edu.au/102898/




Literature Review


2 Literature Review

This chapter begins with a review of transit policy making for the performance

improvement of bus systems (in section 2.1) and a description of the main approaches used

for bus performance measurement (in section 2.2). Thereafter, the literature on DEA-based

transit performance evaluation and ranking for bus systems and routes are reviewed in

section 2.3. Finally, research gaps are outlined in section 2.4. Readers who are not familiar

with the DEA models may read Chapter 3 for further details about this approach.

Transit policy making

This section provides an overview of transit policy making to improve the performance

of bus routes and systems in literature. As the previous discussion in Chapter 1, there are

three main stakeholders who are interested in the transit performance, including:

• Transit users, who make choices of which travel mode to use when they have

more than an option to choose, or which travel route to use (based on the quality

of service) when they do not have a mode choice;

• Transit operators (agencies), who have to make decisions on how to effectively

allocate a finite amount of resources to best meet their goals and objectives, and

who also have to report on transit operation to funding supporters; and

• Community, who may indirectly benefit from the operation of transit (such as

congestion relief, air quality, mobility, source of employment) and may directly

contribute to transit service through taxes.

Each of these major transit stakeholders has its own objectives (points of view). Some

of these points of view may be the first priorities of each stakeholder and others may be

overlapped by those of other transit stakeholders. Therefore, the policy-making process aims

to address the points of view of each stakeholder and/or address the points of view of multiple

transit stakeholders (Ryus, Danaher et al. 2013).

Regarding the users’ perception or satisfaction, there are several studies appearing

in the literature that help identify key quality of service (QoS) factors important to passengers

(Eboli and Mazzulla 2007, Nathanail 2008, Tyrinopoulos and Antoniou 2008, Eboli and

Mazzulla 2009, Eboli and Mazzulla 2011, Ryus, Danaher et al. 2013, de Oña and de Oña

2014). The most common aspects of transit service are the reliability, hours of service,

frequency, convenience of route, capacity, fare, cleanliness, comfort, security, staff,

information, and the ticketing system. Particularly, Transit Capacity and Quality of Service

Literature Review


Manual (TCQSM) (2013) provided the quality of service framework for fixed-route transit

which consists of six quality of service factors (frequency, service span, access, passenger

load, reliability, and travel time) that are important to passengers (refer to Table 2-1). In this

framework, six factors are categorized into (1) transit availability (including frequency, service

span, and access) and (2) transit comfort and convenience (including passenger load,

reliability, and travel time). This framework significantly provides transit decision makers with

detailed and comprehensive criteria to measure the performance of transit routes and

propose appropriate recommendations for transit performance improvement.

In terms of transit operators’ perception, researchers used “efficiency” indicators to

quantify the productivity of the system components (vehicle, routes, stops, and operation),

cost, environment, and safety. The calculation of efficiency indicators is based on the different

input and output variables relevant to transit demand and operation such as ridership/loading,

travel time, route length, frequency, service duration, size of vehicle, operation and

maintenance costs, labors, fuel consumption, accident, and emission (Ceder and Wilson

1986, Viton 1997, Vuchic 2005, Vuchic 2007, Barnum, Tandon et al. 2008, Lao and Liu 2009,

Bunker 2013, Georgiadis, Politis et al. 2014, Rohácová 2015). The empirical analysis in these

studies helps to identify the internal issues of the system operation and components, and

then effectively support the decision-making processes of transit operators. It is notable that

The TCQSM (2013) also provided several bus preferential treatments (infrastructure

improvement) that have been developed in urban areas throughout the world to make bus

transit more competitive with the private cars and to provide a higher quality of service for

passengers. These bus preferential treatments mainly driven by capacity, travel speed, and

travel time reliability include:

• Reducing delay associated with bus stops (deceleration, bus stop failure, boarding

lost time, dwell time, traffic signal delay, reentry delay, and acceleration);

• Reducing delay associated with bus facilities (stop spacing, exposure to general

traffic, facility design, and bus operations);

• Factors determining bus capacity (loading capacity, bus stop capacity, and bus

facility capacity)

• Provision of Busway and freeway managed lanes;

• Provision of urban street bus lanes on arterial urban road;

• Using Transit Signal Priority (TSP) on the bus routes;

Literature Review


• Site-Specific priority treatments (queue jumps, boarding islands, and curb

extensions); and

• Bus stop placement (bus stop relocation and bus stop consolidation).

For community perception, transit performance is measured based on the impact of

transit service on different aspects of a community such as employment and economic

growth. This point of view also includes the contributions of transit to community mobility,

safety, congestion relief, and environment protection (Hassan, Hawas et al. 2013, Alam,

Nixon et al. 2015). Some researchers in the literature address the issues of transit

performance based on multiple points of views (Sheth, Triantis et al. 2007, Yu, Chen et al.

2015).

Due to the unavailability of user’s perception-based dataset of the case study in

Brisbane, this research aims to evaluate the performance of bus routes within a system based

on the perception of transit operators. Therefore, next section reviews the main approaches

for the performance measurement of bus routes/ system using different input and output

variables relevant to system design and transit demand and operation.

The Performance Measurement of Bus System

There are three main approaches to measure the performance of the bus system:

• Comparative Analysis (CA);

• Stochastic Frontier Analysis (SFA); and

• Data Envelopment Analysis (DEA)

The early approach applied for bus performance measurement is known as

comparative analysis. This approach normally uses different key performance indicators

(KPIs) to compare the performance of different bus systems with regard to different

performance concepts, such as labour efficiency, vehicle efficiency, fuel efficiency, operating

safety, and service consumption per expense. KPIs are defined as ratios of bus service

outputs to service inputs (revenue vehicle hours per operating expense or passenger trips

per revenue vehicle hour). Fielding et al. (1985) defined a wide range of KPIs for comparing

the performance of bus systems. Vuchic (2007) provided efficiency ratios (output quantity

produced per resource quantity expended) and utilisation (a ratio of demand to supply) to

measure the performance of a transit system. The Transit Cooperative Research Program

Report 88 (2003) provided a process for developing a performance-measurement program,

including both traditional and non-traditional performance indicators.

Literature Review


The Transit Capacity and Quality of Service Manual (TCQSM) (2013) presented the

quality of service framework for fixed-route quality of service (QOS) measures. In this

framework (refer to Table 2-1) QOS measures are clustered into two groups: (1) availability;

and (2) comfort and convenience. The core availability QOS measures describe how often

(frequency), how long (service span), and where (access) transit service is available, while

the core measures of comfort and convenience reflect passenger load, reliability, and travel

time. Furthermore, each QOS measure at the route level is described by a spectrum of

grades, according to the separate perspectives of passenger and operator. Therefore, transit

professionals are able to employ TCQSM’s framework to evaluate the temporal performance

of a single transit route, or compare the performance of several transit routes for those six

QOS measures. This work contributes to insights into the performance of transit routes for

different core QOS aspects.

Table 2-1: Quality of service measures for fixed-route transit

Availability Comfort and Convenience

Frequency

Service Span

Access

Passenger Load

Reliability

Travel Time

The CA approach is easy to apply for comparing the performance of bus at the route

and system levels, but for a particular performance concept/indicator. The comparison,

implemented for each KPI separately, leads to different levels of efficiency of one bus system

for different KPIs. This approach, therefore, cannot provide a single overall measure of bus

performance (Chu, Fielding et al. 1992).

The latter two approaches, SFA and DEA, are frontier methods, which build up the

frontier production function for evaluating the efficiency level of a set of production units. SFA

(a parametric approach introduced independently by Aigner et al. (1977) and Meeusen and

van Den Broeck (1977)) uses econometric techniques, while DEA (a non-parametric

approach) employs mathematical programming techniques for the frontier production function

estimation. The advantage of the DEA approach is that it does not require a functional form

to estimate the frontier production function. However, if the data are contaminated by

statistical noise, the frontier estimation may be inaccurate. SFA, on the other hand, imposes

an explicit functional form for technology. This can handle statistical noise, but possibly

makes functional form overly restrictive (Bauer 1990). Those two frontier methods provide

a single and comprehensive measure for evaluating the efficiency levels of a set of

production units with multiple input and output variables. Therefore, they were broadly

Literature Review


used for evaluating the performance of bus systems. De Borger et al. (2002) provided a

comprehensive review of the application of both DEA and SFA for performance measurement

of bus systems worldwide.

SFA and DEA each have their own advantages and disadvantages, which raises the

question of which method is superior in measuring bus performance? Michaelides et al.

(2010) employed both SFA and DEA (under constant returns to scale assumption) for

examining the technical efficiency of trolley buses in Athens, Greece. The efficiency scores

obtained from SFA are compared with those from DEA, providing consistent results in general

terms. This indicates that one can use SFA or DEA for efficiency estimation of bus

performance.

The current research employs the DEA method for bus route performance analysis of

the case study in Brisbane for two reasons. The first reason is that DEA requires no specific

functional form for the production function (Fried, Schmidt et al. 1993), and the second reason

is that the drawback of DEA related to data statistical noise can be addressed by using AFC

data, being a fairly accurate data source. Therefore, in the next section, DEA-based

performance evaluation of bus systems and routes in literature are investigated.

Application of DEA for Bus Performance Evaluation

To date, DEA models have been developing for over thirty years and have been

applied widely in many fields, namely banking, hospitals, schools, electricity, farming and

transportation. This section reviews the application of DEA models in transit performance

evaluation, including measuring the technical efficiency of different transit systems (in section

2.3.1 and 2.3.2), both the technical efficiency and cost effectiveness of different transit

systems (in section 2.3.3), and finally transit route performance (in section 2.2.4)

2.3.1 Transit Performance Concepts

As mentioned above, measuring the performance of urban transit systems with regard

to efficiency and effectiveness is greatly challenging to transit agencies, as multiple factors

simultaneously influence the operation of any public transport system. Fielding et al. (1985)

thus used cluster analysis to construct 12 peer groups of fixed-route urban transit systems

based on size, average speed and peak-to-base ratios of urban. Peak-to-base ratio was

computed by the ratio of vehicles in service in the largest peak over the midday base vehicle

requirement. The authors then analysed the variance and discriminant among the peer

groups in terms of operating characteristics to build up a decision tree typology, which is an

intellectual device for clarifying the performance similarities as well as differences among

transit agencies. This approach provided the basics for developing the Irvine Performance

Literature Review


Evaluation methodology (IPEM), which subsequently was used by some researchers to study

the performance of transit agencies like Perry et al. (1986), Yu (1988) and Fielding et al.

(1988). However, the IPEM statistics is a cumbersome method for evaluating transit

performance. It does not provide a single overall measure of transit performance (Chu,

Fielding et al. 1992).

To address this issue, Chu and Fielding et al. (1992) were pioneers in applying DEA

models to measure the efficiency and effectiveness of public transit agencies in the United

States (USA). The output data for efficiency and effectiveness assessment were annual

revenue vehicle hours (RVH) and annual unlinked passenger trips (TPAS) respectively.

Based on the results of analysis, the authors reinforced the notion of Hatry (1980) that in

public agencies, efficiency should be evaluated separately from effectiveness.

The three categories of performance concepts: technical efficiency, operational

effectiveness, and service effectiveness are expressed in Figure 1-2, which is adapted from

the ‘Framework for a transit performance concept model’ of Fielding et al. (1985). This figure

illustrates that there are a number of environmental factors (population density, accessibility,

parking space availability, car ownership) influencing the actual service consumption of a

community with regard to the effectiveness perspective. Furthermore, concerning the

efficiency component, external factors (traffic conditions, location of transit stops) significantly

affect the service outputs. Thus, it is not comprehensive and accurate if one evaluates the

performance of an urban transit system without considering the impacts of these external

(uncontrollable) variables.

2.3.2 Technical Efficiency Assessment for Transit System Performance

Using DEA models to evaluate the performance of transit agencies with regard to

technical efficiency perspective, we can look at some typical research hereafter. Obeng

(1994) utilised the DEA method to examine the influence of subsidies on the efficiency of 73

transit systems in the USA. After employing DEA to estimate the production frontier using

traditional variables (labour, fuel, fleet size, vehicle miles), this study re-estimated the

production frontier with subsidies being considered as one of the independent variables. It

found that subsidies improve technical efficiency in approximately 75% of the transit systems

investigated.

Nolan (1996) also applied the DEA model to evaluate technical efficiency of 25 mid-

sized bus transit agencies in the United States using data from the 1989-1993 Section 15

reports (USDOT). It is notable that this study exploited a two-stage data envelopment analysis

method developed by Oum and Yu (1994) to measure the performance of those transit

Literature Review


agencies. In the first stage, the DEA model was used to compute the average output oriented

technical efficiency scores of the sample for each year. Then in the second stage, the Tobit

model was used to take into account transit characteristics believed to indirectly affect the

technical efficiency scores. These characteristics are not a direct part of the production

process examined in the previous stage.

Kerstens (1996) provided an empirical analysis of 114 French urban transit

companies. Radial efficiency measures in the outputs were calculated for the variable returns

to scale DEA model with strong and weak disposability in both inputs and outputs. At the

same time, the Free Disposal Hull (FDH) model was used to evaluate corresponding

efficiencies. Based on the efficiency distributions coincided with the three different frontier

methods, the study confirmed the important role of the alternatives among deterministic

nonparametric reference technologies for technical efficiency assessment.

Viton (1997) analysed the technical efficiency of 217 multi-mode United States motor-

bus transit systems in 1990 using DEA models with variable returns to scale and weak

disposal. The data sample covered a wide range of system sizes and included both private

and public providers. The results indicated no systematic efficiency differences between

public and private systems with a high proportion of technically efficient systems, accounting

for around 80% compared to only 5.5% of the systems having Russell inefficiency measures

less than 0.8. Furthermore, to answer the question of whether the USA bus transit productivity

had declined recently, Viton (1998) used the Russell and Malmquist DEA models to measure

the productivity changes of multi-mode USA bus transit between 1988 and 1992. All data was

from the Section-15 data-set (USDOT) including a total of 183 systems in 1988, and 169 in

1992. Looking only at the averages, those two approaches demonstrated that bus transit

efficiency has improved slightly throughout the period.

2.3.3 Two Dimensions Assessment for Transit System Performance

Some researchers have examined both technical efficiency and effectiveness of

transit systems. Boilé (2001) proposed a DEA-based method to determine the efficiencies

and scale inefficiencies of 23 transit systems in the United States. In the first case, the inputs

are operating costs and output is vehicle revenue hours. In the second case, inputs are similar

to case 1, but outputs include both vehicle revenue hours and annual unlinked passenger

trips. Data of two cases were analysed under CCR and BCC-DEA models, respectively, to

determine the technical efficiency of DMUs. Inefficient units were then examined for

sensitivity to determine sources of inefficiency and ways to improve the performance of those

units.

Literature Review


Karlaftis (2004) utilised a large data set consisting of 256 US transit systems over a

five-year time period (1990-1994) to measure transit system efficiency and effectiveness as

well as the relationship between these two dimensions of transit performance. Additionally,

economies of scale in transit systems were evaluated based on their performance

assessment. The output oriented-DEA model was applied three times for three different sets

of data. Each of them utilised the same inputs (total vehicles, fuel, total employees) but

different outputs with total annual vehicle-miles as output for efficiency measurement, total

annual ridership for effectiveness, and both those outputs for the combined performance. The

finding results indicated that efficiency and effectiveness are positively related.

Tsamboulas (2006) applied a similar approach to Karlaftis (Karlaftis 2004) to analyse

15 European transit systems. Their data set refers to a ten-year period of time (1990-2000)

and covers a variety of situations concerning regulatory and organisational forms in European

cities. Using a CRS-DEA model to analyse data sets at yearly levels in the first stage, the

results obtained indicated that private systems tended to be more efficient, while public

systems achieved higher effectiveness scores. Furthermore, in the second stage, the Tobit

regression model was employed to identify which factors are the ones causing the inefficiency

and to what extent. The results of a Tobit regression analysis presented that the transit

systems appear to have experienced a certain growth during the examined time period with

respect to their efficiency and effectiveness as well as their overall performance.

Ayadi (2013) measured and compared the levels of efficiency and of pure technical

effectiveness in the twelve urban transit systems in Tunisia during the period 2000-2010 using

the DEA method. After determining technical efficiency according to input orientation and

pure technical efficiency with regard to output orientation, this study applied linear regression

to estimate the link between pure technical efficiency and the explanatory variables (the living

standard of residents, the capital per labour unit, the network length, and the technical

progress). The results indicated that the input-oriented DEA model was the best explaining

this linkage.

Regarding the crucial role of societal and environmental factors in assessing transit

performance, Yu et al. (2006) added accident cost as undesirable output and network length

as environmental input to the data set to measure the cost effectiveness of 24 bus companies

in Taiwan. This study, based on the directional graph distance function and the multi-activity

DEA approach, illustrated that the overall cost effectiveness rankings seem to be fairly

sensitive to whether or not the graph multi-activity DEA approach is adopted. This confirmed

the important role of the conventional DEA model in measuring the cost effectiveness of firms

that carry out various activities while sharing common resources.

Literature Review


2.3.4 Assessment for Transit Route Performance

The focus on the technical efficiency and effectiveness of transit agencies at system

level contributed by providing a general analysis of the actual performance of transit

organisations and problems related to such operations. However, there is a limited number

of studies focusing on the performance evaluation of transit at the transportation process

level (Triantis 2004), although this work is significantly essential to provide insight into the

performance of individual transit routes within a system. Several studies thus have examined

the performance of transit routes/lines within a transit agency.

Lao et al. (2009) combined the BCC-DEA model and geographic information system

(GIS) to measure the performance of bus lines in a transit system. In this study, GIS was

used to generate the input data for the spatial effectiveness DEA model and visualise the

distribution of bus stops and routes. The input data for operational efficiency measurement

includes operation time, round-trip distance, number of bus stops, while those for spatial

effectiveness assessment are bus users, population with disabilities, population 65 and older.

The output variable for the two models is total passengers. On the basis of operational

efficiency and spatial effectiveness scores of 24 fixed bus routes, this research ranked the

performance of individual bus routes and demonstrated that GIS can help to analyse the

spatial variation of efficiency and effectiveness against demographic settings.

Barnum et al. (2008) employed a CRS-DEA model to analyse 46 bus routes of a US

transit agency using weekday data. In the first stage, raw efficiency scores of individual bus

routes were computed by a DEA model without considering the environmental variables.

Then in the second stage, two environmental variables (population density, population), that

are beyond the control of the transit agency, were used to adjust the DEA outputs (Riders

and OTP). Then the adjusted DEA efficiency scores of DMUs are calculated. These external

variables are collected within a 0.805-km-width corridor along an entire bus route. The results

indicated that after adjusting the raw DEA scores, 20 bus routes became more efficient, 12

did not change, and 14 became less efficient.

Sheth et al. (2007) expanded the network DEA model of Färe and Grosskopf (2000)

to assess the performance of 60 different bus routes within a transit network in Virginia, USA.

In this study, all variables related to the service provider, the users, and the societal

perspectives were taken into consideration to compute the DEA efficiency scores with regard

to both CRS and VRS. Making comparison among these efficiency scores helped to rank the

performance of these 60 bus routes and capture the relationship among the supplier, the

customer of the public transportation service as well as the external and environmental

variables related to the urban transit performance. However, the data used in this research

Literature Review


is average weekday data with some qualitative variables like average travel time and

schedule reliability being estimated through the route length, standard for average speed in

urban or suburban areas, traffic congestion, and number of stops. The results achieved thus

could not reflect accurately the actual performance of the given bus routes over the time

period of a weekday. Furthermore, external factors in transit, such as population density and

parking space availability, are used as inputs for a user node in the DEA model. Thus,

external factors are not examined appropriately in this study.

More recently, 60 individual bus lines within a public transport network in Thessaloniki,

Greece were examined by a DEA model (Georgiadis, Politis et al. 2014). For model 1 and 2,

input variables included trip length, span of service, and vehicles, while output variables were

revenue seat-km for efficiency measure (model 1) and passengers for operational

effectiveness assessment (model 2). Model 3 aimed at measuring combined effectiveness,

including revenue vehicle-km and vehicles for input variables, as well as passengers

regarded as an output variable. Along with calculating the efficiency and effectiveness scores

for the three above models, this study also employed bootstrapping techniques to check

robustness of DEA results for model 1 and model 2. This sensitivity analysis explained that it

is more reliable when correcting obtained scores for bias. The results also indicated that there

is not a clear positive or negative relationship between technical efficiency and operational

effectiveness. The results achieved from model 3 were utilised to classify DMUs into different

clusters using a clustering algorithm of Po et al. (2009). Then, variables of the piecewise

production function were defined to ensure that their modification would not influence one

another. Therefore, public agencies can possibly use such functions as a tool for tracking

performance improvement, which is achieved when they gradually modify the individual

design elements of their service. Applying this approach for the situation of Thessaloniki, it is

found that scheduling of buses with fewer seats would be a better solution than reducing their

span of services.

2.3.5 Summary of findings

Table 2-2 provides an overview of the application of DEA models in measuring the

transit performance at both system and route levels. Here, the review is separated into two

groups: the former focuses on the performance of transit systems and the latter focuses on

the performance of individual transit routes/lines. The columns represent the DEA models

used, number of Decision Making Units (DMUs), inputs and outputs selected for DEA models,

time frame of data, and finally the findings.

From the summary of Table 2-2, most of the research focuses on evaluating the

performance of different transit systems on yearly data (first group). Recently, some

Literature Review


researchers have focused on evaluating the performance of individual transit routes within a

system (Triantis 2004). Comparing the performance of different transit systems plays a key

role in determining the average operational efficiency of a transit system and problems related

to the operation of the whole system, but cannot explore the problems related to the internal

activities of each transit route. On the other hand, the performance evaluation of individual

transit routes within a transit system substantially provides the transit agency with opportunity

to understand its internal activities (Benn 1995, Barnum, Tandon et al. 2008), and then

investigate the source of inefficiency. Possible actions then can be taken by transit agencies

to optimise the operational efficiency of inefficient transit routes, and thus leads to

performance improvement for the whole transit system. Evaluating the performance of

individual transit routes therefore is of importance for optimising the operation of transit at the

route and system level.

Most of the studies have focused on technical efficiency and cost effectiveness.

Researchers have evaluated the relationship between the technical efficiency and cost

effectiveness, while the literature has had contrary findings. Chu et al. (1992) supposed that

these two dimensions of transit performance should be evaluated separately, while Karlaftis

(2004) claimed that efficiency and effectiveness seem to be positively related. Hence, the

correlation between technical efficiency and cost effectiveness should be further studied with

a larger sized dataset.

A few studies (Barnum, Tandon et al. 2008, Lao and Liu 2009) have been conducted

on service effectiveness. This is because of the complexity in modelling the service

effectiveness, which is often based on the uncontrolled factors (such as living standards of

the residents, quality of service with respect to passenger perception, parking space, and

private vehicle ownership). Moreover, the availability of the integrated data needed for the

modelling is also hard to obtain.

The DEA model only provides a mean of estimation of DMUs’ technical efficiency. To

evaluate the influence of external factors (socio-economic and demographic variables) on the

efficiency level of DMUs, a two-stage process was adopted (Nolan (1996), Georgiadis et al.

(2014)). Here, at the first stage, the DEA model is applied to estimate the efficiency scores of

DMUs, and thereafter a truncated regression model is applied at the second stage to analyse

the sensitivity of efficiency scores obtained in the first stage to those factors. However, the

limitation of these studies is that they lack information on some potentially uncontrollable

variables such as structure of population, private vehicle ownership, and average income of

residents. The influence of external factors on transit performance thus was not studied

Literature Review


sufficiently. This study attempts to overcome this issue by using external variables at the most

detailed level (the Statistical Areas Level 1 (SA1)) of the case study in Brisbane, Australia.

The performance evaluation of individual routes within a transit system has drawn the

attention of a few researchers (Sheth, Triantis et al. 2007, Barnum, Tandon et al. 2008, Lao

and Liu 2009, Georgiadis, Politis et al. 2014, Rohácová 2015). However, due to the simplistic

transit data collected through manual survey, temporal and spatial performance of routes in

those studies was not examined sufficiently. For instance, actual travel time was not used in

those studies (Lao and Liu 2009). Travel time, in reality, was estimated from operating speed,

which depends upon the distribution of transit routes in the urban or suburban area (Sheth,

Triantis et al. 2007). Most studies used “passenger-km” as an output to represent the service

consumption of a route, while the corresponding input is “seat-km” representing vehicle

passenger carrying capacity. However, due to the data limitation, “passenger-km” was

defined as the total number of passengers transported by a route multiplied by the total

number of kilometres travelled by all vehicles operating on that route during a weekday. This

definition does not reflect the service consumption accurately, because it considers the total

route length travelled by all vehicles instead of the average route length travelled by

passengers. This data limitation is addressed in the current study by using AFC data for the

case study in Brisbane.

Regarding the above relationship between the vehicle passenger carrying capacity

and the service consumption, Vuchic (2007) defined “transportation work” (𝑤) as the number

of transported objectives (𝑢) multiplied by the distance (𝑠) over which they are carried: 𝑤 =

𝑢. 𝑠.

Based on the work of Vuchic, Bunker (2013) introduced “transit work” and “transit

service work efficiency” of an individual transit service h along its route L with n segments

constituting route L. “Transit work” was the sum of the transit work performed along all

consecutive segments along the transit route.

Transit work performed by service h along its route L, given by (passenger-km):

𝑾𝒉,𝑳 = ∑ 𝑷𝑶𝑩,𝒉,𝒊𝒔𝒊𝒏𝒊=𝟏 (Equation 2-1)

Where: 𝑠𝑖 = length of segment 𝑖

𝑃𝑂𝐵,ℎ,𝑖 = Passengers on board for service h along segment 𝑖

𝑛 = Number of consecutive segments constituting line L traversed by h

Compared to “passenger-km”, “transit work” reflects the service consumption more

accurately, because it takes the actual route length traversed by passengers into account

Literature Review


and reflects the vehicle’s loading level along the transit route. This research will provide a

comprehensive framework for DEA application for transit route performance evaluation with

the use of “transit work” as an output to present the service consumption of the community.

Literature Review


Table 2-2: An overview of the application of DEA in measuring the transit performance

Referen-

ces

DEA model DMUs Inputs Outputs Time

frame

conside-

red

The findings

Obeng

(1994)

DEA model 73 bus

agencies in

USA

Labour; Fuel; Fleet size

Vehicle- Miles

Annual

data

Subsidies improve technical efficiency

(TE) in approximately 75% of the

transit systems studied

Nolan

(1996)

DEA model

(BCC-DEA) and

Tobit model

25 mid-sized

bus agencies

in USA

Vehicle operated; Fuel; Labour. Vehicle- Miles

Annual

data

Average fleet age is significantly and

negatively correlated with the TE

measure.

Operating subsidies can create

significant and negative impacts on

TE.

Kerstens

(1996)

DEA model and

Free Disposal

Hull (FDH) DEA

model

114 French

urban transit

companies

Vehicles; Employees; Fuel.

Explanatory variables: Owner; Group;

Linelength; Stoplength; Popdens;

Vehage; Ctype; Cterm; Ssub; Tax.

Vehicle-Km;

Seat-Km.

Annual

data

It confirms the important role of the

alternatives among deterministic

nonparametric approaches for TE

assessment, and the relevance of

ownership and the harmful impact of

subsidies.

Viton

(1997)

Russel DEA

model, with

VRS + Weak

Disposal

217 multi-

mode motor-

bus transit

systems in

USA

Average speed; Average Fleet age;

Number of directional miles; The fleet

sizes; Fuel; Labour hours for

transportation, maintenance, admin,

Vehicle-miles;

Passenger-

trips.

Annual

data

Public and private systems do not

have an observed systematic

efficiency difference.

Literature Review


capital; Tyres and material cost; Service

cost; Utilities cost; Insurance cost.

Around 80% of the sample is

technically efficient. The extent of

inefficiency in the industry is slight.

Viton

(1998)

The Russell and

Malmquist DEA

models

183 US bus

systems in

1988, and

169 systems

in 1992.

Average speed; Average fleet age;

Number of directional miles; The fleet

sizes; Fuel; Labour hours for

transportation, maintenance, admin,

capital; Tyres and material cost; Service

cost; Utilities cost; Insurance cost.

Vehicle-miles;

Passenger-

trips;

Vehicle-hours.

Annual

data

Bus transit efficiency has improved

slightly over the period. The

proportion of technically efficient

systems rose from 74% in 1988 to

82% in 1992. In most inefficiency

categories, there were proportionately

fewer systems in 1992 than in1988.

Chu et al.

(1992)

DEA model 86 bus

agencies in

USA

Vehicle operating cost; Maintenance

cost; General cost; Other expenses;

Revenue vehicle hours; Population

density; % of household with car;

Subsidy passenger

Revenue

vehicle hours

Unlinked

passenger-

trips

Annual

data

Average input-oriented TE: 85%

Average input-oriented cost

effectiveness: 65%

Boilé

(2001)

DEA model 23 bus

agencies in

USA

The operating costs;

Vehicle revenue hours

Vehicle

revenue hours;

Unlinked

passenger-

trips

Annual

data

Systems that operate locally

inefficiently may improve their service

by using operation strategies.

Systems that exhibit scale

inefficiencies may be improved upon

by identifying and dealing with

external factors.

Karlaftis

(2004)

DEA model and

the Return to

scale analysis.

256 US

transit

systems

Total vehicles;

Fuel;

Total employees

Total annual

vehicle-miles;

Annual

data

Efficiency and effectiveness are

positively related.

Literature Review


Total annual

ridership

(1990-

1994)

Optimal scale of operation varies

significantly and depends on the

output specification selected and the

performance dimension.

Tsambo-

ulas

(2006)

DEA model and

Tobit regression

model

15 European

transit

systems

Total vehicles;

Total employees;

Transit system characteristics:

Population; Area.

Vehicle-Km;

Passengers.

Annual

data

(1990-

2000)

Private systems are more efficient,

while public systems are more

effective. The transit systems appear

to have experienced a certain growth

during the examined time period.

Ayadi

(2013)

DEA model and

an econometric

regression

model.

12 urban

transit

systems in

Tunisia

Total number of bus park;

Number of staff;

Annual amount of fuel consumed

Travelled Km Annual

data

(2000-

2010)

The annual technical efficiency (input

orientation) is 92.44%. The average

technical efficiency (output

orientation) is 90.13%

Lao et al.

(2009)

DEA model and

geographic

information

system (GIS)

24 fixed bus

routes in

Monterey

County,

California,

USA.

Operation time;

Round trip distance;

Number of bus stops;

Commuters who use buses; Population

65 and older;

Persons with disabilities

Total number

of passenger.

Total number

of passenger.

Annual

data

For TE: 6 bus lines are technically

efficient, 6 bus lines are fairly efficient

(scores ≥ 0.6), and 12 bus lines are

inefficient.

For spatial effectiveness: 11 of them

are technically efficient (scores ≥ 0.8)

and 13 bus lines are inefficient

Barnum et

al. (2008)

DEA model 46 bus

routes of a

US transit

agency

Seat kilometre (SK);

Seat hours (SH);

Population density;

Population.

Ridership;

Span of

service;

Average

frequency;

The

average

weekday

trips

Comparing the performance of

multiple bus routes of one transit

agency.

Literature Review


Maximum

frequency; On-

time

performance.

20 bus routes became more efficient,

12 did not change, and 14 became

less efficient.

Sheth et

al. (2007)

Network DEA

model

60 bus

routes in

Virginia,

USA.

The provider node: Headway; Service

duration; Costs; Number of

intersections; Priority lanes.

The societal variable: Number of

accidents; Emissions; Noise pollution;

Resources degraded.

The environmental variables:

Accessibility; Parking space availability;

Population density; Connectivity;

Comfort standards factor.

The provider

node and

inputs for the

passenger

node: Vehicle-

mile; Schedule

reliability;

Average travel

time.

The passenger

node:

Passenger-

mile

The

average

weekday

trips

Capture the relationship among the

supplier, the customer of the

transportation service as well as the

external and environmental variables

related to the urban transit

performance.

Georgia-

dis et al.

(2014)

DEA model and

Bootstrap-ping

techniques

60 bus

routes in

Greece.

Model 1: Length; Span of service;

Vehicles.

Model 2: Length; Span of service;

Vehicles.

Model 3: Revenue vehicle-km; Vehicles.

Revenue seat-

km;

Passenger

Passenger

Annual

data

(2009-

2011)

There is not clear relationship

between efficiency and operational

effectiveness.

Evaluating the transit route

performance is more reliable when

correcting for bias.

Literature Review


Research Gaps

The findings in the literature review indicate that a limited number of studies have

examined the performance of individual bus routes composing a transit system, using a DEA

model. For performance evaluation of bus routes, different performance concepts defined in

the framework of Fielding, Babitsky et al. (1985) (technical efficiency, service effectiveness,

and operational effectiveness) were separately examined in preceding studies using a DEA

model. This method thus cannot provide an overall measure for bus route performance.

Additionally, the above-mentioned limitation of an annual dataset only enables one to

measure the average efficiency of bus routes for a given month or year (at a macro level). It

is essential to characterise the detailed operation (at a micro level) of such bus routes during

a shorter period of time (such as every hour or key periods of time within a weekday), and

changes of the efficiency level of bus routes over a time series (different hours or weekdays

for instance) because this offers the chance to identify the operational issues of bus routes

across the daytime. AFC data reveals information on how the transit network is rendered and

used on a continuous basis, promisingly providing practitioners with a rich dataset for practice

and understanding the spatial and temporal performance of bus routes (Trépanier, Morency

et al. 2009). Hence, there is a great need to develop a network DEA-based approach using

AFC data for bus route performance evaluation. This helps to bridge the above research gaps

in literature.

Taylor, Miller et al. (2009) indicated that external factors (population, population

density, personal/household income, employment, auto/highway system characteristics, and

car ownership) substantially affect the variation in transit ridership among urbanised areas.

However, perhaps partially due to the lack of those data, external factors were not studied

sufficiently for route-based transit performance analysis. Previous work has focused only on

the influences of population on transit patronage (Barnum, Tandon et al. 2008, Lao and Liu

2009). Barnum et al. account for the total population of the entire buffer zone (with 0.4025 km

width for each side) along the whole route, and Lao et al. employ the population of pensioners

and persons with a disability within bus route service areas (0.4 km radius around bus stops)

as inputs for bus routes spatial effectiveness analysis. From those limitations, there is a great

need for examination of the influences of external factors (within service areas) on bus routes’

operation. This research addresses this issue by using a wide range of external variables

within the bus stop-based service areas to test the sensitivity of the DEA efficiency scores to

these external variables, and then identifying the factors influencing the efficiency levels of

bus routes.

Methodology


3 Methodology

Introduction

To achieve objectives two and three stated in Chapter 1, this research first employs

the DEA models to compare and rank the performance of some key bus routes of the case

study. The reason is that the DEA model was proved to be an appropriate tool to evaluate

the technical efficiency level of individual DMUs with multiple inputs and outputs by

generating a single efficiency score (Charnes, Cooper et al. 1978, Seiford and Thrall 1990,

Coelli, Prasada Rao et al. 1998, Tone, Cooper et al. 1999, De Borger, Kerstens et al. 2002).

Then, a double bootstrap model (truncated regression model) of Simar and Wilson (2007) is

employed in the second stage of analysis to examine the impact of external factors on

efficiency scores of bus routes obtained in the first stage of analysis (details are shown in

Figure 3-1). To investigate the impact of external factors on the efficiency level of bus routes

in the second stage, one can employ a censored (Tobit) model (Nolan 1996, Tsamboulas

2006) or a linear model by ordinary least squares (OLS) (Thomas, Sally et al. 1994).

However, McDonald (2009) indicated that in case the efficiency scores are not generated by

a censoring process but are fractional data, Tobit estimation is inappropriate. Simar and

Wilson (2007) demonstrated that OLS is inconsistent in the second-stage regression, and

proposed single and double bootstrap procedures to overcome this issue. The double

bootstrap procedure can produce consistent inference and statistical properties and improve

statistical efficiency in the second-stage regression. In the double bootstrap model, the DEA

efficiency scores are dependent variables, while external variables within the stop-based

service areas of individual bus routes are independent variables.

This research uses both static DEA models (CCR and BCC model) and a network

DEA model for empirical analysis. The operational effectiveness of a bus route includes two

sub-processes: (1) the technical efficiency and (2) the service effectiveness. Thus, the

network DEA helps to evaluate the overall performance of bus routes by a single efficiency

score, accounting for the linkage between sub-processes. The DEA model was first

developed by Charnes, Cooper, and Rhodes (CCR) in 1978 and later modified by Banker,

Charnes and Cooper (BCC) in 1984. It builds upon the frontier efficiency concept first

elucidated in Farrell (1957). To better support the readers who have limited background on

the efficiency measurement concepts and the DEA models, this chapter briefly provides basic

information about the modelling processes of the DEA models. Therefore, this chapter first

introduces the efficiency measurement concepts of Farrell (1957), then presents details about

Methodology


CCR and BCC models, and the network DEA model. Furthermore, the sensitivity analysis of

DEA efficiency scores using a double bootstrap model is presented.

To clarify the work and usefulness of DEA in dealing with DMUs with multiple inputs

and outputs, this research compares the two transit productiveness indexes (transit work load

factor and transit service passenger transmission efficiency) with temporal efficiency scores

of a bus route (route 111) for a direction (inbound direction). The results of this comparison

are presented in Section 6.2.2. Thus, these two transit productiveness indexes are introduced

in this chapter.

Figure 3-1: The outlines of research methodology

This chapter is organised as follows: section 3.2 presents the efficiency measurement

concepts of Farrell, followed by the DEA models in section 3.3. Section 3.4 introduces

sensitivity analysis of DEA efficiency scores. Section 3.5 provides two basic transit

productiveness indexes. Finally, the chapter is concluded in section 3.6 where discussion is

provided.

Objectives

Objective 2:Evaluate and rank theperformance of bus routesof the case study

Objective 3:Examine the impact ofexternal factors on theefficiency scores of givenbus routes

Chapter 4: Methodology

CCR-DEA andBCC-DEA model

Transit productivenessindexes

Compare results

Network DEA model

Truncated regressionmodel: Double Bootstrapmodel

BC

C-D

EA

eff

icie

ncy

sco

res

of

node

2 (

dep

enden

t var

iable

s)

External variables withinthe stop-based serviceareas of bus routes

Indep

enden

t var

iable

s

ABS 2011 Census at theSA1 and Arc GIS

Methodology


Efficiency Measurement Concepts

The efficiency of an industry consists of two components: technical efficiency and

allocative efficiency (Farrell 1957). Technical efficiency is defined as the ability of an industry

to achieve maximal output using a given set of inputs. Allocative efficiency is defined as the

ability of an industry to use the inputs in optimal proportion, given certain constraints on prices

and the production technology. The combination of technical and allocative efficiency

provides a measure of total economic efficiency (Coelli, Prasada Rao et al. 1998).

Technical efficiency of an industry can be viewed from two perspectives: input-

oriented; and output-oriented measures. This section would provide the definition of

production function, input-oriented and output-oriented measures of an industry.

3.2.1 Production function

Consider an industry in which each DMU produces a vector of M outputs using a

vector of N inputs. The kth DMU produces outputs 𝑦𝑘 = (𝑦𝑘1, 𝑦𝑘2, … , 𝑦𝑘𝑀) from inputs 𝑥𝑘 =

(𝑥𝑘1, 𝑥𝑘2, … , 𝑥𝑘𝑁). The production function (technology) is described by the production

possibility set 𝑇 of feasible output vectors 𝑦 producible from input vectors 𝑥 (Viton 1997):

𝑇 = {(𝑥, 𝑦): 𝑦 𝑖𝑠 𝑓𝑒𝑎𝑠𝑖𝑏𝑙𝑦 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑑 𝑓𝑟𝑜𝑚 𝑥}

The production technology also can be described using output and input sets:

• The input set, 𝐿(𝑦), consists of all input vectors, 𝑥, which can produce a given

output vector, 𝑦. The input set 𝐿(𝑦) is defined as:

𝐿(𝑦) = {𝑥: (𝑥, 𝑦) ∈ 𝑇}

• The output set, 𝑃(𝑥), includes all output vectors, 𝑦, which can be produced

using a given input vector, 𝑥. The output set 𝑃(𝑥) is defined as:

𝑃(𝑥) = {𝑦: (𝑥, 𝑦) ∈ 𝑇}

3.2.2 Input-Oriented Measure

The purpose of an input-oriented technical efficiency measure is to answer the

question: by how much can input quantities be proportionally reduced to produce the given

quantities of output?

From the original idea of Farrell, consider DMUs that use two inputs (𝑥1 and 𝑥2) to

produce an output (𝑦), under the assumption of CRS. Figure 3-2 graphically presents a given

DMU, defined by point P, and the corresponding production frontier (or isoquant), presented

Methodology


by SS’. The production possibility set, including P, will distribute from SS’ to the upper part.

All DMUs lying on SS’ (such as Q and Q’) use the minimal amount of inputs to produce output.

The line OP intersects SS’ at point Q. Therefore, the distance QP presents the amount of

inputs that could be reduced to produce a given output.

Figure 3-2: Input-oriented technical and allocative efficiencies (Source: Coelli, Prasada Rao et al. (1998))

The Farrell input-oriented technical efficiency of the DMU at point P is measured by

the ratio: TEi = OQ/OP. Its value varies from 0 to 1, presenting the level of inefficiency of this

DMU. If TEi equals to one, this DMU lies on the Isoquant (at point Q) and is efficient.

In addition, if the input prices are available, 𝑤1 and 𝑤2, for 𝑥1 and 𝑥2 respectively, it is

possible to estimate allocative efficiency (AEi) of this DMU: AEi = OR/OQ. The isocost line,

AA’, presents the minimal price of inputs to produce output of this production possibility set.

The ratio, AEi, indicates that although the DMU at point Q is technically efficient, it is inefficient

in terms of allocation. The distance, RQ, presents the reduction of cost that Q can be made

to get the highest value of AEi (equals to 1).

The total economic efficiency (EEi) of DMU operating at point P is calculated by the

ratio: EEi=OR/OP. Here, the distance, RP, represents the cost reduction of this DMU. EEi is

the combination of the technical and allocative efficiency: (OQ/OP) x (OR/OQ) = OR/OP =

EEi. The optimal production option of this production possibility set is point Q’, where all

technical, allocative, and economic efficiencies obtain the value of unity.

X1/Y

X2/Y

o

Production Frontier

or Isoquant- SS'

R

Q

P

Q'S'

S

A

A'

Methodology


3.2.3 Output-Oriented Measure

The output-oriented technical efficiency measure, in contrast to the above input-

oriented measures, will answer the question: by how much can the output quantities be

proportionally increased without increasing the quantities of input used?

Figure 3-3 graphically illustrates the case of the output-oriented measures of a DMU

(at point A) within a production possibility set distributing from the isoquant line, ZZ’, to the

lower part. It means that ZZ’ presents the upper boundary of this production possibility set.

Here, DMUs produce two outputs (𝑦1 and 𝑦2) using an input (𝑥), under the assumption

of CRS. DD’ presents the isorevenue line, if the price of outputs is available.

The Farrell output-oriented efficiency measures are calculated as follows:

The technical efficiency is the ratio: TEo = OA/OB

The allocative efficiency is the ratio: AE0 = OB/OC

The economic efficiency is presented as: EE0 = TE0 x AE0 = OA/OC

The optimal production option of this production possibility set is point B’, where all

technical, allocative, and economic efficiencies obtain the value of unity.

Figure 3-3: Output-oriented technical and allocative efficiencies (Source: Coelli, Prasada Rao et al.

(1998)

Data Envelopment Analysis (DEA)

DEA is a non-parametric method based on linear programming and optimisation. It

measures the relative efficiencies of production units or decision making units (DMUs) using

multi-inputs and multi-outputs. This is the important advantage of DEA over traditional

Y1/X

Y2/X

o

Production Frontier

or Isoquant- ZZ'

A

B

C

B'

D'

D

Z

Z'

Methodology


methods, which have limitations to evaluate efficiency of DMUs when multiple inputs and

outputs need to be considered. This is the reason why literature is abundant with its

application in banking (Mohamed Shahwan and Mohammed Hassan 2013, Depren and

Depren 2016), hospitals (Jat, Sebastian et al. 2013, Torabipour, Najarzadeh et al. 2014),

schools (Agasisti 2013, Rosenmayer 2014), electricity (Andrade, Alves et al. 2014, Azadeh,

Motevali Haghighi et al. 2015), and transportation (Lao and Liu 2009, Zhao, Triantis et al.

2011, Fancello, Uccheddu et al. 2014, Georgiadis, Politis et al. 2014).

The modelling process of DEA includes: a) identification of the production frontier (or

isoquant) of a set of comparable DMUs. Within a set of comparable DMUs, those exhibiting

the best use of inputs to produce outputs are identified, and would form an efficient frontier;

b) measures the efficiency level of each DMU by comparing its production function with the

production frontier (Cook and Seiford 2009).

Measuring the efficiency level of DMUs using DEA models, one may consider

technology under constant returns to scale (CRS) assumption (i.e. CCR model) or under

variable returns to scale (VRS) assumption (i.e. BCC model). Over the three decades since

the appearance of the first work of Charnes et al. in 1978, DEA has been developed by

researchers to substantially meet the actual demands. Therefore, there are different types of

the DEA model, such as the Additive model, Slacks-based measures, Russell measure, other

Non-radial models, upper-efficiency DEA, FDH model, Network model, etc. This research

employs basic DEA models (CCR and BCC model) because they were employed widely in

literature for empirical analysis of transit (refer to Table 2-2).

3.3.1 CCR- DEA Model

Charnes et al. (1978, 1981) introduced the CCR-DEA model to evaluate the efficiency

of each DMUj in a reference set of n DMUs. This model was built on the assumption of

constant returns to scale (CRS) of activities (see Figure 3-4a) and was divided into two

versions, input-oriented model and output-oriented model. While input-oriented model

examines the possibility of reducing inputs to produce a given output, output-oriented model

investigates the possibility of increasing outputs from the DMUs observed input bundle (Viton

1997).

Suppose that each DMUj (j=1, …, n) uses m inputs xij (i=1, …, m) to generate s outputs

yrj (r=1, …, s), and the vi and ur are the variable weights of inputs and outputs, respectively.

This method uses the known inputs and outputs of all DMUs in the given set of data

to determine the efficiency of one member, DMUj (j=1, …, n), which is assigned as DMU0.

Methodology


The efficiency of DMU0 is obtained by solving the following fractional programming problem

n times, each DMU once.

𝐦𝐚𝐱 𝒉𝟎 =∑ 𝒖𝒓 𝒚𝒓𝟎

𝒔𝒓=𝟏

∑ 𝒗𝒊𝒙𝒊𝟎𝒎𝒊=𝟏

Equation 3-1

Subject to:

∑ 𝑢𝑟 𝑦𝑟𝑗𝑠𝑟=1

∑ 𝑣𝑖𝑥𝑖𝑗𝑚𝑖=1

≤ 1; 𝑗 = 1, … , 𝑛

𝑢𝑟, 𝑣𝑖 ≥ 휀 > 0; 𝑟 = 1, … , 𝑠; 𝑖 = 1, … , 𝑚.

Where ε is a “non-Archimedian infinitesimal”, which is smaller than any positive real

number. This means that all variables are constrained to positive values.

The objective is to obtain the input and output weights, vi and ur, as variables that

maximise the ratio of the DMU0, the DMU being evaluated. The value of h0 obtained from this

formulation represents the efficiency score of the DMU0. The constraints mean that h0*, the

optimal value of h0, should not exceed 1 for every DMU. In case h0*=1, this DMU places on

the efficiency frontier (Tone, Cooper et al. 1999).

To solve this problem, the theory of Charnes et al. (1962) is applied to convert this

fractional programming problem to the linear programming (LP) model with the changes of

variables 𝑡(∑ 𝑣𝑖 𝑥𝑖0) = 1𝑚

𝑖=1; 𝜇𝑟 = 𝑡𝑢𝑟 and 𝜗𝑖 = 𝑡𝑣𝑖. The above problem is replaced by the

following equivalent:

𝐦𝐚𝐱 𝒉𝟎 = ∑ 𝝁𝒓 𝒚𝒓𝟎𝒔𝒓=𝟏 Equation 3-2

Subject to

∑ 𝜗𝑖 𝑥𝑖0 = 1

𝑚

𝑖=1

∑ 𝜇𝑟 𝑦𝑟𝑗

𝑠

𝑟=1

− ∑ 𝜗𝑖 𝑥𝑖𝑗 ≤ 0 𝑗 = 1, … , 𝑛

𝑚

𝑖=1

𝜇𝑟, 𝜗𝑖 ≥ 휀 > 0; 𝑟 = 1, … , 𝑠; 𝑖 = 1, … , 𝑚.

The dual problem of the linear programming (DLP) reproduced here for the input-

oriented model is as follows:

𝐦𝐢𝐧 𝜽 Equation 3-3

Subject to

Methodology


𝜃𝑥𝑖0 − ∑ 𝜆𝑗 𝑥𝑖𝑗 ≥ 0

𝑛

𝑗=1

𝑖 = 1, … , 𝑚

∑ 𝜆𝑗 𝑦𝑟𝑗 ≥ 𝑦𝑟0 𝑛

𝑗=1 𝑟 = 1, … , 𝑠

𝜆𝑗 ≥ 0, 𝑎𝑙𝑙 𝑟, 𝑖, 𝑗; 𝜃 𝑓𝑟𝑒𝑒

Here, the constraints of DLP require the activity (𝜽𝒙𝟎, 𝒚𝟎) to belong to the production

possibility set T, while the objective seeks the minimum 𝜃 that reduces the input vector 𝑥0

radially to 𝜃𝑥0 while remaining in T. In DLP, the aim is to look for an activity in T that

guarantees at least the output level 𝑦0 of DMU0 in all components while reducing the input

vector 𝑥0 radially to the smallest value. Therefore, it can be said that (𝑿𝝀, 𝒀𝝀) outperforms

(𝜽𝒙𝟎, 𝒚𝟎) when 𝜃∗ < 1. Regarding this property, the input excesses (𝒔𝒊− ∈ 𝑅) and the output

shortfalls (𝒔𝒊+ ∈ 𝑅) are defined as slack variables. The input and output slack vectors are

identified as follows:

𝒔𝒊− = 𝜽𝒙𝟎 − 𝑿𝝀, 𝒔𝒊

+ = 𝒀𝝀 − 𝒚𝟎 Equation 3-4

Therefore, the dual problem (DLP) for the input-oriented model can be expressed as

follows:

𝐦𝐢𝐧 𝜽 − 𝜺(∑ 𝒔𝒓+𝒔

𝒓=𝟏 + ∑ 𝒔𝒊−𝒎

𝒊=𝟏) Equation 3-5

Subject to

∑ 𝜆𝑗 𝑥𝑖𝑗 + 𝑠𝑖− = 𝜃𝑥𝑖0

𝑛

𝑗=1

𝑖 = 1, … , 𝑚

∑ 𝜆𝑗 𝑦𝑟𝑗 − 𝑠𝑟+ = 𝑦𝑟0

𝑛

𝑗=1 𝑟 = 1, … , 𝑠

𝜆𝑗 , 𝑠𝑖+, 𝑠𝑖

− ≥ 0, 𝑎𝑙𝑙 𝑟, 𝑖, 𝑗; 𝜃 𝑓𝑟𝑒𝑒

Where: (𝑠𝑖+, 𝑠𝑖

−) are output and input slack variables, respectively.

In the case of the output-oriented model, the dual problem can be expressed as

follows:

𝐦𝐚𝐱 𝝋 − 𝜺(∑ 𝒔𝒓+𝒔

𝒓=𝟏 + ∑ 𝒔𝒊−𝒎


Subject to

Methodology


∑ 𝜆𝑗 𝑥𝑖𝑗 + 𝑠𝑖− = 𝑥𝑖0

𝑛

𝑗=1

𝑖 = 1, … , 𝑚

∑ 𝜆𝑗 𝑦𝑟𝑗 − 𝑠𝑟+ = 𝜑𝑦𝑟0

𝑛

𝑗=1 𝑟 = 1, … , 𝑠 𝜆𝑗 , 𝑠𝑖

+, 𝑠𝑖− ≥ 0, 𝑎𝑙𝑙 𝑟, 𝑖, 𝑗 𝜑 𝑓𝑟𝑒𝑒


−) are output and input slack variables, respectively.

3.3.2 BCC-DEA model

Banker et al. (1984) introduced the BCC-DEA model, which exhibits various returns

to scale on the production frontier as shown in Figure 3-4b.

(a) Production frontier of CCR model (b) Production frontier of BCC model

Figure 3-4: Production frontier of (a) CCR and (b) BCC models

According to the BCC model, the production frontiers have piece-wise linear and

concave characteristics, which represent increasing, constant, and decreasing return-to-

scale.

𝐦𝐚𝐱 𝒉𝟎∗ =

∑ 𝒖𝒓 𝒚𝒓𝟎−𝒖𝟎𝒔𝒓=𝟏

∑ 𝒗𝒊𝒙𝒊𝟎𝒎𝒊=𝟏

Equation 3-7

Subject to:

∑ 𝑢𝑟 𝑦𝑟𝑗𝑠𝑟=1 − 𝑢0

∑ 𝑣𝑖𝑥𝑖𝑗𝑚𝑖=1

≤ 1; 𝑗 = 1, … , 𝑛

𝑢𝑟, 𝑣𝑖 ≥ 휀 > 0; 𝑟 = 1, … , 𝑠; 𝑖 = 1, … , 𝑚. 𝑢0 𝑓𝑟𝑒𝑒 𝑖𝑛 𝑠𝑖𝑔𝑛

The linear programming equivalent of equation 3-7 is

𝐦𝐚𝐱 𝒉𝟎∗ = ∑ 𝝁𝒓 𝒚𝒓𝟎

𝒔𝒓=𝟏 − 𝝁𝟎 Equation 3-8

Subject to

Input

Ou

tpu

t

o

Production

Possibility

Set

Production Frontier

Input

Ou

tpu

t

o

Production

Possibility

Set

Production Frontier

Methodology


∑ 𝜗𝑖 𝑥𝑖0 = 1

𝑚

𝑖=1

∑ 𝜇𝑟 𝑦𝑟𝑗

𝑠

𝑟=1

− 𝜇0 − ∑ 𝜗𝑖 𝑥𝑖𝑗 ≤ 0 𝑗 = 1, … , 𝑛

𝑚

𝑖=1

𝜇𝑟, 𝜗𝑖 ≥ 휀 > 0; 𝑟 = 1, … , 𝑠; 𝑖 = 1, … , 𝑚 𝜇0 𝑓𝑟𝑒𝑒

By duality, the input-oriented BCC model evaluates the efficiency of DMU0 (0=1, …,

n) by solving the linear program (Equation 3-9). In terms of evaluating the output-oriented

efficiency, this problem can be converted to maximising ratio 𝜑 like CCR model.

𝐦𝐢𝐧 𝜽𝟎 − 𝜺(∑ 𝒔𝒓+𝒔

𝒓=𝟏 + ∑ 𝒔𝒊−𝒎


Subject to

∑ 𝜆𝑗 𝑥𝑖𝑗 + 𝑠𝑖− = 𝜃0𝑥𝑖0

𝑛

𝑗=1

𝑖 = 1, … , 𝑚

∑ 𝜆𝑗 𝑦𝑟𝑗 − 𝑠𝑟+ = 𝑦𝑟0

𝑛

𝑗=1

𝑟 = 1, … , 𝑠

∑ 𝜆𝑗 = 1 𝑛

𝑗=1 𝜆𝑗 , 𝑠𝑖

+, 𝑠𝑖− ≥ 0, 𝑎𝑙𝑙 𝑟, 𝑖, 𝑗 𝜃 𝑓𝑟𝑒𝑒


−) are output and input slack variables, respectively. Input slack (𝑠𝑖−) is

the amount of input that a DMU could reduce to produce the same output, while output slack

(𝑠𝑖+) is the amount of output that a DMU could increase using unchangeable input. Therefore,

looking at the values of slack variables obtained from DEA-based empirical analysis, transit

practitioners may identify key factors (with slack variables > 0) greatly influencing the

performance of DMUs, and may quantitively indicate the input reduction and output increase

to improve the performance of inefficient DMUs.

3.3.3 Network DEA model

The traditional DEA models (CCR and BCC models) treat their reference technologies

as black boxes. Inputs are transformed in this box into outputs without modelling the actual

process explicitly (see Figure 3-5). One simply specifies what enters and what exits the box

(Färe and Grosskopf 2000).

Methodology


Figure 3-5: The aggregated technology (Source: Färe et al. (2000))

However, some production processes include several divisions that are linked to each

other like hospitals and electric power companies. Traditional DEA models neglect the

intermediate products and the linkage among those divisions. Thus, traditional DEA models

cannot interpret the performance of sub-technologies or components in the box as well as

evaluate the impact of division-specific inefficiencies on the overall efficiency of the

production process (Tone and Tsutsui 2009).

The network DEA model was first developed by Färe et al. (1996) to allow one to look

into the internal structure of a production process and evaluate the performance of the whole

technology as well as its component performance. The network DEA model then was

employed by researchers, such as Löthgren et al. (1999), who utilised this model to assess

the efficiency and productivity as well as customer satisfaction in Swedish pharmacies, Lewis

et al. (2004) focussed on the organisations with complex internal structure, and Tone et al.

(2009) proposed a slack-based network DEA model to evaluate divisional efficiencies along

with the overall efficiency of DMUs.

The network DEA model of Färe and Grosskopf (2000) is expressed as follows:

Assume that there are 𝑘 = 1, … , 𝐾 DMUs or observations of 𝑁 inputs and 𝑀 outputs,

(𝑥𝑘 , 𝑦𝑘) = (𝑥𝑘1, … , 𝑥𝑘𝑁, 𝑦𝑘1, … , 𝑦𝑘𝑀). The coefficients (𝑥𝑘𝑛, 𝑦𝑘𝑚) (𝑛 = 1, … , 𝑁; 𝑚 = 1, … , 𝑀; 𝑘 =

1, … , 𝐾) are required to satisfy certain conditions. These are:

(i) 𝑥𝑘𝑛 ≥ 0, 𝑦𝑘𝑚 ≥ 0, 𝑛 = 1, … , 𝑁; 𝑚 = 1, … , 𝑀; 𝑘 = 1, … , 𝐾

(ii) ∑ 𝑥𝑘𝑛 > 0, 𝑛 = 1, … , 𝑁.𝐾𝑘=1

(iii) ∑ 𝑥𝑘𝑛 > 0, 𝑘 = 1, … , 𝐾.𝑁𝑛=1

(iv) ∑ 𝑦𝑘𝑚 > 0, 𝑚 = 1, … , 𝑀.𝐾𝑘=1

(v) ∑ 𝑦𝑘𝑚 > 0, 𝑘 = 1, … , 𝐾.𝑀𝑚=1

The first conditions in (i) merely state that inputs and outputs are non-negative

numbers. The second requirement (ii) means that each input is used in at least one activity.

The third condition (iii) illustrates that each activity uses at least one input. The condition (iv)

x yThe production process

P

"Black box"

Methodology


requires that each output is produced by some activity, while (v) says that each activity

produces some output.

Assume that there is a production process involving three sub-processes or sub-

technologies (1, 2, and 3), a source (0), and an outlet (4) as illustrated in Figure 3-6. This full

network model includes a total of five nodes (0, …, 4), intermediate products, and allocative

inputs. A product is intermediate to the production system if it is both an input and an output

within the network. For instance, 𝑦13 is both an output of node 1 and an input of node 3. Not

all of the intermediate goods are necessarily consumed or used up within the network. They

may be the final output as well, such as 𝑦14 is the final output of node 1.

Figure 3-6: The network technology (Source: Färe et al. (2000))

Let the vector of (exogenous) inputs be denoted by 𝑥 and let 𝑥0𝑖 , 𝑖 = 1,2,3 denote the

amount of the vector of exogenous inputs that is allocated to node 𝑖.

The constraints for the allocation of the exogenous inputs:

𝒙 ≥ ∑ 𝒙𝟎𝒊

𝟑

𝒊=𝟏 Equation 3-10

Or

𝒙𝒏 ≥ 𝒙𝟎𝟏 + 𝒙𝟎

𝟐 + 𝒙𝟎𝟑 , 𝒏 = 𝟏, … , 𝑵. Equation 3-11

Let the vector of outputs produced by sub-process 𝑖 and delivered to node 𝑗 be

denoted by 𝑦𝑖𝑗

. In Figure 3-6, it can be seen that the total production of node 1 is ( 𝑦13 + 𝑦1

4 ),

where 𝑦13 is its output of intermediate products and 𝑦1

4 is its final output. Note 1 does not use

any intermediate products as inputs. However, sub-process or node 3 uses intermediate

products from node 1 and node 2 as inputs ( 𝑦13 , 𝑦2

3 respectively) as well as exogenous inputs,

𝑥03 . This node produces only final outputs, 𝑦3

4 . Given that each sub-process produces distinct

output vectors, 𝑦𝑗4 ∈ 𝑅+

𝑀𝑗, 𝑗 = 1,2,3, where 𝑀 = 𝑀1 + 𝑀2 + 𝑀3, the outlet or collection node 4

can be written as:

30 4x y

1

2

x0

1

x0

2

x0

3y

1

3

y2

3

y3

4

y1

4

y2

4

Methodology


𝒚 = ( 𝒚𝟏𝟒 , 𝒚𝟐

𝟒 , 𝒚)𝟑𝟒 Equation 3-12

If each node does not produce distinct outputs, total production can be written as the

sum ∑ 𝑦𝑗4

3

𝑗=1 of the individual nodes’ outputs. The appropriate number of zeros must be

added.

The piecewise linear or network DEA technology associated with 𝑘 = 1, … , 𝐾

observations may be written in terms of the output set as:

ᴃ(𝑥) = {𝑦 =( 𝑦14 , 𝑦2

4 , 𝑦)34 :

Node 3 (a) 𝑦𝑚 ≤34 ∑ 𝑧𝑘

3 𝑦𝑘𝑚, 𝑚 =34 1, … , 𝑀3,

𝐾

𝑘=1

(b) ∑ 𝑧𝑘3 𝑥𝑘𝑛 ≤ 𝑥𝑛0

3 , 𝑛 =03 1, … , 𝑁,

𝐾

𝑘=1

(c) ∑ 𝑧𝑘3 𝑦𝑘𝑚 ≤ 𝑦𝑚1

3 , 𝑚 =13 1, … , 𝑀1,

𝐾

𝑘=1

(d) ∑ 𝑧𝑘3 𝑦𝑘𝑚 ≤ 𝑦𝑚2

3 , 𝑚 =23 1, … , 𝑀2,

𝐾

𝑘=1

(e) 𝑧𝑘3 ≥ 0, 𝑘 = 1, … , 𝐾

Node 1 (f) ( 𝑦𝑚13 + 𝑦𝑚) ≤1

4 ∑ 𝑧𝑘1( 𝑦𝑘𝑚1

3 + 𝑦𝑘𝑚), 𝑚 =14 1, … , 𝑀1,

𝐾

𝑘=1

(g) ∑ 𝑧𝑘1 𝑥𝑘𝑛 ≤ 𝑥𝑛0

1 , 𝑛 =01 1, … , 𝑁,

𝐾

𝑘=1

(h) 𝑧𝑘1 ≥ 0, 𝑘 = 1, … , 𝐾

Node 2 (i) ( 𝑦𝑚23 + 𝑦𝑚) ≤2

4 ∑ 𝑧𝑘2( 𝑦𝑘𝑚2

3 + 𝑦𝑘𝑚), 𝑚 =24 1, … , 𝑀2,

𝐾

𝑘=1

(j) ∑ 𝑧𝑘2 𝑥𝑘𝑛 ≤ 𝑥𝑛0

2 , 𝑛 =02 1, … , 𝑁,

𝐾

𝑘=1

(k) 𝑧𝑘2 ≥ 0, 𝑘 = 1, … , 𝐾

Distribution of exogenous

inputs

(l) 𝑥𝑛01 + 𝑥𝑛0

1 + 𝑥𝑛01 ≤ 𝑥𝑛, 𝑛 = 1, … , 𝑁} Equation 3-13

In the network model (Equation 3-13), the three sub-processes can be identified. The

third, ᴃ3( 𝑥03 , 𝑦1

3 , 𝑦)23 , consists of expressions (a)-(e). The first, ᴃ1( 𝑥0

1 ), is given by (f)-(h), and

the last, ᴃ2( 𝑥02 ), by (i)-(k). Here 𝑧𝑘

𝑖 is the weight of input and output variables. It means that

the network model has three sets of intensity variables, compared to one set of such variables

in the standard DEA model. The network model has a distribution node that allows one to

study optimal distribution of the exogenous inputs among sub-processes, whereas the

standard model does not. Furthermore, the network model can model intermediate inputs

explicitly, so it allows practitioners to interpret the sources of inefficiency in the whole system.

Methodology


The framework for evaluating the performance or the operational effectiveness of a

transit system as shown in Figure 1-2 includes two sub-processes, the technical efficiency

and the service effectiveness. Bus routes composing a transit system are regarded as sub-

units in the production process of such a transit system. Therefore, measuring the

performance of bus routes needs to go the two such sub-processes. In which, the technical

efficiency represents the service production process, while the service effectiveness

represents the service consumption process of bus routes. The outputs in the first sub-

process will become the inputs in the second sub-process. From these analyses, the network

DEA (NDEA) model should be used for examining the performance of bus routes.

3.3.4 The need of using DEA model

The advantages and disadvantages of using the DEA approach for efficiency analysis

of a set of peer DMUs are excessive in the literature (Charnes, Cooper et al. 1978, Seiford

and Thrall 1990, Coelli, Prasada Rao et al. 1998, Tone, Cooper et al. 1999, De Borger,

Kerstens et al. 2002). Coelli et al. (1998) provided a comprehensive comparison between

four methods, including: (1) least-squares (LS) econometric production models; (2) total

factor productivity (TFP) indices; (3) DEA; and (4) SFA. Here, the advantage of DEA and SFA

(frontier methods) over traditional methods (LS and the engineering ratio approach) is clearly

indicated that it allows one to evaluate the technical efficiency level of individual DMUs with

multiple inputs and outputs by generating a single efficiency score. The main characteristics

of DEA are summarised as follows:

Advantages of DEA approach

• Compared with traditional econometric methods, DEA using standard

techniques of linear programming allows one to distinguish between efficient

and inefficient production, estimate the degree of inefficiency of each DMU

(efficiency scores), and identify sources of inefficiency. The computation, dual

variables, and clear interpretations are available in DEA (Seiford and Thrall

1990).

• Compared with the usual index number approaches, DEA does not require

one to prescribe weights for each input and output. Compared with the

parametric approach (SFA), DEA does not require the functional form for

production frontier estimation (Tone, Cooper et al. 1999).

• DEA is useful to evaluate the efficiency of non-profit entities operating in public

programs where the apparent market for outputs is unavailable, such as

schools and hospitals (Charnes, Cooper et al. 1978). This is because a

Methodology


variable that is neither an economic resource nor a product but is an attribute

of the production process can be used in the DEA model (Charnes, Cooper et

al. 1985, Seiford and Thrall 1990).

Limitations of DEA approach

• DEA could be sensitive to data errors. The production frontier function is built

up directly from the dataset, so any noise in data may influence the placement

of the DEA frontier.

• DEA could also be sensitive to variable selection. The exclusion of an

important input or output can lead to biased results.

• The DEA efficiency scores of DMUs are only relative to the best DMUs in a

given sample. The changes of sample size may reduce efficiency scores of

DMUs.

Based on the characteristics of DEA compared with other approaches, Coelli et al.

(1998) concluded that the SFA approach is only well-developed for single-output

technologies, and that in the non-profit service area where multiple-output production is

important and prices are difficult to define, the DEA approach should be applicable. This

research aims to evaluate the operational efficiency of bus routes with multiple outputs.

Therefore, DEA is selected for empirical analysis.

Sensitivity analysis in DEA

3.4.1 Sensitivity analysis of DEA efficiency scores

The DEA model only provides a mean of estimation of DMUs’ efficiency scores. Many

researchers thus employed truncated regression models in the second stage to analyse the

sensitivity of efficiency scores obtained in the first stage to factors possibly affecting the

efficiency level of DUMs. Factors used to test the sensitivity of efficiency scores are usually

socio-economic factors, regarded as environmental/external variables.

Some studies used the censored (Tobit) model in the second stage to evaluate the

performance of transit systems (Nolan 1996, Tsamboulas 2006), while others employed the

bootstrapping technique (Georgiadis, Politis et al. 2014). However, McDonald (2009)

indicated that in case the efficiency scores are not generated by a censoring process but are

fractional data, Tobit estimation is inappropriate, while ordinary least square (OLS) is a

consistent estimator. Interestingly, Simar and Wilson (2007) proposed single and double

bootstrap procedures, and demonstrated that both procedures can produce consistent

inference and statistical properties, and the double bootstrap procedure improves statistical

Methodology


efficiency in the second-stage regression. The bootstrapping technique thus will be applied

to the present study, in which DEA efficiency scores are dependent variables and

environmental factors are independent variables.

3.4.2 The bootstrap approach

Simar and Wilson (1998) were the first to introduce the bootstrap approach in DEA to

obtain statistical properties of the efficiency scores. Then they extended their approach to

consider the impact of environmental variables on efficiency (Simar and Wilson 2007). The

importance of the procedure introduced by Simar and Wilson (2007) is that it estimates the

bias-corrected efficiency scores of all DMUs, valid estimates for the parameters in the

regression model (Barros and Assaf 2009). Based on the work of Simar and Wilson (2007),

Barros and Assaf (2009) describe the bootstrap algorithm as follows:

i. Calculate the DEA output-orientated efficiency score ��𝒊 for each DMU, using

the linear programming technique.

ii. Estimate the truncated regression of 𝛿𝑖 on the environmental variable 𝑧𝑖, using

the maximum likelihood estimation method to provide (𝛽, ��𝜀) of (𝛽, 𝜎𝜀). Here,

the efficiency model is described as 𝛿𝑖 = 𝛽𝑧𝑖 + 휀𝑖 in which 𝛽 refers to a vector

of parameters with some statistical noise 휀𝑖, and 𝜎𝜀 is standard deviation of 휀𝑖.

iii. For each DMUi (𝑖 = 1, … , 𝑛), the following four steps (1-4) are repeated B1

times to produce a set of bootstrap estimates, {��𝑖,𝑏∗ , 𝑏 = 1, … , 𝐵1}.

1. Draw 휀𝑖 from the 𝑁(0, 휀��) distribution with left truncation at (1 − ��𝑧𝑖).

2. Compute 𝛿𝑖∗ = ��𝑧𝑖 + 휀𝑖.

3. Construct a pseudo data set (𝑥𝑖∗, 𝑦𝑖

∗) based on 𝛿𝑖∗, 𝛿𝑖

∗ and the actual data set,

where 𝑥𝑖∗ = 𝑥𝑖 and 𝑦𝑖

∗ = 𝛿𝑖𝑦𝑖/𝛿𝑖∗.

4. Compute a new DEA score, 𝛿𝑖∗, based on the pseudo data set.

iv. For each DMU, compute the bias-corrected efficiency score 𝛿𝑖 = 𝛿𝑖 − 𝑏𝑖��𝑠𝑖,

where 𝑏𝑖��𝑠𝑖 is the bootstrap estimator of bias obtained as: 𝑏𝑖��𝑠𝑖 =

1/𝐵1 ∑ 𝛿𝑖,𝑏∗ − ��𝑖

𝐵1𝑏=1 .

v. Use the maximum likelihood method to estimate the truncated regression of

𝛿𝑖 on 𝑧𝑖 providing estimates (𝛿, ��𝜀) of (𝛽, 𝜎𝜀).

Methodology


vi. Repeat the following three steps (1-3) B2 times to obtain a set of estimates

{��𝑏∗, ��∗, 𝑏 = 1, … , 𝐵2}.

1. For 𝑖 = 1, … , 𝑛, 휀𝑖 is drawn from 𝑁(0, ��) with left truncation at (1 − ��𝑧𝑖)

2. For 𝑖 = 1, … , 𝑛, compute 𝛿𝑖∗∗ = ��𝑧𝑖 + 휀𝑖

3. Use the maximum likelihood method to estimate the truncated regression of

𝛿𝑖∗∗ on 𝑧𝑖, providing estimates (𝛿∗, ��∗

𝜀)

vii. Use the bootstrap results to construct the confidence interval for the efficiency

scores.

Transit Productiveness Indexes

This section provides the two basic transit productiveness indexes: Transit work load

factor; and Transit service passenger transmission efficiency of Bunker (2013, 2015). The

DEA efficiency scores of a bus route will be compared with these two indexes in section 6.2.2

of chapter 6. Such comparison helps to elaborate the difference between the DEA efficiency

scores and transit productiveness indexes, validate the obtained results of the DEA model,

and demonstrate the significance of a DEA approach in dealing with multiple input and output

DMUs.

Bunker (2015) defined transit work load factor (passenger-km/space-km), of transit

route R within time window Z by:

𝑳𝑭𝑹,𝒁𝒘𝒐𝒓𝒌 =

∑ (𝒔𝒊 ∑ 𝑷𝑶𝑩,𝒌,𝒊)𝒎𝒌=𝟏

𝒏𝒊=𝟏

∑ (𝒔𝒊 ∑ 𝑷𝑴𝑺𝑳,𝒌)𝒎𝒌=𝟏

𝒏𝒊=𝟏

Equation 3-14

Where:

𝑠𝑖 = length of segment 𝑖 (km)

𝑃𝑂𝐵,𝑘,𝑖 = passenger on board kth service on segment 𝑖 (passenger)

𝑃𝑀𝑆𝐿,𝑘 = maximum scheduled load of kth service (passenger)

Bunker (2013) defined transit service passenger transmission efficiency of service 𝑘

in completing transit route R as:

𝜼𝑹,𝒌 =𝑻𝑺,𝒌,𝑹(∑ 𝑷𝑶𝑩,𝒌,𝒊𝒔𝒊)𝒏

𝒊=𝟏

𝑻𝒌,𝒏(∑ 𝑷𝑴𝑺𝑳,𝒌𝒔𝒊)𝒏𝒊=𝟏

Equation 3-15

Where:

𝑇𝑆,𝑘,𝑅 = scheduled time for kth service to complete route R (min)

Methodology


𝑇𝑘,𝑛 = actual time for kth service to complete route R (min)

It is clear that 𝐿𝐹𝑅,𝑍𝑤𝑜𝑟𝑘

describes how productive a service or line is over a time period

of interest with regard to vehicle loading, while 𝜂𝑅,𝑘 reflects the productiveness of a service or

line in terms of both loading and travel time used.

Discussion

Regarding transit, due to the constraint of capacity (for instance bus station capacity)

and operating vehicle speed (because of schedule travel time), the output (OTP, transit work,

average vehicle speed) might not have a constant increase when increasing the inputs (bus

size, service frequency etc.). Therefore, the constant return to scale is not always existent

and it needs to consider VRS so as to reflect this constraint.

In terms of the model orientation, as mentioned in the section 3.2 the technical

efficiency of an industry can be viewed from two perspectives: input-oriented; and output-

oriented measures. For CCR model, input-oriented and output-oriented models will yield the

same results regarding technical inefficiency. However, the input-oriented and output-

oriented BCC models may give different estimates when inefficiencies are present (Tone,

Cooper et al. 1999). The appropriate selection of input or output orientation in the DEA

analysis should be based on what is to be achieved from that analysis (Cook, Tone et al.

2014). If the objective is the identification of DMUs that are over-utilising resources, then the

input reduction should be the central focus. In this situation, the input-oriented DEA model

would be more appropriate than output-oriented model. On the other hand, if the output

enhancement is desirable objectives in an application, then the output-oriented DEA model

may be more appropriate to evaluate the performance of DMUs. The overall objective of this

study is to evaluate the performance of bus routes based on the operator’s perception

(maximising ridership and quality of service). Thus, the output-oriented measure is adopted

for empirical analysis.

This study aims to develop a framework for transit routes’ performance evaluation on

the basis of maximising the outputs. DMU is, thus, defined as the performance of each bus

route during a given hour (all bus services of the corresponding route in an hour for both

inbound and outbound directions). However, because one bus service may operate across

two different hours, bus services in a given hour are selected based on the schedule start

time.

Applying the proposed approach for data analysis of the case study in Brisbane,

Australia, this research first evaluates the temporal performance of each selected bus route

Methodology


across the working days of a week (which excludes public holidays). This work helps to gain

more understanding of the performance of individual bus routes without the impact of external

factors on the results obtained. In the second stage, NDEA models are employed for

comparing the performance of several bus routes within the bus network of the case study.

This helps to provide insights into the spatial and temporal performance and investigate the

internal reasons for inefficiency of given bus routes.

This study compares the two basic transit productiveness indexes developed by

Bunker (2013, 2015) with DEA efficiency scores obtained from temporal performance

analysis of a typical route for one direction (inbound direction). Results obtained from those

two approaches, using the similar variables for analysis, can be useful to indicate the

significance of the DEA approach for bus route performance analysis.

The double bootstrap approach of Simar and Wilson (2007), proven to be a reliable

tool for investigating the influences of external variables on DMUs’ efficiency scores, will be

used in the second-stage analysis. This helps to identify the external sources of inefficiency

of bus routes’ performance.

Framework for Bus Routes Performance Measurement


4 Framework for Bus Route Performance Measurement

Introduction

The literature review section has shown that the performance of bus routes is

examined by a limited number of studies. In those studies, bus routes’ performance

measurement is conducted explicitly for particular performance concepts such as technical

efficiency, service effectiveness or operational effectiveness (Lao and Liu 2009, Georgiadis,

Politis et al. 2014). It thus cannot provide an overall and single measure for the production

process of bus routes. To provide an overall performance evaluation of bus routes, this

chapter aims to develop a network framework, which consists of two linked divisions (nodes):

technical efficiency (node 1); and service effectiveness (node 2).

Additionally, data used to examine the bus routes’ performance are broadly clustered

into two groups: (1) internal variables; and (2) external variables (Taylor and Fink 2003, Alam,

Nixon et al. 2015). The first group consists of bus performance indicators and relevant

variables within the control of a transit agency (such as route length, schedule, headway,

quality of service), while the latter refers to socio-economic and demographic factors beyond

the control of the transit agency (such as private car ownership, parking facility, transit

accessibility, road system, traffic condition, and employment distribution). In this research,

internal factors are employed in DEA-based data analysis to produce DMUs’ efficiency

scores, and external factors then are used in a truncated regression model. Thus, there is a

need to discuss and select appropriate internal and external variables for bus route

performance measurement.

Section 4.2 identifies the study goals needing to be achieved. Thereafter, section 4.3

presents the proposed framework for bus route performance measurement, which is followed

by the selection of corresponding inputs and outputs in section 4.4, and the selection of

external variables in section 4.5. Finally, the chapter concludes in section 4.6 where

discussion is given.

The Study Goals Needed To Be Achieved

To develop an appropriate DEA-based framework for efficiency analysis of a set of

DMUs, identifying the study’s goals is of importance, because these goals substantially

influence the model choice (input or output orientation) and input and output variable

selection. For example, Lao et al. (2009) selected the total number of passengers as output,

because their study goal was to measure the productivity of supply. Barnum et al. (2008)



aimed to identify the variations of bus route performance regarding operational effectiveness,

so ridership, span of service, average frequency, maximum frequency, and on-time

performance were selected as outputs in their DEA model (refer to Table 4-1)

In this research, the aim is to compare the operational effectiveness of several bus

routes within the case study in Brisbane on the basis of transit operators’ perception. This

means that the aim is to optimize the service outputs and assist transit agencies in identifying

the underlying reasons for inefficient performance of some bus routes. Therefore, the output-

oriented NDEA model is adopted.

Develop the Framework for Bus Route Performance Measurement

As an individual route is a subunit within a system, its performance evaluation should

follow the framework of transit system performance evaluation (see Figure 1-2), which

consists of three separate dimensions: technical efficiency; service effectiveness; and

operational effectiveness. To evaluate the overall performance of bus routes, this research

develops a network framework which consists of two linked divisions: (1) Technical efficiency;

and (2) Service effectiveness. Service outputs are intermediate variables in this framework

(which are output variables of technical efficiency measure and input variables of service

effectiveness measure). By this network framework, the operational effectiveness measure

accounting for both divisions (1 and 2) generates the overall efficiency scores of bus routes.

At the same time, divisions 1 and 2 can be evaluated separately to provide insights into the

performance of the bus route production process.

Considering the performance of a route, it can be seen clearly that service outputs

include two major groups of performance elements: quantity of service (such as vehicle-km,

seat-km, and space-km); and level of service (such as operating speed, schedule reliability,

and safety) (Vuchic 2007). In these, performance elements regarding level of service greatly

affect transit users’ travel decisions. Therefore, the proposed framework for transit route

performance evaluation considers both quantity of service and level of service (see Figure

4-1).



Figure 4-1: Framework for a transit route performance evaluation

Inputs and Outputs Selection for Bus Routes

After building up the appropriate framework for bus route performance evaluation, the

selection of input and output variables and the combination of those inputs and outputs play

a crucial role in achieving the accurate results. Hence, this section discusses and selects the

appropriate variables for bus route performance measurement.

4.4.1 Some crucial recommendations for input and output variables selection, and

the combination of inputs and outputs in DEA

Rohácová et al. (2015) noted some qualifications in selecting inputs and outputs, and

the combination among those variables as follows:

• All input and output variables should characterise the operation of DMUs.

• The availability of the data required.

• The combination of inputs and outputs ensures the suitability of variables with

respect to the economic purpose of technical efficiency (the production process).

• The number of DMUs needs to be at least three times greater than the total

number of inputs and outputs (Cooper, Seiford et al. 2007).

• Uniqueness of information contained in inputs and outputs, and high information

value of the relationship among them.

The last point means that all individual inputs and outputs should not duplicate

information, and there should be strong relationship between inputs and outputs. The outputs

should be generated directly by the respective inputs. Thus, the number of inputs or outputs

should be reduced based on the correlation analysis before using in DEA model. Table 4-1

presents several typical studies for bus route performance evaluation using DEA models in

Service

Inputs

Service

Consumption

Service

Outputs Service effectivenessTechnical efficiency

Operational effectiveness

Quantity of Service

Level of Service

(for consumption process)(for production process)



literature. In these, the selection of input and output variables is based on the aforementioned

recommendations and the study goals.

Table 4-1: An overview of inputs and outputs selection for bus route performance evaluation

Studies Models

used

Input variable Output variable Purpose of In-Output selection

Lao et al.

(2009)

1,2Output

orientation

BCC-DEA

model.

1Operation time;

Round trip distance;

Number of bus stops.

2Commuters who use

buses;

Population 65 and

older;

Persons with

disabilities.

1Total number of

passengers.

2Total number of

passengers.

1Operational efficiency measures the

productivity of supply. In the absence

of actual costs (labour, fuel, others),

this study used those inputs as

operational costs. The total number

of passengers represents the total

revenue.

2Spacial effectiveness measures the

benefit of demand (service

consumption).

Barnum

et al.

(2008)

1Output

orientation

CCR- DEA

model.

1Seat kilometres (SK);

Seat hours (SH);

2Population density;

Population; Title 6

Routes (at least 1/3

route length in zones

with high percentage

of minority

population); Key

Routes (the most

productive routes).

1Ridership;

Span of service;

Average frequency;

Maximum frequency;

On-time performance

(OTP).

1Assist the agency management in

identifying differences in route

performance. Inputs are the

resources that supply the transit

service. Outputs are the use and the

quality of service.

2Adjusting the raw DEA scores to

account for the environmental

influences on riders and OTP.

Sheth et

al.

(2007)

Network

DEA model.

1The inputs for the

provider node:

Headway; Service

duration; Costs;

Number of

intersections; Number

of priority lanes.

The environmental

variables:

Accessibility factor;

Parking space

availability factor;

Population density

1,2The outputs for

the provider node

and inputs for the

passenger node:

Vehicle-miles;

Schedule reliability;

Average travel time.

2The outputs for the

passenger node:

Passengers-miles

The externalities:

Number of accidents;

Emissions; Noise

Taking into consideration the service

providers, the users, and the societal

perspectives.

1Inputs are scarce resources used

and outputs are service provided for

society (the quantity and quality of

service)

2Output relates to service

consumption and the societal

influences.



factor; Connectivity

factor; Comfort

standards factor.

pollution; Resources

degraded.

Georgia-

dis et al.

(2014)

DEA model

and

Bootstrap

model.

1Model 1: Length;

Span of service;

Vehicles. (output

orientation)

2Model 2: Length;

Span of service;

Vehicles. (output

orientation)

3Model 3: vehicle-km;

Vehicles. (input

orientation)

1Revenue seat-km;

2Passengers

3Passengers

1Model 1 explores the productivity of

the available resources allocated to

each bus line (cost efficiency).

2Model 2 investigate the relationship

between available supply and

observed demand.

3Model 3 explores the possibilities of

balancing supply with observed

demand.

1, 2, 3: models used for data analysis

4.4.2 Selection of inputs and outputs

There are two divisions in the whole production process of a bus route (see Figure

4-1), the service production and the service consumption. In the first process, service inputs

are defined as all resources needed to produce service outputs (quantity of service and level

of service) for a community. Then, in the next process, service outputs (regarded as

intermediate products) are used as inputs, while observed demand is considered as the final

output.

Service inputs include labour, vehicle, operational cost, and bus route infrastructure

such as the length of route, bus stops, bus lane priority, and signalised intersections along

the bus routes. Service outputs that a bus route offers to a community include service

availability (such as vehicle-km, seat-km, and space-km) and performance elements related

to the level of service (such as on-time performance (OTP) and average operating speed)

(Vuchic 2007). Finally, the service consumption is observed demand, such as the total

number of passengers, passenger-km or passenger-mile. However, some service inputs

such as fuel consumption, operating cost, and maintenance cost are unavailable at the route

level of the case study. Therefore, this research uses proxies to refer to those service inputs.

Based on the proposed framework in Figure 4-1 and relevant arguments in the

literature review section of Chapter 2, the corresponding inputs and outputs are adopted and

shown in Table 4-2. The rationale behind this selection of inputs and outputs is as follows:

Technical efficiency: the output variables should present service outputs offered by

the operator, which include variables regarding quantity of service and level of service.



However, to ensure the close relationship between inputs and outputs, this research employs

quantity of service only for a technical efficiency measure (division 1). Here, space-km is

selected as an output because space-km provided in a given period of time (an hour, peak

period, a day) represents the offered quantity of service outputs, accounting for the vehicle

capacity. Space-km is estimated by equation 4-1:

𝑺𝒑𝒂𝒄𝒆 − 𝒌𝒎 = ∑ 𝑪𝒌𝒍𝒌𝒏𝒌=𝟏 Equation 4-1

Where: 𝐶𝑘 is the number of spaces (seat and stand) of a bus vehicle used for service

𝑘; 𝑙𝑘 is the route length travelled by service 𝑘; 𝑛 is the number of services performed within a

given period of time.

The relevant inputs to the technical efficiency should correspond to the resources

used by the operator to produce the quantity of service (space-km). Here, route length,

Busway length, service duration, and number of services are considered as inputs to the

technical efficiency measure. Route length and Busway length is a proxy for the operation

and maintenance resources (Sheth, Triantis et al. 2007, Lao and Liu 2009, Georgiadis, Politis

et al. 2014). Number of services is a proxy for the number of vehicles and drivers used (Lao

and Liu 2009, Georgiadis, Politis et al. 2014). Service duration is a proxy for the fuel

consumption and operating expenses (information system and working hours etc.) (Lao and

Liu 2009, Georgiadis, Politis et al. 2014).

Service effectiveness: the outputs should represent the service consumption. Here,

we select Transit work and OTP as outputs. Transit work by definition represents the service

consumption of the community. Regarding schedule reliability, OTP is one of the most widely

used reliability measures in transit sector (Kittelson, Associates et al. 2003, Chen, Yu et al.

2009, Ryus, Danaher et al. 2013, Qu, Oh et al. 2014). The TCQSM (2003, 2013) defined

OTP as the percentage of trips arriving at the stops on time (less than five minutes later and

less than one minute earlier than scheduled arrival). However, Camus, Longo et al. (2005)

indicated that the TCQSM method for estimation of transit schedule reliability (OTP) was not

be able to consider the amount of delay, and proposed a new performance measure called

weighted delay index to address this issue using the automated vehicle location (AVL) data

collected in Trieste, Italy. This method allows one to both estimate the OTP and the amount

of delay of transit trips. This study uses the OTP defined by TCQSM (2013) as an output in

the DEA models because it was widely used in the preceding studies (Sheth, Triantis et al.

2007, Barnum, Tandon et al. 2008).

Note: OTP is generally used as a variable of service output (Sheth, Triantis et al.

2007). We argue that transit operators, in principle, desire to maximise the OTP to increase



the transit quality of service. Therefore, we consider OTP as the service consumption output

variable. Space-km and average vehicle speed are corresponding inputs for this dimension.

For the service effectiveness measure, this research uses average vehicle speed as

the second variable of service outputs along with space-km. The rationale behind this

selection is that average vehicle speed represents the time efficiency of offered services

along the corresponding bus route, and is one of the most important performance elements

determining bus level of service (Vuchic 2007). The higher average vehicle speed is, the

more attractive to users the bus route is. In literature, Sheth et al. (2007) also used average

travel time (with unit: hour-1) as a variable of service outputs, and Zhao et al. (2011) built up

a network framework to evaluate the performance of a transportation network, which uses

average speed as one of the inputs of user node. Thus, average speed in both theory and

practice was widely used to present service outputs regarding level of service.

The operational framework for a bus route is depicted in Figure 4-2. There are two

nodes (1 and 2) in the overall production process of a bus route, including production process

(node 1) and consumption process (node 2). The production process is to produce the

availability of bus service, while the consumption process transfers space-km, average

vehicle speed to final outputs (transit work, OTP). Here, space-km is used as an

intermediate/linked variable of those two nodes (which is an output of node 1 and then

becomes an input of node 2). The detailed definition of all variables is given in the notes

below Table 4-2.

Figure 4-2: The operational framework for a bus route performance evaluation

Ave. vehicle speed

Space-Km

OTP

Transit work

Pro

du

ctio

n p

roce

ss

Co

nsu

mp

tio

n p

roce

ss

Route length

Number of service

Service duration

Service Inputs

(resources)

Service

Consumption

Service

OutputsService effectivenessTechnical efficiency

Operational effectiveness

Busway length

Node 1

Node 2



Table 4-2: Selection of inputs and outputs for bus route performance measurement

Model Performance

dimension

Orientation Returns

to scale

Input variables Output

variables

Node 1

(model 1)

Technical efficiency Output VRS Route length;

Service duration;

Number of services;

Busway length

Space-km

Node 2

(model 2)

Service

effectiveness

Output VRS Space-km;

Average vehicle speed

Transit work;

OTP

Notes:

1- Space-km (p-km): bus vehicle capacity multiplied by total kilometres traversed by

vehicle on the corresponding route and summed for all services that start within a

given hour (see equation 4-1).

2- Service duration (hour): total actual travel time taken by all services on the route

during a given hour.

3- Number of services: total number of services operated on the route in a given hour

for both inbound and outbound directions.

4- Busway length (km): length of Busway (roadways that are accessible by buses

only) used by bus vehicles on the route.

5- Average vehicle speed (km/h): length of route divided by the average travel time

taken by all completed services on the route during a given hour.

6- Priority lane (%): percentage of Busway length to total route length.

7- Stop spacing (km/stop): length of bus route divided by total number of stops on

the route.

8- Signalised intersection spacing (km/intersection): the length of bus route divided

by total number of signalised intersections on the route.

9- Vehicle-km (km): the total number of kilometres travelled by all the vehicles

operating on that route.



10- OTP/ Schedule reliability (%): the proportion of observed services that arrive at

the destination on time, where “on time” is less than 1 min early or less than 5 min

later than the scheduled arrival (Ryus, Danaher et al. 2013).

External Variables (EVs) Selection

External variables (EVs) should be the potential factors that greatly affect the final

outputs (Transit work, OTP), because this model aims to maximise outputs. Miller et al. (2009)

categorised external factors, which can influence the transit ridership among urbanised areas

in the United States (USA), into four divisions: (1) regional geography (area of urbanisation,

population, population density, and regional location); (2) metropolitan economy

(personal/household income, income distribution, and unemployment level); (3) population

characteristics (age distribution, percent of population in college, and percent of population

in poverty); and (4) auto/highway system (congestion level, fuel prices, the precent carless

households, vehicle per capita, and parking availability). For DEA-based transit performance

evaluation, only a few studies used population within the service area of bus systems or

routes to explain the variation of transit ridership (Chu, Fielding et al. 1992, Kerstens 1996,

Tsamboulas 2006, Sheth, Triantis et al. 2007, Barnum, Tandon et al. 2008, Lao and Liu

2009). Therefore, the influences of external factors on the efficiency level of bus routes were

not studied sufficiently.

In this research, EVs are selected, broadly based on the relevant literature and data

availability, comprising of population for ages, car ownership, and individual income. These

EVs are relevant to ridership of bus routes, which is of primary focus. The presented approach

can be repeated with additional EVs related to OTP, if available.

Population (Pop) is clustered into the following four typical groups, which generally

have different patterns of travelling, so the clustering helps to identify the impact of each age

group on transit demand:

• POPC: Pop under 18, which includes children and school students;

• POPYA: Pop from 18 to 35, which includes senior students and young adults)

• POPOA: Pop from 36 to 64, which includes older adults; and

• POPP: Pop 65 and older, which includes pensioners.

The corresponding population density of the above age groups is labelled as follows:

• PODC: average Pop density of age group under 18;

• PODYA: average Pop density of age group from 18 to 35;

• PODOA: average Pop density of age group from 36 to 64; and



• PODP: average Pop density of age group 65 and older.

Regarding the individual income (Pop 15 and older only), this research clusters it into

three major groups, based on the taxable incomes applied to Australian residents for tax

purposes (ATO 2017) and Australia community profile (Profile.id 2017):

• LI: Low income with income under 400 AUD per week;

• MI: Medium income with income between 400 to 1500 AUD per week; and

• HI: High income with income over 1500 AUD per week.

Car ownership (CO) is given by cars per capita, in which Pop 18 and older is taken

into account only because those in that category are eligible to drive a car.

Discussion

AFC data is a rich source of data offering opportunities for insights into the bus route

performance. However, there are still some limitations for mining this data. One of the

drawbacks of AFC data is that if there is no passenger boarding or alighting at a given bus

stop, the boarding or alighting time cannot be recorded leading to the missing information of

bus arrival time at this stop. Therefore, using AFC data to calculate the OTP at intermediate

stops along a bus route may result in different values for different services, although those

services have similar operation in reality. Furthermore, OTP at the destination is of

importance because it can positively impact on the arrival time of a bus at previous stops.

Thus, this research estimates the OTP at the destination (final stop) of bus routes only. In

other words, the value of OTP at the final stop represents the OTP of the whole service.

According to TCQSM (2013), on-time at the intermediate stops means that the arrival

time of a bus is less than 1 minute early and 5 minutes late compared to the scheduled time,

and at the destination on time is less than 5 minutes late only. In other words, the on-time at

the destination accounts for all early services. This research estimates the OTP at the

destination of a bus route only, so it should apply the standard of less than 5 minutes late for

OTP estimation. However, the actual situation in Brisbane is that limited parking space is

available in bus stations for early arrival of buses. This research, thus, adopts less than 1

minute early and 5 minutes late at the destination as on-time.

The framework for bus route performance evaluation was proposed in this chapter

with appropriate inputs and outputs. To run this framework, it needs a process for extracting

bus performance indicators from AFC data, and a suitable method to obtain accurate EVs’

data for a single bus route of the case study in Brisbane. Therefore, Chapter 5 presents the

data collection process, for empirical analysis in Chapters 6 and 7.

Data Collection


5 Data Collection

Introduction

Brisbane, the case study area in this research, is the capital of Queensland, Australia.

The Brisbane Statistical Division has a population of 2.4 million people (around 49% of

Queensland’s population is in Brisbane) (ABS 2016). The transit network in Brisbane

comprises more than 380 km of heavy rail and numerous bus lines, including three

segregated busway lines: South East Busway; Northern Busway; and Eastern Busway (a

total of 25 km of busway was built up to 2011) (Yang and Pojani 2017). Figure 5-1 illustrates

the high frequency bus routes along major corridors in Brisbane. Here, the backbone of the

bus system is composed of two continuous Bus Rapid Transit corridors; the South East

Busway (see spine route 111 for example) and the Inner Northern Busway (see spine route

333 for example). The AFC smart card was used on 86.6 percent of all trips taken across the

TransLink Division transit network during the second quarter (Q2) of the financial year

2016/2017 (TransLink 2017). The case study sample comprises 52 key bus routes in the

South East Queensland (SEQ) bus network, which connect suburban areas with the Brisbane

central business district (CBD).

Regarding internal variables, bus performance indicators are drawn from AFC data

supplied by the TransLink Division of the Queensland Department of Transport and Main

Roads, Australia. AFC data of one week (working days only), from 19th to 23nd August 2013,

is employed for the empirical data analysis in this research. Other relevant data such as route

length, section length between stops, and timetable, were obtained from the TransLink

website (http://translink.com.au). On the other hand, external variables are collected in the

service corridor of each bus route using Geographic Information System (GIS) and database

of the Australia Bureau of Statistics (ABS). Therefore, this chapter introduces the process for

extracting key bus performance indicators from AFC data, and external variables of bus

routes from ABS using GIS.

Section 5.2 presents the process for internal variable collection. The collection of

external variables is represented in section 5.3. Finally, the chapter is concluded in section

5.4, where discussion is presented.

Internal Variables

AFC data from TransLink provides details of individual passenger journeys. This

includes the following fields:

http://translink.com.au/

Data Collection


• Operator, operation date (date corresponding to the bus operation);

• Smart card ID (encrypted at the passenger level);

• Route (bus route used by the passenger);

• Direction (inbound or outbound);

• Schedule start (the schedule start time of corresponding trip);

• Actual start (actual timestamp of bus departing from origin stop);

• Actual end (actual timestamp of bus arriving at terminus stop);

• Boarding and alighting stop (by passenger, IDs of stops used to board and alight);

• Boarding and alighting times (timestamps when passengers touched on when

boarding and touched off when alighting);

• Vehicle ID (encrypted ID of bus vehicle);

• Journey ID (encrypted ID of bus trip); and

• Ticket type (type of smart card used by passengers such as adult, student or

child).

Figure 5-1: Brisbane, Australia high frequency bus network map (Source: http://translink.com.au)


Data Collection


The smart-card data provides information that can be used to reconstruct a vehicle’s

service performed along all consecutive segments composing a transit route during a given

time window (a day or an hour).

Steps implemented to extract needed inputs and outputs are shown in Figure 5-2,

where inputs and outputs are extracted utilising the smart-card data fields:

1. Based on the raw smart-card data, data for a given route and direction (inbound

and outbound) is separated.

2. Based on the working day calendar and month index, data for a given month and

working days only are extracted. Here, working days exclude school holidays.

3. Based on the day index, data for a given working day are extracted. Data for a

given vehicle will then be extracted on the basis of vehicle index.

4. Based on the schedule starting time index, data for each service (revenue trip) of

a given vehicle are extracted.

5. Service data for a given segment of bus route are extracted on the basis of

alighting stop index and boarding stop index. Transit work can then be calculated

for each service based on segment data (see Equation 2-1).

6. Based on the actual starting time (𝑡0 ) and actual ending time (𝑡1 ) index of each

service, the actual travel time (∆𝑡 ) of a given service is calculated: ∆𝑡 = 𝑡1 − 𝑡0 .

Comparing the arrival time of a vehicle at bus stops and destination with

scheduled time yields the OTP indicator.

7. The total number of passengers equals the total number of boarding passengers

or alighting passengers. At each bus stop, smart-card data can provide the first

and last alighting time as well as the first and last boarding time, if there are

passengers boarding and alighting. This is used to determine a proxy dwell time

(Widana Pathiranage, Bunker et al. 2013), and the time that a service arrives at a

given stop.

Data Collection


Figure 5-2: Flowchart for extracting transit route performance indicators

Based on the steps in Figure 5-2, performance indicators of the 52 case study bus

routes with both inbound and outbound directions have been extracted from the raw smart-

card data during a period of one working week, from Monday 19th to Friday 23rd August 2013.

Table 5-1 summarises the statistical description of the inputs and outputs of 52 bus routes

for a morning peak hour (7:00 to 8:00), an afternoon peak hour (16:00 to 17:00), and an off-

peak hour (10:00 to 11:00) for Wednesday 21st August 2013.

Raw Smart-card data

Data for route and

direction

Data for a month and

working days only

Data for a given

working day

Data for a given

vehicle

Data for a given

service of vehicle

Data for a given

segment of route

Transit work of

service

Total passenger

Average dwell

time

On time

performance

Route

Direction

Month

Working calendar

Working calendar

Vehicle Index

Schedule starting time Index

Smart-card ID IndexActual starting time

Actual ending time

Travel time

Alighting stop Index

Boarding stop Index

Alighting time

Boarding time

First and last alighting time

First and last boarding time

Inputs and

outputs extracted

Data Collection


Table 5-1: Statistical description of the inputs and outputs of the 52 bus routes for a morning and an

afternoon peak hour, and an off-peak hour of 21 August 2013

Variables Mean Minimum Maximum Standard deviation

Route length (km) 20.22 9.30 29.46 5.37

Busway length (km) 4.7 0.81 17 3.87

Signalised intersection spacing

(km/intersection)

0.88 0.27 5.67 0.96

Stop spacing (km/stop) 0.64 0.29 1.55 0.33

Lane priority (%) 24.18 4.74 100 21.3

Morning peak hour (7:00 to 8:00)

Service duration (hour) 5.2 1.05 13.43 3.33

Number of services 5.87 1 18 4.08

Space-km 8177.39 1891.12 28383.81 6449.16

Average vehicle speed (km/h) 21.69 14.69 36.09 5.06

OTP (%) 44.42 0 100 31.96

Transit work (p-km) 1808.29 113.49 9668.89 1984.26

Afternoon peak hour (16:00 to 17:00)



Space-km 7982.8 1303.61 31916.36 6556.13


OTP (%) 42.48 0 100 26.99

Transit work (p-km) 1569.59 10.26 8285.18 1956.81

Morning off-peak hour (10:00 to 11:00)



Space-km 6064.07 1170.89 20980.54 4618.95


OTP (%) 40.7 0 100 33.54

Transit work (p-km) 801.18 61.7 4901.13 958.8

External Variables

EVs are collected in the service corridor of a single bus route using GIS and ABS

2011 Census. There are two ways to generate this service corridor:

Data Collection


• Stop buffering (Murray, Davis et al. 1998); and

• Route buffering (Peng and Dueker 1993, Peng and Dueker 1995).

The first one generates the buffer zones around bus stops, while the later creates the

buffer zone along the entire route with a certain access distance. The access distance of 400

metres is normally used because it is widely regarded as the most appropriate walking

distance for bus riders (Horner and Murray 2004, Burke and Brown 2007, Ryus, Danaher et

al. 2013). It is clear that the stop-level buffer is the more appropriate basis for estimating the

service corridor of a given transit route, because stops are the actual points where

passengers access this route (Horner and Murray 2004). Thus, stop buffering will be applied

in this research to generate service corridor of each bus route.

Using GIS tool, the buffer zones around all bus stops of a given route are first

generated by 400 metre radius circles with centres being bus stops. The service corridor of

this bus route then is formed by merging overlapping buffer zones into a single polygon.

Figure 5-3: An example of a bus route service area

Data Collection


Figure 5-3 presents the service corridor of a typical bus route (route 111) of the case

study. Here, the buffer zones of some close stops on the upper part of the map are merged

into a single polygon, so this helps to avoid the double counting of service areas around the

bus stops. The service corridor of a bus route is then overlaid with the census block group

map to determine the intersection between them. In this research, the ABS 2011 Census map

at the Statistical Areas Level 1 (SA1) is used to collect EVs within the service corridor of given

bus routes. The SA1s have generally been designed as the smallest unit for the release of

census data. Each SA1 region has a unique identification (ID).

Based on the boundaries of SA1 regions, the bus service corridor is divided into

several pieces of land (POL) (see Figure 5-4). Each POL belongs to a certain SA1 region

which stores the database of population for ages, individual income for ages, car ownership,

land area, education and employment, etc. Using GIS, a POL inherits the ID and features of

a SA1 region that covers it. Thus, the SA1 data of a given POL can be estimated based on

its area (which is obtained by GIS) and the available data of SA1 region. This is the basis for

the estimation of EVs for the whole service corridor of a bus route. For example, Figure 5-4

shows that POLs 5 and 6 inherit the ID and SA1 data of region 6.

Figure 5-4: An example of pieces of land (POL) within the service corridor of bus route

The population (Pop) variables a of a given route are calculated within its service

corridor using the ABS 2011 (SA1) Census data as follows:

Boundaries of SA1Regions

POL 1

POL 3

POL 2

POL 4 POL 5POL 6

POL 7

POL 8

Region 1

Region 4

Region 2

Region 5

Region 6

Region 3

Region 7

Service corridor

Data Collection


• Identify the area and the SA1 population density for different ages of each POL

within the service corridor of a bus route;

• Estimate the Pop of different age groups (under 18, age 18-35, age 36-64, and

age 65 and over) of each piece within the service corridor based on its area and

corresponding population density; and

• Calculate Pop of different age groups (under 18, age 18-35, age 36-64, and age

65 and over) of a single route by summing Pop values of all POLs within its service

corridor.

From the Pop obtained for each age group, the average Pop density of each age

group can be calculated by the ratio of Pop to the area of service corridor of a bus route (the

sum of areas of all POLs within the service corridor).

For income variables, based on the individual income data in ABS 2011 Census (for

age 15 and over), Pop density for different income levels are identified for each SA1 census

region. This SA1 Pop density then is used to calculate income variables of each bus route as

follows:

• Estimate the Pop of different income levels (low income, medium income, and

high income) of each POL within the service corridor based on its area and

corresponding SA1 Pop density;

• Calculate Pop of different income levels (low income, medium income, and high

income) of a single route by summing Pop values of all POLs within its service

corridor; and

• Calculate the percentage of each income group by the ratio of its Pop to the total

Pop of all income groups.

Finally, car ownership is determined by the ratio of the total number of cars to the Pop

with ages 18 and over in the service corridor of a given route. In this case, the Pop (age 18

and over) is estimated in similar way with the afore-mentioned Pop variable. The total number

of cars is determined as follows:

• Identify the car density of each SA1 census region. Car density of a given SA1

region is calculated based on its area and SA1 car ownership available in the ABS

2011 Census.

• Identify the number of cars within each POL based on its area and the SA1 car

density.

• Calculate the total number of cars of a route by summing the number of cars of all

POLs within the service corridor.

Data Collection


Table 5-2a and Table 5-2b show the statistical description and correlation analysis

results of EVs used for the second stage regression analysis. It is notable that HI and CO

have a negative correlation (the correlation coefficient is -0.25), whilst correlation between MI

and CO is notably strong (which is 0.58). This indicates that within the bus service areas, the

private car seems to be unfavourable to the high-income group, who tend to live near transit

stations and use transit for travelling conveniently.

Table 5-2: a) Statistical description; and b) Correlation analysis results of EVs of 52 bus routes of the case

study in Brisbane, Australia

a) Statistical description of EVs

Variable Mean Minimum Maximum Standard deviation

PODC (person/km2) 389 241 507 55

PODYA (person/km2) 1014 665 1697 243

PODOA (person/km2) 817 553 1214 137

PODP (person/km2) 253 174 330 43

LI (%) 31 25 41 4

MI (%) 42 37 46 2

HI (%) 17 10 24 3

CO (car/capita) 0.59 0.48 0.71 0.05

b) Correlation analysis results of EVs

Variable PODC PODYA PODOA PODP LI MI HI CO

PODC 1.00 PODYA 0.17 1.00 PODOA 0.62 0.82 1.00 PODP 0.45 0.26 0.42 1.00 LI -0.07 -0.60 -0.60 -0.27 1.00 MI 0.33 -0.16 0.15 0.43 -0.36 1.00 HI 0.09 0.64 0.62 0.05 -0.86 -0.04 1.00 CO 0.48 -0.64 -0.17 0.09 0.21 0.58 -0.25 1.00

Bold values present the high correlation between variables

Summary

The flowchart for extracting several key bus performance indicators from AFC data of

the case study in Brisbane, Australia was introduced in this chapter. Then, based on this

process, the inputs and outputs (internal factors) of 52 key bus routes were collected at the

service level (each trip) during five continuous working days of a week (19th to 23rd August

2013). This sample dataset will be employed to estimate efficiency scores of bus routes using

DEA models in the next chapters. By this, temporal and spatial performance of selected bus

routes will be explored.

Data Collection


Applying a stop buffering method for building up the service corridor of a single bus

route and using ABS 2011 Census at SA1, selected EVs were collected sufficiently within the

service areas of each bus route. Here, Pop is categorised into four age groups, and individual

income is clustered into three levels. Those EVs are employed in Chapter 7 for regression

analysis. One of the limitations is that the ABS 2011 Census does not correspond with 2013

AFC data. However, assuming that the changes of those EVs are not significant over the

period of two years from 2011 to 2013, this research employs EVs from ABS 2011 and 2013

AFC data for empirical analysis.

Data Analysis for Individual Bus Route of the Case Study


6 Data Analysis for Individual Bus Route of the Case Study

Introduction

Before comparing the temporal and spatial performance of 52 bus routes in the case

study, exploring the temporal performance of a single route is essential. This helps to verify

the proposed framework and models applied, and to gain more understanding of a single bus

route operation over the time period of a day, and different days of a week without the impact

of external factors on the results obtained. The temporal performance investigation of a single

bus route provides the changes of efficiency score of the corresponding route across the

daytime and over weekdays. The most and the least efficient periods of time of a given route

can be identified. Transit operator may easily further discuss the operating issues leading to

the performance of a given route during the least efficient periods of time.

This chapter, therefore, first examines the temporal performance of bus route 111 (a

busy spine bus route on the South-East Busway corridor) during a working day (19th August

2013), and verifies results by comparing the DEA efficiency scores obtained with the two

transit productiveness indexes introduced in Chapter 3. Here, two basic transit

productiveness indexes are used to present the application of two measures in TCQSM 2013

(load factor and travel time). Then, the temporal performance of individual bus routes of the

sample is investigated and clustered during five continuous working days of a week, from 19th

(Monday) to 23rd (Friday) August 2013.

Section 6.2 represents the data analysis of bus route 111, which includes the

comparison of DEA efficiency scores and two transit productiveness indexes presented in

Chapter 3. Section 6.3 analyses and clusters the temporal performance of individual bus

routes of the sample. Finally, this chapter is concluded in section 6.4, where a summary of

findings is provided.

Data Analysis for Bus Route 111

Bus route 111 is one of the major spine bus routes in Brisbane with high passenger

demand. It connects the south side suburbs between Eight Mile Plains and the Brisbane CBD

(see Figure 6-1) along a continuous Bus Rapid Transit corridor. The date 19th August 2103

is adopted for temporal performance analysis of route 111. There are a total of 11 bus stops

along this route for each direction (inbound or outbound). The inbound direction (toward CBD)

commences at Eight Mile Plains Busway Station and terminates at Roma Street Busway



Station. The total length of the route is 17 km, and the average schedule travel time is 27

minutes.

6.2.1 DEA-based performance evaluation of route 111

To evaluate the temporal performance of one route, the operational effectiveness is

applied for measurement only, because on a single route, DMUs have a similar scale of

service inputs and outputs. Therefore, inputs are Number of services and Total travel time,

and outputs are OTP and Transit work. The performance indicators (OTP, Transit work, and

Total travel time) of route 111 have been extracted for both inbound and outbound directions

from the raw smart-card data of 19th Aug 2013. The operation of route 111 during an hour is

regarded as a DMU in the DEA model. For example, hour 8 includes all services with a start

time from 7:00 to 8:00.

Table 6-1 and Table 6-2 summarise the statistics of the inputs (Number of services

and Total travel time) and outputs (OTP and Transit work) of route 111 for inbound and

outbound direction, respectively. The Hour starts from 6 because there is no bus service from

0:00 to 5:00. In some hours (such as from 22:00 to 24:00 for inbound direction), no services

arrive at the destination on time, so the value of OTP equals 0. In the evening, the arrival time

of bus services at the destination is normally earlier than scheduled time, but more than 1

minute earlier.



Figure 6-1: Bus route 111 map (Source: Google map)

Table 6-1: Statistical description of the inputs and outputs of route 111 for inbound direction


Number of services 4 1 11 2.74

Total travel time (hour) 1.73 0.32 6.52 1.54

Average travel time (hour) 0.43 0.32 0.59 0.06

OTP (%) 25 0 82 22.99

Transit work (p-km) 1193 46 7832 1975



Table 6-2: Statistical description of the inputs and outputs of route 111 for outbound direction


Number of services 4 1 10 2.32

Total travel time (hour) 1.65 0.5 4.87 1.23

Average travel time (hour) 0.41 0.36 0.54 0.05

OTP (%) 33 0 100 25.32

Transit work (p-km) 767 86 5649 1546

Both CRS and VRS-DEA are used for examination. To demonstrate the influence of

variables to the DEA efficiency scores of DMUs, the CRS-DEA efficiency scores are

estimated for three cases, whereby each case has a different combination between input and

output variables. Here, case 1 (with one input and one output) illustrates the direct

relationship between bus capacity and actual bus loading; case 2 considers the influence of

travel time on the efficiency score of DMUs; and case 3 takes travel time as the second input

and the OTP as the second output into account. Case 4 uses the VRS-DEA model with two

inputs and two outputs. Table 6-3 illustrates the inputs and outputs of those four cases.

Table 6-3: Inputs and outputs using for DEA models in cases 1, 2, 3, and 4

Case DEA model Orientation Input variables Output variables

1 CCR (CRS) output Number of service Transit work

2 CCR (CRS) output No of service, Total travel time Transit work

3 CCR (CRS) output No of service, Total travel time Transit work, OTP

4 BCC (VRS) output No of service, Total travel time Transit work, OTP



Inbound direction: The results obtained from the efficiency analysis of the four cases

are expressed in Figure 6-2; here, the score axis illustrates the efficiency scores of DMUs

(hourly operation of bus route). A DMU is efficient if its score equals 1, whereas a lower score

indicates that it is more inefficient. For instance, hour 8 in case 1 is efficient (score equals to

1) and becomes the benchmark for other inefficient DMUs (score < 1), whereas hour 6 with

a score of 0.56 is inefficient against hour 8. It is possible to increase the output of hour 6 by

78.6% (= (1-0.56)/0.56), using the similar inputs.

Figure 6-2: The DEA efficiency score of the case 1, 2, and 3 for inbound direction

In cases 1 and 2, there is only one efficient DMU at hour 8 (from 7:00 to 8:00), which

is a morning peak hour with the highest passenger demand. However, case 2 witnesses a

slight increase of efficiency scores of DMUs during the afternoon time (between 12:00 and

16:00) compared to case 1 because they experience the lower travel time. Case 3 shows a

significant increase of efficiency scores of most DMUs with two efficient DMUs at hours 8 and

10. It also expresses the significant growth of efficiency scores at hours 10 and 22 because

at these two hours the OTP values are notably higher than the average value of the sample

(25%). Those results indicate that OTP significantly influences the DEA efficiency scores,

and the DEA efficiency scores of inefficient DMUs are relative to the best performing DMUs

(hours 8 and 10). Case 4 illustrates the DMUs’ efficiency scores under VRS assumption with

6 efficient DMUs (Hours 7, 8, 9, 10, 23, and 24) and higher efficiency scores for most DMUs

compared to those in case 3. This demonstrates that the VRS model generates higher

efficiency scores than the CRS model.

0

0.2

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0.6

0.8

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

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DEA efficiency score

Efficiency score of case 1 Efficiency score of case 2




Outbound direction: The results obtained from the efficiency analysis of the four

cases are expressed in Figure 6-3. Both case 1 and 2 have one efficient DMU at hour 17

(from 16:00 to 17:00), which drops in the afternoon peak period with the highest passenger

demand. Similar to the inbound direction, case 2 witnesses a slight increase of efficiency

scores of DMUs during the off-peak morning and evening time compared to case 1, due to

lower travel time. Case 3 shows a significant increase of efficiency scores of most DMUs with

two efficient DMUs at hours 6 and 17. Here, hour 6 is efficient because its OTP value obtains

100%. Case 4, including three efficient DMUs at hours 6, 17, and 18, experiences the higher

efficiency scores for all DMUs compared to case 3, especially in the evening.

Figure 6-3: The DEA efficiency score of the case 1, 2, and 3 for outbound direction

Both directions: Figure 6-4 and Figure 6-5 present the efficiency scores of DMUs

under CRS and VRS assumption (with two inputs and two outputs), respectively, for inbound,

outbound, and both directions of route 111. It can be seen that 111 is efficient during the

morning peak period for the inbound direction, and is efficient during the afternoon peak

period for the outbound direction. Those results are appropriate to the variation of actual

travel demand in a day, in that it normally reaches a peak during the morning peak period for

the inbound direction and during the afternoon peak period for the outbound direction.

For both inbound and outbound directions (combined directions), the operation during

the morning and afternoon peak period (hours from 6 to 9, and from 15 to 18) is more efficient

than off-peak periods (hours 10 to 14, and from 19 to 23). It is notable that hour 24 is the

most inefficient DMU under the CRS assumption (efficiency score equals to 0.209) whereas

it is efficient under the VRS assumption (efficiency score equals to 1).

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To clarify the difference between CRS and VRS models, the scale efficiency is

calculated. The scale efficiency is the ratio of efficiency scores of CRS/VRS (Banker, Charnes

et al. 1984). The results of the measures of scale efficiency are depicted in Table 6-4. It can

be seen that of seven efficient DMUs under VRS assumption, only two DMUs (hours 6 and

8) are scale efficient. This illustrates that hours 6 and 8 operate at an appropriate scale of

operations (neither too big nor too small). There are 6 DMUs displaying increasing returns-

to-scale, including hours 7, 13, 14, 20, 23, and 24. The scale of operations of those DMUs is

too small, and needs to expand the operation by possibly increasing the frequency. The

remaining DMUs, on the other hand, exhibit decreasing returns-to-scale, suggesting that its

operations are too large and need to be downsized. The possible way is to reduce the

frequency or travel time.

Figure 6-4: The CRS-DEA efficiency score of the inbound, outbound, and combined directions

Figure 6-5: The VRS-DEA efficiency score of the inbound, outbound, and combined directions

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CRS-DEA efficiency score

Efficiency score for inbound Efficiency score for outbound

Efficiency score for both directions

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Efficiency score for inbound Efficiency score for outbound

Efficiency score for both directions



Table 6-4: Efficiency scores and scale efficiency of route 111 (combined directions)

DMU CRS VRS

Scale

efficiency

Returns to

scale

6 1 1 1 Constant

7 0.841 0.951 0.884 Increasing

8 1 1 1 Constant

9 0.866 1 0.866 Decreasing

10 0.739 0.857 0.862 Decreasing

11 0.573 0.615 0.932 Decreasing

12 0.712 0.809 0.88 Decreasing

13 0.829 0.848 0.978 Increasing

14 0.613 0.697 0.879 Increasing

15 0.894 1 0.894 Decreasing

16 0.871 1 0.871 Decreasing

17 0.891 1 0.891 Decreasing

18 0.798 0.983 0.812 Decreasing

19 0.693 0.755 0.919 Decreasing

20 0.597 0.685 0.871 Increasing

21 0.558 0.681 0.82 Decreasing

22 0.552 0.679 0.812 Decreasing

23 0.197 0.388 0.507 Increasing

24 0.209 1 0.209 Increasing

6.2.2 Comparison between DEA efficiency score and basic transit productiveness

indexes

This section compared the DEA efficiency scores of 111 for inbound direction with

two basic transit productiveness indexes introduced in Chapter 3: transit work load factor;

and passenger transmission efficiency. Figure 6-6 illustrates the results of those two indexes

for inbound direction of 111 on 19th August 2013. Here, maximum schedule load is 85 spaces,

and schedule time to complete a trip is 27 minutes. The correlation coefficient between those

two indexes is significantly high, at 0.979.

Figure 6-7 illustrates the comparison between transit work load factor and DEA

efficiency score in case 1 based on the similar variables used. The correlation coefficient

between those two indexes is 1.00 representing the similar result when using those two

indexes to rank the performance of a bus route. Figure 6-8 illustrates the comparison between

passenger transmission efficiency and DEA efficiency score in case 2 based on the similar



variables used. The correlation coefficient between those two indexes is 0.992. Those results

provide the valid argument to substantiate the usefulness of DEA in measuring the

operational efficiency of DMUs with multiple input and output variables in general and bus

routes in particular.

Figure 6-9 shows the comparison between passenger transmission efficiency and

DEA efficiency score in case 3, in which DEA efficiency score considers OTP as the second

output variable. The correlation coefficient between those two indexes (r= 0.884) is

significantly lower than the result obtained in Figure 6-8. Those results are evident to state

that OTP significantly influences the DEA scores, and DEA provides additional advantages

in that it deals with DMUs consisting of multiple input and output variables.

The comparison between passenger transmission efficiency and VRS-DEA efficiency

score in case 4 (expressed in Figure 6-10) represents a noticeable decrease of the correlation

between those two indexes (r= 0.553). Those results indicate that the CRS-DEA efficiency

score is closer to basic transit productiveness indexes than VRS-DEA efficiency score in

measuring the temporal performance of one bus route for one direction during a working day.

The reason why the DEA efficiency scores in Figure 6-7 and Figure 6-8 are different

from the values of the two transit productiveness indexes is because those indexes compare

the actual work to the ideal work of transit, whereas DEA compares each DMU to the most

productive DMUs (production frontier) in the existing production possibility set. Therefore, the

two basic transit productiveness indexes can only compare the performance of a bus route

for one direction in different time-space windows, or different bus routes with similar features

such as schedule time, fleet size, and the length of route. On the other hand, the DEA

approach provides the opportunity to compare the performance of different bus routes with

different features and multiple variables.

Regarding the above usefulness of the DEA model and the high correlation of CRS-

DEA efficiency scores and transit productiveness indexes, the CRS-DEA model is employed

to analyse the temporal performance of individual bus routes in section 6.3. In transit, due to

capacity constraints (bus station capacity) the output (on time performance, transit work)

might not have a constant increase by increasing the inputs (the size of the bus, service

frequency etc.). Therefore, the return to scale might not always be constant. However, the

next section (6.3) can consider CRS under the assumption that the system is operating below

capacity. For comparing the performance of different bus routes in Chapter 7, it needs to

consider VRS so as to reflect the transit capacity constraint.



Figure 6-6: Transit work load factor and Passenger transmission efficiency of 111

Figure 6-7: Correlation of Transit work load factor and DEA efficiency scores in case 1

Figure 6-8: Correlation of Transit passenger transmission efficiency and DEA efficiency scores

in case 2

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ue

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Transit work efficiency/ Transit work load factor Passenger transmission efficiency

Pearson's correlation coefficient, r = 0.979

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Efficiency score of case 1 Transit work efficiency/ Transit work load factor


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Efficiency score of case 2 Passenger transmission efficiency





in case 3


in case 4

DEA-based Performance Analysis of Individual Routes

Most bus routes of the sample taken from the Brisbane area are located mainly on

the south east and north corridors, with the exception of routes 200 and 222 running along

the east corridor, and route 444 running along the west corridor. Regarding bus frequency,

those routes can be categorised into two clusters: high frequency (the headway for one

direction is equal or less than 15 minutes) and low frequency (the headway for one direction

is over 15 minutes). Across a working day, high frequency bus routes normally serve between

5:00 and 00:00, whereas low frequency bus routes have two patterns of service time period:

short service period (between 6:00 and 20:00); and long service period (between 5:00 and

00:00).

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The framework for fixed-route quality of service (QOS) measures in TCQSM (2013)

indicates that frequency and service span are core measures for transit availability (refer to

Table 2-1). Therefore, bus frequency and service span may influence the ridership and the

efficiency level of bus routes. The results obtained from the empirical analysis of 52 individual

bus routes of the case study also illustrate that there is a significant difference between the

temporal performance of high or low frequency bus routes, and long or short service period.

Hence, in this research, bus routes are categorised into three clusters:

1) High frequency;

2) Low frequency for long service period; and

3) Low frequency for short service period.

In this section, the performance of those three clusters of bus routes is introduced.

Additionally, some patterns of the changes of efficiency scores over different weekdays are

calculated.

6.3.1 High frequency bus routes

The results obtained from CRS-DEA based data analysis of a single bus route across

the time of a working week indicate that efficiency scores of different days follow a similar

pattern during the daytime (by 20:00), while those vary significantly over the evening time.

This demonstrates that each route attracts a stable number of regular passengers during the

daytime, while they have a larger number of irregular passengers during the evening. Regular

passengers are defined as workers and/or students that regularly travel to the same

destination on regular time basis. Irregular passengers are those who are less frequent and

have more irregular travel patterns (Pitstick, Siddall et al. 2006, Krizek and El-Geneidy 2007,

Le Minh Kieu, Bhaskar et al. 2015). Therefore, the travel demand in the evening fluctuating

randomly leads to the variations of efficiency scores during the evening time. For each bus

route, there are variations of efficiency scores on different working days of the week (see

Figure 6-11 for an example) because the actual travel demand changes over daytime and

different working days of the week.

Based on the variations of efficiency scores of each route over the daytime, some

patterns of the operation of bus routes can be reasoned, as follows:

• Pattern 1: efficiency score reaches the highest values (nearly 1) during the

morning and afternoon peak period, and has the lowest values during off-peak

period (from 10am to 1pm). This is the major pattern of the given sample. Bus

routes typically following this pattern are 100, 111, 180, 222, and 333. Figure 6-11

and Figure 6-12, present efficiency scores of routes 100 and 111, respectively.



This pattern possibly represents the travel pattern of people working eight hours

a day, such as officers and students. They travel to the work place during the

morning peak hours and return home during the afternoon peak hours on a similar

bus route.

• Pattern 2: efficiency score reaches the highest values during the afternoon peak

period, while it achieves modest values for the morning peak period. Routes 140

and 150 are examples for this pattern. Figure 6-13 presents efficiency scores of

route 140. This phenomenon can be interpreted as regular passengers mainly use

those bus routes for return trips during the afternoon peak hours. For inbound

trips, they may use other routes or transit modes for travelling, or the time for

inbound trips varies across the morning time.

• Pattern 3: the first service hours reach the highest efficiency scores. For example,

routes 330, 340, 345, and 444. Figure 6-14 presents efficiency scores of route

444. This pattern represents the early travel to work of a large number of

passengers within the service corridor of these bus routes, and the appropriate

bus schedule (bus frequency) for the first service hours.

• Pattern 4: off-peak hours (between 10:00 and 13:00) experience high efficiency

scores. Route 200 is an example for this pattern. The efficiency score of route 200

is illustrated in Figure 6-15. This indicates that travel demand is significantly high

at midday because regular passengers of those routes may work mainly in the

morning or afternoon. This travel behaviour leads to the high travel demand at

midday.

Figure 6-11: CRS-DEA efficiency score of route 100 (follows pattern 1)

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6.3.2 Low frequency bus routes for long service period

The results obtained from empirical analysis of low frequency bus routes indicate that

within the daytime, efficiency scores of a given hour across different days vary significantly

compared to those of high frequency bus routes. For example, the averages of standard

deviations of efficiency scores of routes 333 and 444 during the daytime are 0.051 and 0.048,

respectively, while those of routes 124 and 125 are 0.105 and 0.115, respectively. Efficiency

scores of routes 124 and 125 are presented in Figure 6-16 and Figure 6-17, respectively.

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This can be evidence to state that high frequency bus routes attract a more stable number of

regular passengers daily than low frequency bus routes.

It is notable that some bus routes become efficient during the late evening time

(between 21:00 and 00:00), such as routes 125 and 220. The reason is because there is only

one service per hour (the headway is 60 minutes) during this period of time, so the ridership

increases considerably for each service. Additionally, the low traffic flow rate on the bus

corridor at this time leads to high value of OTP.

Figure 6-16: CRS-DEA efficiency score of route 124


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The changes of efficiency score over the daytime follow the typical patterns given in

the previous section. For example, route 185 follows pattern 1 (see Figure 6-18); route 230

follows pattern 2 (see Figure 6-19); routes 170, 220, and 310 introduce pattern 3 (Figure 6-20

and Figure 6-21 represents efficiency scores of routes 170 and 220, respectively); and route

335 follows pattern 4 (see Figure 6-22). However, there is a new pattern of the changes of

bus route efficiency scores (named pattern 5), which reaches a peak during the morning peak

hours and achieves modest values during the afternoon peak hours. Pattern 5 is illustrated

in efficiency scores of routes 135 and 210. Figure 6-23 shows the efficiency scores of routes

135. Regular passengers mainly use those routes for inbound trips during the morning peak

hours, and then the time for outbound trips varies broadly during the daytime and evening.



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6.3.3 Low frequency bus routes for short service period

The efficiency analysis results for this bus group show that efficiency scores of a given

hour vary significantly across different days. For example, the average of standard deviation

of route 113 is 0.158 (see Figure 6-24). This indicates that the operation of those bus routes

is unstable for different days. Due to low bus frequency (normally only one service per hour),

those bus routes attract a limited number of regular daily passengers.

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On some bus routes, the efficiency scores over the daytime follow the pattern (named

pattern 6) in that it reaches the highest value for starting and ending hours of the service

period, while it experiences modest values for the remaining hours. Routes 115 and 116

follow this pattern. The efficiency scores of route 115 is expressed in Figure 6-25.


Over the daytime, the changes of efficiency scores of some routes follow pattern 2

(such as route 184), pattern 3 (such as routes 192 and 202), and pattern 5 (such as routes

155 and 203). The efficiency scores of routes 192 and 155 are illustrated in Figure 6-26 and

Error! Reference source not found., respectively.

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From the temporal performance evaluation of individual bus routes within the sample,

six patterns of the changes of efficiency scores across the daytime were figured out. Table

6-5 introduces these six patterns along with their features and several bus routes following

each pattern. The efficiency scores of other bus routes within the given sample are presented

in Appendix A.

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Table 6-5: Typical patterns describing the changes of efficiency scores of bus routes during a day

Pattern Features Typical bus routes

Pattern 1 Efficiency score reaches the highest values (nearly

1) during the morning and afternoon peak period,

and the lowest values during off-peak period

(between 10:00 and 13:00)

1Routes 100, 111, 180,

222, and 333;

2Routes 185 and 370

Pattern 2 Efficiency score reaches the highest values during

the afternoon peak period, while it has modest values

for the morning peak period.

1Routes 140 and 150;

2Route 230

3Routes 184

Pattern 3 The first service hours reach the highest efficiency

scores.

1Routes 330, 340, 345,

and 444;

2Routes 170, 220, and

310;

3Routes 192 and 202

Pattern 4 Off-peak hours (between 10:00 and 13:00) achieve

high efficiency scores.

1Route 200;

2Route 335

Pattern 5 Efficiency score reaches a peak during the morning

peak hours and achieves modest values during the

afternoon peak hours.

2Routes 135, 212, 210,

and 325;

3Routes 155, 203, 321,

and 334

Pattern 6 Efficiency score reaches the highest values for

starting and ending hours of the service period.

3Routes 115, 116, and

353

1, 2, 3 are three clusters of bus routes

Summary of Findings

The temporal performance analysis of bus route 111 has indicated that bus route

performance becomes efficient during the morning peak hours for the inbound direction and

becomes efficient during the afternoon peak hours for the outbound direction. For the

combined directions, bus performance during peak hours is more efficient than that during

off-peak hours. It has also confirmed that DEA provides additional advantages in dealing with

DMUs consisting of multiple input and output variables. In measuring the temporal

performance of a bus route for one direction, CRS-DEA efficiency score is closer to basic

transit productiveness indexes than VRS-DEA efficiency score.



Applying the DEA model under the CRS assumption for analysing the temporal

performance of a single bus route over the five continuous working days helps to characterise

the performance of each route. Bus routes are categorised into three clusters: (1) high

frequency; (2) low frequency for a long service period; and (3) low frequency for a short

service period. Within the daytime, cluster 1 shows that efficiency score of a given hour

remains constant over different weekdays, whereas clusters 2 and 3 experience significant

variations in efficiency scores of DMUs across different weekdays. Those results

demonstrate that bus frequency possibly affects the service consumption of each bus

route. Here, high frequency bus routes may attract a more consistent number of regular

passengers daily, so their operations remain stable during a week.

The changes of efficiency scores of each route across the daytime differentiate, so

six different patterns of bus routes operation were figured out. Pattern 1 is popular for most

bus routes in cluster 1 and 2. Pattern 5 only appears in cluster 2 and 3. Regarding the

operation of bus routes during the evening (after 20:00), efficiency scores change significantly

among different hours and days, suggesting that there are greater numbers of irregular

passengers who use bus services during the evening time.

The performance during peak periods typically presents the peak performance of a

bus route and could be used for comparing the performance of different bus routes. However,

for testing the sensitivity of external factors to efficiency scores of bus routes, bus

performance of a working day should be used to provide more appropriate results.

Empirical Analysis for Bus System in the Case Study


7 Empirical Analysis for Bus System in the Case Study

Introduction

This chapter aims to examine the temporal and spatial performance of 52 key bus

routes of the case study, and to identify underlying reasons leading to the poor performance

of some bus routes.

To investigate the internal sources of inefficiency of those bus routes, empirical

analysis is conducted separately for node 1 and 2 in the proposed framework in Chapter 4.

This allows one to identify sources of inefficiency related to different performance concepts:

(1) technical efficiency for service production process; and (2) service effectiveness for

service consumption process. Here, empirical analysis for nodes 1 and 2 are termed as model

1 and model 2, respectively. Network DEA is employed to generate an overall efficiency score

of each DMU, accounting for both nodes 1 and 2.

To identify the external sources of inefficiency of those bus routes, the sensitivity

analysis is conducted for node 2 using the double bootstrap model presented in Chapter 3.

Here, efficiency scores obtained from model 2 are dependent variables, while EVs are

independent variables. Results obtained are useful for policy makers to improve the operating

environment of inefficient routes.

Section 7.2 presents the empirical analysis of nodes 1 and 2 for three typical hours (a

morning and an afternoon peak hour, and an off-peak hour) using the VRS model. Section

7.3 analyses the performance of bus routes for three typical hours using the NDEA model.

Section 7.4 represents the empirical analysis of bus routes at three scales of time: every hour;

different periods of time within a day; and on a daily basis. Based on the obtained results, the

ranking of bus routes is also provided in this section. The sensitivity analysis of model 2

efficiency scores to EVs are given in section 7.5. This chapter concludes in section 7.6 with

a summary of findings.

Efficiency Analysis of Key Bus Routes for Separate Node

The technical efficiency and service effectiveness of 52 bus routes of the case study

are estimated based on maximising the outputs. The output-oriented VRS-DEA model is

adopted to calculate the efficiency scores of DMUs for two nodes (two models) expressed in

Table 4-2. A DMU, as mentioned in Chapter 4, is the performance of each bus route during

a given hour (all bus services of the corresponding route with start time falling in an hour for

both inbound and outbound directions). Three typical hours are selected in this section to



compare the performance of those routes to explore the influences of internal variables on

the efficiency level of DMUs, including:

• A morning peak hour (7:00 to 8:00);

• An afternoon peak hour (16:00 to 17:00); and

• An off-peak hour (10:00 to 11:00).

Table 7-1 presents the summary statistics of the results obtained from two nodes

across the three given hours. A DMU is efficient if its score equals to 1, whereas a lower

score indicates that it is inefficient compared to the one with higher score. It could be noted

that the mean efficiency score in model 1 is remarkably high over the three hours (score >

0.85) and the minimum score is greater than 0.6, suggesting that all bus routes considered

have fairly good performance in terms of technical efficiency. However, model 2 witnesses

wide dispersion of efficiency scores because some bus routes have an efficiency score lower

than 0.5. Of the three given hours, the afternoon peak hour in both model 1 and model 2

experiences the higher standard deviation of efficiency scores, which reflects the wide spread

of efficiency scores during the afternoon peak hour compared to other hours.

Table 7-1: The summary statistics of efficiency scores obtained through DEA for models 1 and 2

Model Time Mean Minimum Maximum Standard

deviation

Model 1 Morning peak hour 0.881 0.694 1 0.111

Off-peak hour 0.877 0.633 1 0.12

Afternoon peak hour 0.869 0.629 1 0.127

Model 2 Morning peak hour 0.746 0.218 1 0.227

Off-peak hour 0.585 0.074 1 0.249

Afternoon peak hour 0.669 0.059 1 0.261

The results obtained from the efficiency analysis of the aforementioned models for

three given hours are presented in Figure 7-1 and Figure 7-2, respectively. The score axis

illustrates the efficiency scores of DMUs. For the VRS model, some efficient DMUs in the

given sample become benchmarks for some inefficient DMUs that have similar input and

output characteristics compared with those efficient DMUs. For instance, considering route

175 in model 1 for the morning peak hour, its score of 0.73 indicates that it is possible to

increase the outputs by 37% (=1−0.73

0.73) using similar inputs. Its benchmarks are routes 130

(𝜆130 = 0.145), 321 (𝜆321 = 0.405), 334 (𝜆334 = 0.361), and 444 (𝜆444 = 0.088). Here, 𝜆𝑖 is the

weight for 𝐷𝑀𝑈𝑖. The combination of 14.5%, 40.5%, 36.1%, and 8.8% inputs and outputs of



routes 130, 321, 334, and 444, respectively, can build up the virtual DMU of route 175, which

locates on the production frontier. The input and output values needed to bring route 175 into

efficient status can be expressed as:

(Input of 175) = 0.145 x (Input of 130) + 0.405 x (Input of 321) + 0.361 x (Input of 334)

+ 0.088 x (Input of 444); and Equation 7-1

1.37 x (Output of 175) = 0.145 x (Output of 130) + 0.405 x (Output of 321) + 0.361 x

(Output of 334) + 0.088 x (Output of 444). Equation 7-2

a) The VRS-DEA efficiency score of the first 26 routes (model 1)

b) The VRS-DEA efficiency score of the last 26 routes (model 1)

Figure 7-1: The VRS-DEA efficiency score of bus routes in model 1

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a) The VRS-DEA efficiency score of the first 26 routes (model 2)

b) The VRS-DEA efficiency score of the last 26 routes (model 2)

Figure 7-2: The VRS-DEA efficiency score of bus routes in model 2

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Table 7-2: Inputs and outputs of a) route 175 and its benchmarks in model 1; and b) route 220 and its

benchmarks in model 2 during the morning peak hour

a) Inputs and outputs of route 175 and its benchmarks in model 1

DMUs Inputs Outputs

No of services

Route length (km)

Service duration (hour)

Busway length (km)

Space-km

(p-km)

Route 175 5 16.87 4.93 2.93 5622

Route 130 15 27 12.83 11.46 31195

Route 321 3 13.20 2.25 1.42 2334

Route 334 2 14.37 1.83 1.42 1781

Route 444 10 27.20 12.68 2.04 17736

b) Inputs and outputs of route 220 and its benchmarks in model 2

DMUs Inputs Outputs Other variables

Space-km

(p-km)

Average vehicle speed (km/h)

Transit work

(p-km)

OTP (%) No of services

Lane priority (%)

Stops

Route 220 1732 27 113 0 1 11 38

Route 115 1675 22 454 100 1 11 36

Route 334 1781 16 578 50 2 32 48

Model 1: Figure 7-1 illustrating the results from model 1 shows that among the three

given hours there are 10 efficient DMUs (routes 111, 130, 150, 161, 192, 200, 202, 220, 321,

and 325), while routes 124, 170, 174, 175, and 230 typically have the lowest efficiency scores

(lower than 0.85). A comparative analysis of characteristics of the best and the worst

performance routes can help to explain why some routes are efficient whereas others are

inefficient. For instance, comparing route 175 and its benchmarks (routes 130, 321, 334, 444)

for the morning peak hour (see Table 7-2a), route 321 is efficient compared to 175 because

of its moderate use of busway length (only 1.42 km for route 321 compared to 2.93 km for

route 175) to produce output.

For the morning peak hour, Table 7-3 illustrates that the slacks (input slack is the

amount of input that one DMU could reduce to produce the similar output) mostly occur for

service duration. Thus, reducing the service duration can be one of the possible solutions to



improve performance of inefficient routes. For instance, route 185 and 204 can reduce by

1.38 and 1.45 hours, respectively.

Table 7-3: Slacks for inefficient routes in model 1 during the morning peak hour

DMU

Efficiency

score

Route

length

Service

duration Services

Priority

lane

Space-

km

Route 105 0.865 0 0 0 0 0 Route 110 0.798 0 0 0 0 0

Route 112 0.699 0 -0.23 0 0 0

Route 113 0.864 0 -0.535 0 0 0

Route 116 0.754 0 -0.756 0 0 0

Route 120 0.831 0 -0.59 0 0 0

Route 124 0.726 0 -0.536 0 0 0

Route 125 0.807 0 -0.176 0 0 0

Route 135 0.822 -0.42 0 0 -6.51 0

Route 155 0.855 -0.8 -0.028 0 -5.02 0

Route 170 0.705 0 0 0 -1.8 0

Route 172 0.744 0 -0.001 0 0 0

Route 174 0.742 0 -1.304 0 0 0

Route 175 0.731 0 -0.375 0 0 0

Route 180 0.797 0 -0.413 0 0 0

Route 184 0.758 0 -0.691 0 0 0

Route 185 0.793 0 -1.389 0 0 0

Route 203 0.918 0 0 0 0 0

Route 204 0.873 0 -1.452 0 0 0

Route 210 0.722 0 -0.142 0 -0.51 0

Route 215 0.784 0 0 0 0 0

Route 222 0.77 0 -0.198 0 0 0

Route 230 0.765 0 -1.144 0 0 0

Route 235 0.823 0 -0.389 0 -0.89 0

Route 310 0.815 0 -0.091 0 -1.67 0

Route 325 0.882 0 -0.086 0 0 0

Route 330 0.874 0 0 0 0 0

Route 333 0.694 0 0 0 -2.27 0

Route 340 0.751 0 0 0 0 0

Route 345 0.888 0 -0.859 0 0 0

Route 346 0.981 -2.92 0 0 0 0

Route 353 0.968 -1.17 -0.294 0 0 0

Model 2: Figure 7-2 illustrates the results obtained from model 2 showing that the

effectiveness scores of DMUs vary significantly among routes and hours. Routes 111, 130,

345 and 370 are the most effective DMUs whereas routes 105, 113, 124, 155, 200, 220, and

310 have the poorest performance (scores are lower than 0.5) across the three hours. It can



also be seen that route 115 and 155 have very low scores for the afternoon peak hour (0.07

and 0.01 respectively) because each has a very small value of transit work.

Considering route 220 for the morning peak hour, which typically has the lowest

effectiveness of the three hours, this route (score of 0.218) is able to increase the outputs by

358.7% using the similar inputs. The benchmarks for route 220 are routes 115 (𝝀𝟏𝟏𝟓 = 𝟎. 𝟒𝟔𝟖)

and 334 (𝝀𝟑𝟑𝟒 = 𝟎. 𝟓𝟑𝟐). The corresponding inputs and outputs of route 220 and its

benchmarks are depicted in Table 7-2b. It is useful to compare route 220 and route 115,

which have similar inputs: the former is inefficient because its outputs are remarkably low

(accounting for 113 and 0 of transit work and OTP, respectively).

In this model, the slacks mainly occur for space-km and OTP. Therefore, reducing

space-km and increasing OTP of inefficient routes may help to improve the performance of

inefficient routes. Table 7-4 presents the slacks of inputs and outputs during the morning

peak hour. Here, route 150 can reduce 6,242 units of space-km and increase 8.45 units of

OTP. The decrease of space-km can be achieved by reducing the capacity of dispatched

vehicles or shortening route length. However, it is not always feasible to modify such variables

because this action may have adverse impacts on broader quality of service objectives

including span of service, and connection to suburban areas. Transit agencies may consider

analysing onboard passenger loading of low performance routes with respect to frequencies

and bus models applied.



Table 7-4: Slacks for some inefficient routes in model 2 during the morning peak hour

DMU Efficiency

score Space-km

Average

vehicle Speed

Transit

work OTP

Route 100 0.913 -1935 0 0 0 Route 105 0.5 -1414 -2.9 13.62 0 Route 110 0.843 -1290 0 0 0 Route 112 0.54 -729 0 132.43 0 Route 113 0.389 0 0 0 33.47 Route 120 0.961 -4311 0 0 0 Route 124 0.452 0 0 0 0 Route 125 0.439 0 -1.2 0 40.54 Route 130 0.935 -7921 0 0 9.44 Route 140 0.389 0 0 0 40.17 Route 150 0.88 -6202 0 0 8.45 Route 155 0.522 0 -1.8 0 0 Route 160 0.617 -2846 -5.3 0 0 Route 170 0.681 0 -1.5 0 0 Route 172 0.77 -919 0 37.71 0 Route 174 0.526 0 0 0 0 Route 175 0.502 0 0 0 0 Route 180 0.868 0 0 0 0 Route 184 0.586 -880 0 0 0 Route 185 0.64 0 0 0 42.1 Route 192 0.277 0 0 0 0 Route 200 0.454 0 0 0 0 Route 202 0.554 0 0 121.88 0 Route 203 0.699 0 0 0 0 Route 204 0.778 -1975 0 0 17 Route 210 0.48 0 0 0 3.13 Route 212 0.788 0 0 0 49.14 Route 215 0.5 -836 0 192.52 0 Route 220 0.218 0 -8.1 0 73.41 Route 235 0.907 0 0 0 0 Route 310 0.609 0 0 0 0 Route 325 0.743 0 -3.8 0 46.19 Route 340 0.668 0 0 0 0 Route 346 0.667 -2040 -1.3 0 0 Route 353 0.835 -567 0 0 0 Route 359 0.895 0 -4.2 0 44.31 Route 370 0.886 0 0 0 0 Route 390 0.993 0 0 0 22.62

For this reason, attracting more ridership and enhancing schedule reliability are

possible ways for performance improvement of inefficient bus routes. To increase ridership,

the external and environmental factors of the best and the worst DMUs need to be further

investigated, with comparative analysis between them to identify the source of inefficiency.

For instance, route 220 connects Wynnum (a coastal suburb in Brisbane’s east) to the CBD

whilst route 115 connects Calamvale (southern suburb of Brisbane) to the CBD. Wynnum



has lower population density with high proportion of retirees, while Calamvale and

intermediate areas crossed by route 115 have higher population density with ages between

15 and 65 dominant (ABS, June 2014). Further, more shopping centres and schools located

in the south of Brisbane possibly contribute to the higher ridership of 115.

This empirical analysis indicates the actual performance of 52 bus routes of the case

study in Brisbane, Australia, suggesting the following messages for the operator: (1) it should

be useful to reduce service duration of some inefficient routes in model 1 (see Table 7-3),

and (2) there is a great need to investigate the influences of external factors on the efficiency

scores of inefficient routes in model 2, especially geographic information, and then to adjust

the current bus schedule to meet the actual demand of residents within the service areas of

each route.

Efficiency Analysis of Key Bus Routes Using Network model

The network technology of bus routes performance is illustrated in Figure 7-3,

including two linked sub-technologies (nodes 1 and 2). Node 1 represents the production

process, while node 2 presents the consumption process of bus routes. Node 1 and node 2

are linked by an intermediate variable, which is output of node 1 and input of node 2. Here,

space-km is used as an intermediate variable. Input 1 presents inputs of node 1, including

route length, service duration, number of services, and busway length. Output 2 introduces

outputs of node 2, including Transit work and OTP. Node 2 uses its own inputs (named as

input 2) and intermediate variables to produce its outputs (output 2). Here, Inputs of node 2

include space-km (an intermediate variable) and average vehicle speed (its own input).

In the network model, the intermediate inputs/outputs are called link flows. Let the link

leading from node 𝑘 to node ℎ be denoted by (𝑘, ℎ), and the number of items in link (𝑘, ℎ) by

𝑡(𝑘,ℎ). The intermediate inputs/outputs from node 𝑘 to node ℎ: {𝑧𝑗(𝑘,ℎ)

∈ 𝑅+

𝑡(𝑘,ℎ)} (𝑗 = 1, … , 𝑛),

where 𝑛 is the number of DMUs in the production possibility set. As regard to the link flow

constraints, two possible cases are proposed (Tone and Tsutsui 2009):

• Discretionary link flow constraints: the flow between nodes is determined freely

while keeping continuity between input and output (the link values may increase

or decrease in the optimal solution of the linear programming formulation).

𝒁(𝒌,𝒉) 𝝀𝒉 = 𝒁(𝒌,𝒉) 𝝀𝒌, (∀(𝒌, 𝒉)) Equation 7-3

• Non-discretionary link flow constraints: the flow between nodes is kept unchanged

(the link values are fixed).

http://www.abs.gov.au/AUSSTATS/[email protected]/Latestproducts/3235.0Main%20Features252014?opendocument&tabname=Summary&prodno=3235.0&issue=2014&num=&view=



𝑧0(𝑘,ℎ) = 𝑍(𝑘,ℎ) 𝜆ℎ, (∀(𝑘, ℎ))

𝒛𝟎(𝒌,𝒉) = 𝒁(𝒌,𝒉) 𝝀𝒌, (∀(𝒌, 𝒉)) Equation 7-4

This research uses the discretionary case for empirical analysis because it does not

restrict the flow between nodes. The sample of 52 bus routes used in the previous section is

employed for empirical analysis in this section. The morning peak hour (7am to 8am) is opted

for empirical data analysis in this section only. In order to present the work of the NDEA

model, network efficiency scores are compared with the efficiency scores of each node (1

and 2) obtained in the section 7.2.

Figure 7-3: The network technology of bus route performance

Figure 7-4 illustrates the efficiency scores of the network model, and efficiency scores of node

1 (model 1) and node 2 (model 2) for the morning peak hour (7:00 to 8:00) on 21st Sep 2013.

Results from network efficiency analysis show that there are 11 efficient DMUs, including

routes 111, 115, 116, 135, 222, 230, 321, 334, 335, 345, and 444, and that the most inefficient

DMUs (scores ≤ 0.4) are routes 113, 125, 140, 192, and 220.

Production process

Consumption process

(technical efficiency measure)Node 1

Node 2

Input 1

Output 2

Intermediate variable

(output 1/input 2)Input 2

(service effectiveness measure)



a) The efficiency score of the first 26 routes

a) The efficiency score of the last 26 routes

Figure 7-4: DEA efficiency scores of network and separate nodes (the morning peak hour)

Results obtained from correlation analysis between efficiency scores of network and

nodes 1 and 2 for the morning peak hour indicate that efficiency scores of the network and

those of node 2 represent a strong correlation (correlation coefficient equals to 0.98), whereas

the correlation between efficiency scores of node 1 and those of the network is positively

weak (correlation coefficient is 0.25). This indicates that node 2 is the most important node

in the proposed network framework. The value of the node 2 efficiency score greatly

influences the network efficiency score of DMUs.

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Table 7-5 and Table 7-6 show the input and output slacks, respectively, of the most

inefficient routes in the network model for morning peak hour. Results in Table 7-5 indicate

that the slacks mostly occur for service duration and lane priority, suggesting similar results

obtained from efficiency analysis for separate nodes in the previous section. Those inefficient

DMUs can be improved by reducing the service duration and Busway length. Table 7-6

illustrates that slacks mainly occur for OTP, which coincides with the results obtained from

data analysis of separate nodes (models 1 and 2). Increasing OTP can be a solution for

efficiency improvement of those inefficient DMUs.

Table 7-5: Input slacks for the most inefficient routes in the NDEA model during the morning peak hour

DMU Efficiency

score

Number of

services

Route

length

Service

duration

Busway

length

Space-

km

Ave. vehicle

speed

Route 220 0.218 0 0 0 0 0 -8.15

Route 192 0.277 0 0 0 0 0 0

Route 113 0.35 0 0 -0.535 0 411 0

Route 125 0.352 0 0 -0.176 0 1131 0

Route 140 0.389 0 0 0 0 0 0

Route 124 0.406 0 0 -0.886 0 1715 0

Route 210 0.438 0 0 -0.142 -0.51 1421 0

Route 175 0.448 0 0 -0.676 0 1709 0

Route 200 0.454 0 0 0 0 0 0

Route 174 0.473 0 0 -1.053 0 1384 0

Route 170 0.494 0 0 0 -1.80 2138 -0.57

Route 105 0.5 0 0 -0.026 -2.97 257 -3.65

Route 155 0.5 0 -1.277 0 -5.15 435 -0.8

Table 7-6: Output slacks for the most inefficient routes in the NDEA model during the morning peak

hour

DMU Efficiency score Transit work OTP (%)

Route 220 0.218 0 73.41

Route 192 0.277 0 0

Route 113 0.35 0 25.45

Route 125 0.352 0 43.21

Route 140 0.389 0 40.17

Route 124 0.406 0 0

Route 210 0.438 0 0

Route 175 0.448 0 0

Route 200 0.454 0 0

Route 174 0.473 0 0

Route 170 0.494 0 0

Route 105 0.5 161.23 0

Route 155 0.5 0 0



To highlight the usefulness of this network DEA model, an aggregate model is applied

for empirical analysis of this sample, and then the results obtained are compared with network

DEA efficiency scores of DMUs. The aggregate model (termed as operational effectiveness),

used broadly by preceding studies, represents the direct relationship between service inputs

and service consumption, but neglects the role of service outputs (space-km and Average

vehicle speed). Here, for the aggregate model, inputs are number of services, route length,

Busway length, and service duration, and outputs are transit work and OTP. Figure 7-5

presents the efficiency scores of the network model and aggregate model. The correlation

coefficient between efficiency scores obtained from those two models (r= 0.623) is not high,

suggesting that results of the network model are significantly different from those of the

aggregate model. The reason is because the network model accounts for the performance of

linked sub-processes within the overall production process in its optimal solution.

Routes 100 and 353 are good examples for the comparison of those two models. In

the aggregate model, routes 100 and 353 are efficient (the efficiency score equals to 1),

whereas in the network model those routes are inefficient (efficiency scores of routes 100

and 353 are 0.91 and 0.84, respectively). This means that those routes convert inputs into

outputs optimally in the aggregate model, but do not in the network model.

Table 7-7 shows the results obtained from the efficiency analysis of those routes for

the network DEA model. Here, original outputs present the actual values of output variables,

and projection of an output illustrates its optimal value in the DEA corresponding to the

projected point of this DMU on the production frontier. Proportionate movement presents the

difference between original and projected value of an output. The results indicate that routes

100 and 353 should increase 481 and 125 units of transit work, respectively, and increase 4

and 13 units of OTP, respectively, for efficiency improvement. Furthermore, input slacks also

indicate that those routes can reduce inputs for performance improvement. For instance,

routes 100 and 353 are able to reduce 1.12 and 0.18 units of service duration or reduce 1935

and 567 units of space-km, respectively. In the aggregate model, routes 100 and 353 are

efficient, so there is no need to increase outputs or reduce inputs of those routes. From this

investigation, it can be seen that the network model is more comprehensive than the

aggregate model for bus route performance evaluation, because it takes all linked nodes and

intermediate/linked variables in the network technology into account.



Table 7-7: Efficiency analysis of routes 100 and 353 for the morning peak hour using the NDEA model

a) Statistics of inputs

DMU

Efficiency

score

Slack

movement of

route length

(km)

Slack

movement of

service duration

(hour)

Slack movement

of number of

services

(service)

Slack

movement of

space-km

(space-km)

Route 100 0.91 -0.909 -1.115 -0.972 -1935.21

Route 353 0.84 -3.655 -0.897 -0.184 -566.91

b) Statistics of outputs

DMU

Original

transit

work

Proportionate

movement of

transit work

Projection

of transit

work

Original

OTP

(%)

Proportionate

movement of

OTP (%)

Projection

of OTP (%)

Route 100 5034.13 481.35 5515.48 40 3.83 43.83

Route 353 635.34 125.17 760.51 66.67 13.13 79.80



a) The efficiency score of the first 26 routes

b) The efficiency score of the last 26 routes

Figure 7-5: Efficiency score of the network and aggregate model (the morning peak hour)

Ranking the Performance of 52 Bus Routes

This section employs the proposed approach for empirical analysis of 52 bus routes

of the case study of Brisbane to provide insights into the temporal and spatial performance

of those routes. Based on the efficiency scores obtained, bus routes are ranked to identify

the benchmarks and the least efficient routes within the sample. The date of 21st August 2013

(Wednesday), which is a working day, is opted for empirical analysis.

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Network model Aggregate model

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7.4.1 Technical efficiency measure for bus routes (Model 1)

This section employs model 1 (refer to section 7.2) for empirical analysis of the sample

for different time windows (an hour, peak or off-peak periods, and a day). Model 1 separately

uses an output-oriented VRS model for empirical analysis of node 1.

Table 7-8 and Table 7-9 illustrate the efficiency scores of those bus routes hourly,

from hour 7 (between 6:00 and 7:00) to hour 19 (between 18:00 and 19:00). Blank cells mean

that the data for these cells are unavailable. Based on these results, one can rank the

performance of those routes at the hourly level.

Table 7-10 shows the efficiency scores of those bus routes for key periods of time

within a working day, including:

• Morning peak period (from 5:00 to 9:00);

• Off-peak period (from 9:00 to 15:00);

• Afternoon peak period (from 15:00 to 21:00); and

• Evening period (from 21:00 to 00:00)

Based on the results in Table 7-10, one can rank the performance of those bus routes

for different key periods of time across a working day.




NO DMU Hour 7 Hour 8 Hour 9 Hour 10 Hour 11 Hour 12 Hour 13

1 Route 100 1 1 0.99 0.937 0.972 0.967 0.993 2 Route 105 1 0.865 0.794 0.831 0.789 0.886 1 3 Route 110 0.912 0.798 0.81 0.845 0.797 0.836 0.854 4 Route 111 1 1 1 1 1 1 1 5 Route 112 0.646 0.699 1 1 0.732 0.704 0.89 6 Route 113 0.727 0.864 0.808 1 0.711 0.923 7 Route 115 1 1 0.867 0.978 0.983 0.788 0.901 8 Route 116 0.695 0.754 0.824 1 1 0.697 0.886 9 Route 120 0.855 0.831 0.811 0.803 0.875 0.882 0.945

10 Route 124 0.979 0.726 0.691 0.78 0.714 0.885 0.816 11 Route 125 0.865 0.807 0.828 0.928 0.844 0.847 0.847 12 Route 130 1 1 1 0.969 1 1 1 13 Route 135 0.842 0.822 0.809 0.858 0.85 0.823 0.885 14 Route 140 0.929 1 0.99 0.884 0.898 0.946 1 15 Route 150 1 1 1 1 1 1 1 16 Route 155 0.855 0.817 1 0.851 0.822 0.971 17 Route 160 1 1 1 1 0.918 1 1 18 Route 161 1 1 1 1 1 1 19 Route 170 0.79 0.705 0.678 0.979 0.633 0.708 0.711 20 Route 172 0.737 0.744 0.699 0.737 0.73 0.684 0.82 21 Route 174 0.695 0.742 0.717 0.728 0.719 0.74 0.839 22 Route 175 0.738 0.731 0.655 0.708 0.7 0.731 0.802 23 Route 180 0.926 0.797 0.798 0.836 0.758 0.911 0.837 24 Route 184 0.758 0.758 0.728 0.755 0.754 0.703 0.829 25 Route 185 0.811 0.793 0.798 0.836 0.786 0.911 0.829 26 Route 192 1 1 1 1 1 1 1 27 Route 200 0.899 1 1 1 0.986 0.963 0.982 28 Route 202 1 1 1 1 1 1 1 29 Route 203 0.652 0.918 0.657 0.717 0.688 0.607 0.858 30 Route 204 0.825 0.873 0.98 0.928 0.993 0.979 1 31 Route 210 0.975 0.722 0.81 0.871 0.734 0.778 0.781 32 Route 212 0.851 1 0.739 1 0.878 0.656 1 33 Route 215 1 0.784 0.77 0.828 0.779 0.802 0.832 34 Route 220 1 1 1 1 1 0.864 0.928 35 Route 222 1 0.77 0.808 1 1 1 1 36 Route 230 0.57 0.765 0.699 0.694 0.668 0.67 0.737 37 Route 235 0.664 0.823 0.812 0.732 0.721 0.693 0.77 38 Route 310 0.873 0.815 0.808 0.846 0.956 0.774 0.893 39 Route 321 0.909 1 1 0.994 0.997 1 1 40 Route 325 0.875 0.882 0.923 0.898 0.898 0.855 0.876 41 Route 330 0.853 0.874 0.851 0.818 0.839 0.886 0.921 42 Route 333 0.953 0.694 0.697 0.882 0.911 0.838 0.827 43 Route 334 1 1 1 1 1 0.839 0.999 44 Route 335 1 1 1 1 1 1 1 45 Route 340 0.784 0.751 0.705 0.671 0.696 0.727 0.843 46 Route 345 1 0.888 0.897 1 1 0.941 1 47 Route 346 1 0.981 1 1 0.967 1 1 48 Route 353 0.954 0.968 1 1 1 1 1 49 Route 359 0.922 1 1 1 0.907 1 1 50 Route 370 1 1 1 1 1 1 1 51 Route 390 0.71 1 1 0.962 0.993 0.95 1 52 Route 444 1 1 1 1 1 1 1




NO DMU Hour 14 Hour 15 Hour 16 Hour 17 Hour 18 Hour 19

1 Route 100 1 0.967 1 1 1 1 2 Route 105 1 0.789 0.787 1 0.98 1 3 Route 110 0.824 0.822 0.766 0.834 0.88 0.858 4 Route 111 1 1 1 1 1 1 5 Route 112 0.754 0.971 0.925 0.649 0.756 0.942 6 Route 113 0.737 0.899 0.811 0.723 0.738 7 Route 115 0.941 0.903 0.97 0.946 1 1 8 Route 116 0.697 0.941 0.734 0.701 0.67 1 9 Route 120 0.917 0.88 0.756 0.793 0.794 0.884

10 Route 124 0.726 0.881 0.767 0.704 0.69 0.689 11 Route 125 0.858 0.866 0.815 0.834 0.866 0.829 12 Route 130 0.999 0.937 1 0.96 1 0.952 13 Route 135 0.885 1 0.894 0.83 0.842 0.793 14 Route 140 1 0.898 0.897 0.863 1 1 15 Route 150 1 1 1 1 1 1 16 Route 155 0.886 1 0.956 0.931 1 17 Route 160 1 1 1 1 1 1 18 Route 161 1 1 1 1 1 1 19 Route 170 0.731 0.701 0.73 0.64 0.674 0.656 20 Route 172 0.744 0.888 0.749 0.718 0.733 0.961 21 Route 174 0.707 0.763 0.764 0.661 0.685 0.766 22 Route 175 0.729 0.746 0.735 0.719 0.634 0.607 23 Route 180 0.958 0.808 0.713 0.804 0.805 0.999 24 Route 184 0.771 0.769 0.733 0.74 0.741 0.721 25 Route 185 0.81 0.789 0.786 0.762 0.893 0.987 26 Route 192 1 1 1 1 1 1 27 Route 200 0.953 0.969 1 1 1 0.896 28 Route 202 1 1 1 1 1 1 29 Route 203 0.633 0.898 0.68 0.655 0.613 0.964 30 Route 204 1 0.947 0.915 0.868 0.906 0.762 31 Route 210 0.816 0.731 0.767 0.736 0.892 32 Route 212 0.724 0.913 0.731 0.794 0.699 1 33 Route 215 0.8 0.931 0.924 1 1 1 34 Route 220 0.967 1 0.99 0.906 0.904 0.891 35 Route 222 1 1 0.976 0.965 0.945 1 36 Route 230 0.723 0.703 0.741 0.629 0.649 0.63 37 Route 235 0.768 0.734 0.689 0.778 0.717 38 Route 310 0.836 1 1 0.809 0.856 1 39 Route 321 1 1 1 0.998 1 1 40 Route 325 0.915 0.899 0.912 0.872 0.886 1 41 Route 330 0.913 0.836 0.789 0.815 0.899 1 42 Route 333 0.892 0.806 0.896 1 1 0.897 43 Route 334 1 1 1 1 1 0.946 44 Route 335 1 1 1 1 1 1 45 Route 340 0.824 0.731 0.69 0.694 0.727 1 46 Route 345 0.968 0.918 0.873 0.942 1 0.819 47 Route 346 1 0.943 0.953 1 1 1 48 Route 353 1 1 1 0.993 1 1 49 Route 359 1 1 1 1 1 0.924 50 Route 370 1 1 1 1 1 1 51 Route 390 1 1 0.979 0.923 0.87 0.913 52 Route 444 1 1 1 1 1 1



Table 7-10: Efficiency scores of 52 bus routes in model 1 for different periods of time and a day

NO DMU Hour 6-9 Hour 10-15 Hour 16-19 Hour 20-24 Day

1 Route 100 1 0.97 1 0.984 1 2 Route 105 0.997 0.925 0.927 1 1 3 Route 110 0.818 0.869 0.82 0.708 0.779 4 Route 111 1 1 1 1 1 5 Route 112 0.716 0.877 0.711 0.748 0.774 6 Route 113 0.763 1 0.833 0.886 7 Route 115 0.946 0.962 1 1 8 Route 116 0.778 1 0.71 0.706 0.763 9 Route 120 0.781 0.881 0.805 0.855 0.845

10 Route 124 0.732 0.911 0.702 0.595 0.726 11 Route 125 0.849 0.858 0.843 0.746 0.827 12 Route 130 1 0.987 1 1 1 13 Route 135 0.82 0.954 0.831 0.897 0.867 14 Route 140 1 0.909 0.936 0.976 0.952 15 Route 150 1 1 1 1 1 16 Route 155 0.887 0.996 1 1 17 Route 160 1 1 1 0.799 1 18 Route 161 1 1 1 1 19 Route 170 0.713 0.719 0.679 0.605 0.698 20 Route 172 0.745 0.839 0.754 0.792 21 Route 174 0.715 0.76 0.723 0.588 0.72 22 Route 175 0.737 0.736 0.692 0.583 0.701 23 Route 180 0.878 0.85 0.822 0.83 0.852 24 Route 184 0.788 0.83 0.717 0.693 0.768 25 Route 185 0.806 0.913 0.757 0.745 0.778 26 Route 192 1 1 1 1 1 27 Route 200 0.973 0.988 1 0.967 1 28 Route 202 1 1 1 1 1 29 Route 203 0.72 0.82 0.643 0.75 30 Route 204 0.932 0.981 0.874 0.586 0.85 31 Route 210 0.725 0.765 0.8 0.628 0.731 32 Route 212 0.848 0.996 0.7 0.674 0.754 33 Route 215 0.922 0.913 1 0.693 0.955 34 Route 220 1 1 0.917 0.78 0.954 35 Route 222 0.975 1 1 1 1 36 Route 230 0.681 0.701 0.643 0.674 0.649 37 Route 235 0.736 0.725 0.766 0.508 0.68 38 Route 310 0.841 0.934 0.881 0.89 0.907 39 Route 321 1 1 1 1 40 Route 325 0.91 0.893 0.877 0.898 0.911 41 Route 330 0.857 0.859 0.824 0.902 0.849 42 Route 333 0.81 0.858 0.982 1 0.946 43 Route 334 1 1 1 1 44 Route 335 1 1 1 0.964 1 45 Route 340 0.703 0.729 0.697 0.795 0.715 46 Route 345 0.989 1 0.996 1 1 47 Route 346 1 1 1 1 48 Route 353 0.971 1 1 1 1 49 Route 359 1 1 1 0.777 1 50 Route 370 1 1 1 1 1 51 Route 390 1 1 0.908 0.803 0.985 52 Route 444 1 1 1 1 1



Table 7-11: Ranking of 52 bus routes in model 1 for a day (21 Aug 2013)

Ranking DMU Efficiency

scores


scores

1 Route 100 1 6 Route 333 0.946 1 Route 105 1 7 Route 325 0.911

1 Route 111 1 8 Route 310 0.907

1 Route 115 1 9 Route 113 0.886

1 Route 130 1 10 Route 135 0.867

1 Route 150 1 11 Route 180 0.852

1 Route 155 1 12 Route 204 0.85

1 Route 160 1 13 Route 330 0.849

1 Route 161 1 14 Route 120 0.845

1 Route 192 1 15 Route 125 0.827

1 Route 200 1 16 Route 172 0.792

1 Route 202 1 17 Route 110 0.779

1 Route 222 1 18 Route 185 0.778

1 Route 321 1 19 Route 112 0.774

1 Route 334 1 20 Route 184 0.768

1 Route 335 1 21 Route 116 0.763

1 Route 345 1 22 Route 212 0.754

1 Route 346 1 23 Route 203 0.75

1 Route 353 1 24 Route 210 0.731

1 Route 359 1 25 Route 124 0.726

1 Route 370 1 26 Route 174 0.72

1 Route 444 1 27 Route 340 0.715

2 Route 390 0.985 28 Route 175 0.701

3 Route 215 0.955 29 Route 170 0.698

4 Route 220 0.954 30 Route 235 0.68

5 Route 140 0.952 31 Route 230 0.649

Table 7-11 illustrates the ranking of given bus routes based on the efficiency scores

obtained from the empirical analysis for the time window of a day (21 Aug 2013). Here, there

are 22 efficient DMUs (such as routes 100, 105, and 111) and 30 inefficient DMUs (such as

routes 170, 175, 230 and 235).

Figure 7-6 presents the variations of efficiency scores of routes for the time window

of a day and of different periods of time within a day, with the gradual decrease of a day’s

efficiency scores. Here, the efficiency scores of some routes like 155, 161, and 172 are

unavailable for the time period between 21:00 and 0:00. The results indicate that of 22 first

ranking routes from Table 7-11, 10 routes are efficient for all time periods within a day,

which are 111, 150, 161, 192, 202, 321, 334, 346, 370, and 444 (see Table 7-10 or Figure

7-6a). Those bus routes are the benchmarks of this sample.

Table 7-12 illustrates the correlation relationship between efficiency scores of different

time periods within a day, and a day. Results indicate that efficiency scores of both morning



and afternoon peak periods experience a high correlation with those of a day (correlation

coefficients are 0.84 and 0.90, respectively), while efficiency scores between the off-peak

period and a day have a lower correlation (which is 0.68 for the period from 9:00 to 15:00).

This demonstrates that the technical efficiency of bus routes during peak periods, especially

the afternoon peak period, is significantly related to the daily efficiency.


5:00-9:00 9:00-15:00 15:00-21:00 21:00-0:00 Day

5:00-9:00 1

9:00-15:00 0.66 1

15:00-21:00 0.78 0.49 1

21:00-0:00 0.46 0.36 0.57 1

Day 0.84 0.68 0.90 0.71 1



a) Efficiency scores of the first 20 routes for different periods of time

b) Efficiency scores of the last 32 routes for different periods of time

Figure 7-6: Efficiency score variations of bus routes in model 1 for different periods of time, following

the gradual decrease of a day’s efficiency scores

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7.4.2 Service effectiveness measure (Model 2)

This section employs model 2 for empirical analysis of the given bus routes. Model 2

separately uses an output-oriented VRS model for empirical analysis of node 2.

Table 7-13 and Table 7-14 illustrate efficiency scores of bus routes for different hours

during the daytime (from 6:00 to 19:00) of the given date. The results indicate that efficiency

scores of a bus route change significantly between hours, because of the large variations of

travel demand across the daytime. For example, route 111 is efficient at hour 8, but its

efficiency scores reduce gradually before reaching the bottom of 0.67 at hour 12, then it is

efficient again at hours 16 and 17. On the other hand, route 140 experiences poor

performance during the peak morning hour (its efficiency score at hour 8 equals to 0.38), but

it is almost efficient at hour 12 (efficiency score equals to 0.93). Several routes in the sample,

such as routes 130 and 334, are efficient for most hours. Those routes are considered as

the benchmarks of this sample for model 2.

Table 7-15 shows the efficiency scores of the given bus routes for key periods of time

of a day and for a day. This information is useful to rank the performance of those routes for

peak periods or off-peak periods of time within a day, as well as an entire day.

Table 7-16 shows the ranking of those bus routes based on the performance of a

given day. Here, there are eight efficient routes (130, 160, 161, 192, 230, 333, 334, and 370),

which are the benchmarks of this sample for a given day. Routes 130 and 334 are efficient

for all periods of time, so those routes are the typical benchmarks of this sample. Routes

174, 200, 184, 325, 185, 335 and 155, on the contrary, are the most inefficient routes

that need further investigation to identify the sources of inefficiency. Then, possible solutions

should be made for performance improvement of those routes.





1 Route 100 1 0.913 0.875 0.731 0.815 1 0.772 2 Route 105 1 0.5 0.502 0.516 0.283 1 1 3 Route 110 0.71 0.843 0.407 0.703 0.284 0.255 0.584 4 Route 111 0.653 1 0.977 0.744 0.764 0.673 0.782 5 Route 112 0.734 0.54 1 1 1 1 0.779 6 Route 113 0.299 0.389 0.221 1 0.325 1 7 Route 115 0.66 1 1 0.507 1 0.181 1 8 Route 116 1 1 0.689 1 1 0.516 1 9 Route 120 0.501 0.961 0.767 0.853 0.621 0.477 0.558

10 Route 124 1 0.452 0.323 0.668 0.57 1 0.928 11 Route 125 0.72 0.439 0.478 0.498 1 0.924 0.765 12 Route 130 1 0.935 1 1 1 1 1 13 Route 135 0.665 1 1 0.961 1 0.754 0.875 14 Route 140 0.353 0.389 0.443 0.75 0.58 0.932 0.805 15 Route 150 0.588 0.88 0.601 1 0.711 1 1 16 Route 155 0.522 0.268 0.21 0.566 0.212 0.513 17 Route 160 0.748 0.617 0.957 0.542 0.478 0.516 0.862 18 Route 161 1 0.878 0.612 0.196 1 0.513 19 Route 170 0.725 0.681 0.752 0.613 0.53 0.404 0.571 20 Route 172 0.448 0.77 1 0.363 0.328 1 0.708 21 Route 174 0.42 0.526 0.464 0.665 0.602 0.426 0.53 22 Route 175 0.378 0.502 0.598 0.531 0.52 1 0.516 23 Route 180 0.367 0.868 0.783 0.47 0.445 0.581 0.81 24 Route 184 1 0.586 0.539 0.446 0.383 0.355 0.637 25 Route 185 0.27 0.64 0.309 0.406 0.508 0.169 0.606 26 Route 192 1 0.277 0.384 0.532 0.466 1 0.931 27 Route 200 0.451 0.454 0.451 0.604 0.366 0.69 0.731 28 Route 202 0.567 0.554 0.369 0.44 0.262 0.561 0.286 29 Route 203 0.5 0.699 0.948 1 0.511 0.673 0.779 30 Route 204 0.857 0.778 0.553 0.405 0.683 0.958 0.62 31 Route 210 1 0.48 0.591 0.314 0.608 0.783 0.6 32 Route 212 0.708 0.788 0.761 0.591 0.529 1 1 33 Route 215 1 0.5 0.553 0.519 0.403 0.5 0.65 34 Route 220 1 0.218 0.292 0.535 0.163 0.562 0.545 35 Route 222 0.552 1 1 1 0.773 0.641 0.57 36 Route 230 1 1 0.728 0.785 0.701 0.883 1 37 Route 235 0.661 0.907 1 1 0.814 0.501 0.698 38 Route 310 0.73 0.609 0.288 0.363 0.201 0.561 0.543 39 Route 321 1 1 0.27 0.503 0.14 1 1 40 Route 325 0.605 0.743 0.387 0.265 0.558 0.562 0.395 41 Route 330 0.983 1 1 0.98 0.839 0.88 0.697 42 Route 333 0.807 1 1 1 0.885 1 1 43 Route 334 0.529 1 1 0.672 0.504 1 0.895 44 Route 335 0.628 1 0.368 0.242 0.506 1 0.527 45 Route 340 0.784 0.668 0.719 0.513 0.594 0.604 0.524 46 Route 345 0.873 1 0.867 0.737 0.798 0.56 0.751 47 Route 346 0.497 0.667 1 0.504 0.501 1 0.503 48 Route 353 0.485 0.835 1 0.278 0.074 0.281 0.429 49 Route 359 0.854 0.895 0.643 0.875 0.579 0.65 0.728 50 Route 370 0.365 0.886 1 0.655 0.984 0.739 0.804 51 Route 390 0.445 0.993 0.605 0.678 0.688 0.857 1 52 Route 444 0.781 1 0.793 0.907 0.785 1 0.888





1 Route 100 0.699 1 0.92 0.773 0.903 0.719 2 Route 105 0.355 0.449 0.392 0.373 0.073 1 3 Route 110 0.521 0.374 0.535 0.686 0.674 0.363 4 Route 111 0.769 0.981 1 1 0.945 0.75 5 Route 112 1 0.937 1 0.437 0.826 0.264 6 Route 113 1 0.757 0.346 0.363 0.247 7 Route 115 0.5 0.449 0.296 0.073 1 0.003 8 Route 116 1 0.88 0.796 0.2 0.712 0.075 9 Route 120 0.488 0.559 0.658 0.744 0.637 1

10 Route 124 0.507 0.871 0.392 0.608 0.517 0.516 11 Route 125 0.342 0.755 0.35 0.483 0.645 0.705 12 Route 130 1 1 1 1 1 1 13 Route 135 0.58 1 0.41 0.363 0.226 0.5 14 Route 140 0.673 0.888 0.798 0.887 0.965 1 15 Route 150 1 1 1 0.939 1 1 16 Route 155 0.417 0.079 0.073 0.059 0.006 17 Route 160 0.857 0.473 1 0.834 0.8 0.748 18 Route 161 1 1 0.412 1 0.754 0.714 19 Route 170 0.521 0.333 0.763 0.846 0.877 0.75 20 Route 172 1 0.849 0.344 0.468 0.625 0.317 21 Route 174 0.55 1 0.374 0.398 0.586 0.36 22 Route 175 1 0.565 0.921 0.526 0.551 1 23 Route 180 0.412 0.705 0.588 0.621 0.94 0.788 24 Route 184 0.65 1 0.418 0.481 0.264 0.5 25 Route 185 0.623 1 0.704 0.591 0.261 0.419 26 Route 192 0.579 0.898 1 0.591 1 1 27 Route 200 0.318 0.291 0.429 0.414 0.437 0.377 28 Route 202 0.388 0.487 0.761 0.334 0.509 0.287 29 Route 203 0.537 1 0.573 0.82 0.341 0.157 30 Route 204 0.587 0.627 0.509 0.726 0.651 0.642 31 Route 210 0.783 1 0.784 0.804 0.27 32 Route 212 0.516 1 0.659 0.469 1 1 33 Route 215 0.245 0.486 0.694 1 1 1 34 Route 220 0.504 0.805 0.875 0.548 0.358 1 35 Route 222 0.686 0.787 0.724 0.684 1 1 36 Route 230 0.569 0.918 1 0.911 1 1 37 Route 235 0.758 0.798 0.681 1 1 1 38 Route 310 0.543 1 1 0.466 0.363 0.398 39 Route 321 0.508 1 0.36 0.982 0.709 1 40 Route 325 0.616 0.295 0.463 0.423 0.544 0.537 41 Route 330 0.622 1 1 1 0.864 0.751 42 Route 333 0.899 1 1 0.918 1 0.8 43 Route 334 1 1 1 1 1 0.428 44 Route 335 0.562 0.311 0.362 0.384 0.359 0.245 45 Route 340 0.618 0.61 0.663 0.776 0.631 0.488 46 Route 345 0.96 1 1 1 1 1 47 Route 346 1 0.888 0.26 0.926 0.287 48 Route 353 1 0.36 0.696 0.485 0.468 0.374 49 Route 359 0.745 0.557 0.533 0.716 0.627 0.616 50 Route 370 0.79 0.54 1 1 0.702 0.632 51 Route 390 0.719 0.798 0.576 0.692 0.887 0.804 52 Route 444 0.916 1 0.88 0.94 0.622 0.627



Table 7-15: Efficiency scores of 52 bus routes in model 2 for different periods of time and a day


1 Route 100 0.948 0.879 0.834 0.701 0.877 2 Route 105 1 0.478 0.38 0.591 0.552 3 Route 110 0.603 0.446 0.731 0.339 0.612 4 Route 111 1 0.819 1 0.699 0.943 5 Route 112 0.903 1 0.573 1 0.986 6 Route 113 0.284 0.777 0.454 0.573 7 Route 115 1 0.601 0.294 0.75 8 Route 116 1 1 0.544 0.956 0.921 9 Route 120 0.871 0.587 0.702 0.714 0.716

10 Route 124 0.511 0.925 0.536 0.636 0.586 11 Route 125 0.633 0.992 0.638 0.447 0.603 12 Route 130 1 1 1 1 1 13 Route 135 1 0.942 0.417 1 0.701 14 Route 140 0.41 0.8 0.912 0.817 0.783 15 Route 150 0.672 0.968 0.937 0.955 0.873 16 Route 155 0.459 0.334 0.082 0.366 17 Route 160 0.978 0.673 1 0.802 1 18 Route 161 0.992 1 0.855 1 19 Route 170 0.797 0.526 1 0.473 0.865 20 Route 172 0.901 0.744 0.582 0.775 21 Route 174 0.486 0.803 0.401 0.539 0.546 22 Route 175 0.481 1 0.679 0.851 0.645 23 Route 180 0.67 0.592 0.68 0.542 0.641 24 Route 184 1 0.765 0.455 0.366 0.518 25 Route 185 0.402 0.491 0.583 0.472 0.467 26 Route 192 0.343 0.867 1 1 1 27 Route 200 0.469 0.55 0.539 0.274 0.541 28 Route 202 0.413 0.646 0.637 0.943 0.569 29 Route 203 0.918 0.807 0.592 0.777 30 Route 204 0.875 0.753 0.663 0.599 0.763 31 Route 210 0.578 0.766 0.976 1 0.853 32 Route 212 0.706 0.88 0.763 0.436 0.755 33 Route 215 0.8 0.514 0.797 1 0.643 34 Route 220 1 0.541 0.774 0.853 0.785 35 Route 222 0.918 0.753 0.984 0.658 0.884 36 Route 230 1 0.899 1 0.26 1 37 Route 235 0.776 0.996 1 1 0.954 38 Route 310 0.637 0.476 0.504 0.443 0.557 39 Route 321 0.823 0.661 1 0.843 40 Route 325 0.567 0.439 0.543 0.598 0.509 41 Route 330 1 0.861 0.914 0.597 0.92 42 Route 333 0.948 1 0.951 0.795 1 43 Route 334 1 1 1 1 44 Route 335 0.876 0.395 0.336 0.382 0.453 45 Route 340 0.82 0.572 0.637 0.453 0.627 46 Route 345 0.932 0.8 1 0.768 0.928 47 Route 346 0.607 0.79 0.563 0.7 48 Route 353 0.906 0.354 0.682 0.646 0.61 49 Route 359 0.908 0.781 0.717 0.808 0.868 50 Route 370 0.894 1 1 0.561 1 51 Route 390 0.668 0.938 0.781 0.68 0.804 52 Route 444 0.937 1 0.778 0.956 0.926



Table 7-16: Ranking of 52 bus routes in model 2 for a working day (21 Aug 2013)


scores


scores

1 Route 130 1 20 Route 172 0.775 1 Route 160 1 21 Route 204 0.763 1 Route 161 1 22 Route 212 0.755 1 Route 192 1 23 Route 115 0.75 1 Route 230 1 24 Route 120 0.716 1 Route 333 1 25 Route 135 0.701 1 Route 334 1 26 Route 346 0.7 1 Route 370 1 27 Route 175 0.645 2 Route 112 0.986 28 Route 215 0.643 3 Route 235 0.954 29 Route 180 0.641 4 Route 111 0.943 30 Route 340 0.627 5 Route 345 0.928 31 Route 110 0.612 6 Route 444 0.926 32 Route 353 0.61 7 Route 116 0.921 33 Route 125 0.603 8 Route 330 0.92 34 Route 124 0.586 9 Route 222 0.884 35 Route 113 0.573 10 Route 100 0.877 36 Route 202 0.569 11 Route 150 0.873 37 Route 310 0.557 12 Route 359 0.868 38 Route 105 0.552 13 Route 170 0.865 39 Route 174 0.546 14 Route 210 0.853 40 Route 200 0.541 15 Route 321 0.843 41 Route 184 0.518 16 Route 390 0.804 42 Route 325 0.509 17 Route 220 0.785 43 Route 185 0.467 18 Route 140 0.783 44 Route 335 0.453 19 Route 203 0.777 45 Route 155 0.366

Figure 7-7 presents the variations of efficiency scores of bus routes in model 2 for

different periods of time, which follow the gradual reduction of efficiency scores of a day. This

indicates that the temporal and spatial performance of bus routes vary significantly because

of the changes of travel demand over time for a single route, and among different routes. For

instance, routes 111, 222, and 345 have high efficiency scores for peak periods of time

(nearly 1) and lower efficiency scores for off-peak periods of time. On the other hand, routes

124 and 175 have higher efficiency scores of off-peak periods compared to peak periods.

Routes 112 and 116 have considerably low efficiency scores for only the afternoon peak

period, but high efficiency scores for the remaining periods of time. Routes 192 and 140, by

contrast, experience low efficiency scores for only the morning peak period, but high

efficiency scores for the remaining periods of time.

The results obtained from the correlation analysis between efficiency scores in model

2 of different periods of time are presented in Table 7-17. Here, efficiency scores of the

afternoon peak period have fairly high correlation with a day’s efficiency scores, suggesting

the important contribution of this period to the overall performance of bus routes a day.




5:00-9:00 9:00-15:00 15:00-21:00 21:00-0:00 Day

Day 0.52 0.67 0.79 0.48 1



Figure 7-7: Efficiency score variations of bus routes in model 2 for different periods of time, following

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7.4.3 Network performance measurement

This section employs a NDEA model for data analysis of the similar sample of 52 bus

routes. The results obtained for every single hour are expressed in Table 7-18 (hours 7 to

13) and Table 7-19 (hours 14 to 19). Those results provide information about the overall

performance of bus routes at hour level across a working day.

Table 7-20 represents the efficiency scores of bus routes for different periods of time

within a day (peak periods and off-peak periods) and for a day 21st August 2013. Based on

the efficiency scores of a day, the given bus routes are ranked and shown in Table 7-21.

The results from Table 7-21 indicate that there are seven efficient DMUs, including

routes 130, 160, 161, 192, 230, 334, and 370. Those routes are benchmarks for the given

sample. On the contrary, routes 174, 310, 325, 340, 335, 124, 185, and 155 are the most

inefficient routes (efficiency score is less than 0.5). Those inefficient routes need to be further

investigated to identify the underlying reasons for their poor performance.

Figure 7-8 presents the efficiency scores of bus routes for different periods of time

with the gradual decrease of day’s efficiency scores. The results indicate the significant

variations of efficiency scores among different routes and different time periods of a single

route. Only two routes, 130 and 334, are efficient for all periods of time.



Table 7-18: Network efficiency scores of 52 bus routes from hour 7 to hour 13


1 Route 100 1 0.913 0.873 0.697 0.795 0.998 0.769 2 Route 105 1 0.5 0.5 0.515 0.228 1 1 3 Route 110 0.645 0.843 0.342 0.588 0.219 0.201 0.538 4 Route 111 0.653 1 0.977 0.744 0.764 0.673 0.782 5 Route 112 0.734 0.54 1 1 1 1 0.65 6 Route 113 0.296 0.35 0.164 1 0.234 1 7 Route 115 0.66 1 1 0.507 1 0.134 1 8 Route 116 1 1 0.516 1 1 0.514 1 9 Route 120 0.499 0.961 0.761 0.84 0.553 0.444 0.535

10 Route 124 1 0.406 0.211 0.542 0.401 0.757 0.719 11 Route 125 0.72 0.352 0.421 0.489 1 0.91 0.765 12 Route 130 1 0.935 1 1 1 1 1 13 Route 135 0.557 1 0.81 0.797 0.923 0.679 0.725 14 Route 140 0.328 0.389 0.441 0.68 0.526 0.91 0.805 15 Route 150 0.588 0.88 0.601 1 0.711 1 1 16 Route 155 0.5 0.219 0.21 0.535 0.166 0.513 17 Route 160 0.748 0.617 0.957 0.542 0.453 0.516 0.862 18 Route 161 1 0.878 0.612 0.196 1 0.513 19 Route 170 0.567 0.494 0.687 0.594 0.53 0.37 0.556 20 Route 172 0.447 0.77 1 0.363 0.25 1 0.613 21 Route 174 0.394 0.473 0.449 0.559 0.559 0.414 0.487 22 Route 175 0.378 0.448 0.514 0.501 0.397 1 0.458 23 Route 180 0.342 0.853 0.758 0.431 0.412 0.574 0.808 24 Route 184 1 0.586 0.521 0.393 0.282 0.222 0.45 25 Route 185 0.269 0.598 0.238 0.303 0.508 0.154 0.576 26 Route 192 1 0.277 0.384 0.532 0.466 1 0.931 27 Route 200 0.404 0.454 0.451 0.604 0.362 0.681 0.731 28 Route 202 0.567 0.554 0.369 0.44 0.262 0.561 0.286 29 Route 203 0.5 0.683 0.948 1 0.511 0.586 0.623 30 Route 204 0.857 0.778 0.553 0.389 0.683 0.958 0.62 31 Route 210 1 0.438 0.489 0.287 0.545 0.765 0.577 32 Route 212 0.704 0.788 0.517 0.591 0.529 1 1 33 Route 215 1 0.5 0.545 0.515 0.332 0.5 0.471 34 Route 220 1 0.218 0.292 0.535 0.163 0.545 0.535 35 Route 222 0.552 1 0.957 1 0.773 0.641 0.57 36 Route 230 1 1 0.481 0.619 0.484 0.883 1 37 Route 235 0.447 0.906 1 1 0.705 0.41 0.663 38 Route 310 0.634 0.501 0.218 0.359 0.189 0.531 0.532 39 Route 321 1 1 0.27 0.506 0.139 1 1 40 Route 325 0.603 0.644 0.38 0.233 0.532 0.545 0.316 41 Route 330 0.838 0.972 0.955 0.839 0.718 0.874 0.664 42 Route 333 0.768 0.739 0.776 0.955 0.815 0.916 0.93 43 Route 334 0.529 1 1 0.676 0.504 1 0.893 44 Route 335 0.628 1 0.368 0.242 0.506 1 0.527 45 Route 340 0.765 0.655 0.683 0.412 0.444 0.576 0.486 46 Route 345 0.873 1 0.798 0.737 0.798 0.536 0.751 47 Route 346 0.497 0.667 1 0.506 0.501 1 0.503 48 Route 353 0.464 0.835 1 0.278 0.074 0.281 0.429 49 Route 359 0.786 0.895 0.643 0.875 0.554 0.65 0.728 50 Route 370 0.365 0.886 1 0.707 0.984 0.751 1 51 Route 390 0.442 0.993 0.605 0.665 0.683 0.828 1 52 Route 444 0.781 1 0.793 0.907 0.785 1 0.888



Table 7-19: Network efficiency scores of 52 bus routes from hour 14 to hour 19


1 Route 100 0.699 1 0.92 0.773 0.903 0.719 2 Route 105 0.355 0.441 0.292 0.373 0.072 1 3 Route 110 0.514 0.354 0.535 0.686 0.674 0.346 4 Route 111 0.769 0.981 1 1 0.945 0.75 5 Route 112 1 0.909 0.836 0.437 0.642 0.24 6 Route 113 1 0.717 0.344 0.363 0.179 7 Route 115 0.5 0.442 0.284 0.067 1 0.003 8 Route 116 0.741 0.857 0.796 0.117 0.712 0.075 9 Route 120 0.488 0.54 0.599 0.744 0.589 1

10 Route 124 0.335 0.812 0.279 0.488 0.454 0.369 11 Route 125 0.286 0.755 0.35 0.483 0.633 0.655 12 Route 130 1 1 1 1 1 1 13 Route 135 0.574 1 0.352 0.359 0.189 0.5 14 Route 140 0.673 0.849 0.728 0.792 0.965 1 15 Route 150 1 1 1 0.939 1 1 16 Route 155 0.358 0.079 0.069 0.054 0.006 17 Route 160 0.857 0.473 1 0.834 0.8 0.748 18 Route 161 1 1 0.412 1 0.754 0.714 19 Route 170 0.521 0.331 0.763 0.846 0.877 0.75 20 Route 172 0.939 0.81 0.344 0.468 0.613 0.3 21 Route 174 0.358 1 0.301 0.369 0.586 0.31 22 Route 175 1 0.446 0.921 0.38 0.35 1 23 Route 180 0.403 0.66 0.527 0.568 0.81 0.787 24 Route 184 0.424 1 0.355 0.47 0.202 0.5 25 Route 185 0.623 0.829 0.703 0.591 0.233 0.413 26 Route 192 0.579 0.898 1 0.591 1 1 27 Route 200 0.318 0.291 0.429 0.414 0.437 0.377 28 Route 202 0.388 0.487 0.761 0.334 0.509 0.287 29 Route 203 0.287 0.949 0.54 0.82 0.206 0.148 30 Route 204 0.587 0.627 0.505 0.726 0.651 0.57 31 Route 210 0.783 1 0.783 0.799 0.238 32 Route 212 0.516 0.725 0.441 0.413 1 1 33 Route 215 0.181 0.426 0.615 1 1 1 34 Route 220 0.504 0.805 0.862 0.513 0.323 1 35 Route 222 0.686 0.787 0.709 0.675 1 1 36 Route 230 0.496 0.745 1 0.885 0.967 1 37 Route 235 0.758 0.728 0.498 1 1 1 38 Route 310 0.535 1 1 0.423 0.352 0.398 39 Route 321 0.512 1 0.36 0.982 0.709 1 40 Route 325 0.547 0.254 0.424 0.372 0.478 0.537 41 Route 330 0.564 0.935 0.835 1 0.793 0.697 42 Route 333 0.79 0.953 0.946 0.918 1 0.758 43 Route 334 1 1 1 1 1 0.428 44 Route 335 0.562 0.311 0.362 0.384 0.359 0.245 45 Route 340 0.618 0.524 0.516 0.596 0.536 0.463 46 Route 345 0.925 0.977 0.9 0.981 1 1 47 Route 346 1 0.887 0.245 0.926 0.287 48 Route 353 1 0.36 0.696 0.481 0.468 0.374 49 Route 359 0.745 0.557 0.533 0.716 0.627 0.574 50 Route 370 0.892 0.546 1 1 0.715 0.632 51 Route 390 0.719 0.798 0.565 0.62 0.776 0.74 52 Route 444 0.916 1 0.88 0.94 0.622 0.627



Table 7-20: Network efficiency scores of 52 bus routes for different periods of time and a day


1 Route 100 0.948 0.856 0.834 0.692 0.877 2 Route 105 1 0.435 0.339 0.591 0.552 3 Route 110 0.572 0.406 0.701 0.339 0.612 4 Route 111 1 0.819 1 0.699 0.943 5 Route 112 0.899 1 0.479 0.804 0.986 6 Route 113 0.22 0.777 0.421 0.573 7 Route 115 1 0.601 0.294 0.754 8 Route 116 1 1 0.528 0.747 0.849 9 Route 120 0.871 0.564 0.685 0.714 0.716

10 Route 124 0.496 0.724 0.366 0.38 0.421 11 Route 125 0.633 0.992 0.62 0.442 0.603 12 Route 130 1 1 1 1 1 13 Route 135 0.832 0.869 0.379 1 0.66 14 Route 140 0.41 0.734 0.863 0.798 0.748 15 Route 150 0.672 0.968 0.937 0.955 0.873 16 Route 155 0.4 0.332 0.082 0.366 17 Route 160 0.978 0.673 1 0.674 1 18 Route 161 0.992 1 0.855 1 19 Route 170 0.658 0.507 1 0.473 0.865 20 Route 172 0.901 0.744 0.563 0.775 21 Route 174 0.472 0.754 0.353 0.316 0.495 22 Route 175 0.47 1 0.603 0.851 0.62 23 Route 180 0.634 0.592 0.6 0.451 0.574 24 Route 184 1 0.619 0.432 0.247 0.511 25 Route 185 0.378 0.469 0.536 0.347 0.378 26 Route 192 0.343 0.867 1 1 1 27 Route 200 0.462 0.55 0.539 0.274 0.541 28 Route 202 0.413 0.646 0.637 0.943 0.569 29 Route 203 0.91 0.737 0.555 0.777 30 Route 204 0.875 0.753 0.663 0.599 0.763 31 Route 210 0.537 0.766 0.947 1 0.853 32 Route 212 0.696 0.88 0.698 0.353 0.755 33 Route 215 0.8 0.426 0.797 1 0.642 34 Route 220 1 0.541 0.739 0.816 0.784 35 Route 222 0.91 0.753 0.984 0.658 0.884 36 Route 230 1 0.892 0.966 0.158 1 37 Route 235 0.716 0.996 0.917 1 0.952 38 Route 310 0.525 0.459 0.476 0.392 0.489 39 Route 321 0.823 0.661 1 0.859 40 Route 325 0.554 0.366 0.498 0.598 0.488 41 Route 330 0.96 0.752 0.788 0.597 0.79 42 Route 333 0.83 0.926 0.935 0.795 0.968 43 Route 334 1 1 1 1 44 Route 335 0.876 0.395 0.336 0.376 0.453 45 Route 340 0.756 0.47 0.487 0.395 0.479 46 Route 345 0.929 0.8 0.998 0.768 0.928 47 Route 346 0.607 0.796 0.563 0.701 48 Route 353 0.906 0.354 0.682 0.646 0.61 49 Route 359 0.908 0.781 0.717 0.643 0.868 50 Route 370 0.91 1 1 0.561 1 51 Route 390 0.668 0.938 0.709 0.67 0.793 52 Route 444 0.937 1 0.778 0.956 0.926



Table 7-21: Ranking of 52 bus routes in network model for a working day (21 Aug 2013)


scores


scores 1 Route 130 1 21 Route 204 0.763

1 Route 160 1 22 Route 212 0.755

1 Route 161 1 23 Route 115 0.754

1 Route 192 1 24 Route 140 0.748

1 Route 230 1 25 Route 120 0.716

1 Route 334 1 26 Route 346 0.701

1 Route 370 1 27 Route 135 0.66

2 Route 112 0.986 28 Route 215 0.642

3 Route 333 0.968 29 Route 175 0.62

4 Route 235 0.952 30 Route 110 0.612

5 Route 111 0.943 31 Route 353 0.61

6 Route 345 0.928 32 Route 125 0.603

7 Route 444 0.926 33 Route 180 0.574

8 Route 222 0.884 34 Route 113 0.573

9 Route 100 0.877 35 Route 202 0.569

10 Route 150 0.873 36 Route 105 0.552

11 Route 359 0.868 37 Route 200 0.541

12 Route 170 0.865 38 Route 184 0.511

13 Route 321 0.859 39 Route 174 0.495

14 Route 210 0.853 40 Route 310 0.489

15 Route 116 0.849 41 Route 325 0.488

16 Route 390 0.793 42 Route 340 0.479

17 Route 330 0.79 43 Route 335 0.453

18 Route 220 0.784 44 Route 124 0.421

19 Route 203 0.777 45 Route 185 0.378

20 Route 172 0.775 46 Route 155 0.366

The results of the correlation analysis between efficiency scores in the network model

of different periods of time are shown in Table 7-22. Among all periods of time, efficiency

scores of the afternoon peak period have the highest correlation with those of a day

(correlation coefficient is 0.8), presenting the similar result with model 1 and 2. This

demonstrates that the afternoon peak period is the most important period within a day of bus

services in the case study of Brisbane.


5:00-9:00 9:00-15:00 15:00-21:00 21:00-0:00 Day

Day 0.53 0.68 0.80 0.50 1





Figure 7-8: Efficiency score variations of bus routes in network model for different periods of time,

following the gradual decrease of a day’s efficiency scores

The comparison between efficiency scores of model 1 (the Technical efficiency

measure) and model 2 (the Service effectiveness measure) for a day is shown in Figure 7-9,

with the gradual decrease of model 2 efficiency scores. The correlation coefficient between

those two models is 0.12, suggesting that there is a weak relationship between the technical

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efficiency and the service effectiveness of the given bus routes. This result supports the

findings in the literature that the efficiency and effectiveness measures are different

perspectives of transit (Chu, Fielding et al. 1992).

a) Efficiency scores of the first 26 routes of models 1 and 2

b) Efficiency scores of the last 26 routes of models 1 and 2

Figure 7-9: Efficiency score variations of bus routes in models 1 and 2 for a day following the gradual

decrease of model 2 efficiency scores

From the results in Figure 7-9, there are six efficient routes in both model 1 and 2,

while some routes have low efficiency scores for both models. Some bus routes are efficient

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in model 1, but significantly inefficient in model 2. By contrast, some routes are efficient in

model 2, but significantly inefficient in model 1. Details of those routes are presented in Table

7-23 with the six bus routes (130, 160, 161, 192, 334, and 370) being the benchmarks of the

considered sample.

Table 7-23: Efficiency scores statistics of some routes for models 1 and 2

DMU Model 1 efficiency score Model 2 efficiency score Notes

Route 130 1 1 Routes are efficient in

both models. Route 160 1 1

Route 161 1 1

Route 192 1 1

Route 334 1 1

Route 370 1 1

Route 174 0.72 0.546 Low efficiency score in

both models. Route 184 0.768 0.518

Route 185 0.778 0.467

Route 202 1 0.569 High score in model 1,

but low score in model 2. Route 105 1 0.552

Route 200 1 0.541

Route 335 1 0.453

Route 155 1 0.366

Route 230 0.649 1 Low score in model 1,

but high score in model

2 Route 235 0.68 0.954

Identification of External Sources of Inefficiency and

Recommendations

Using DEA models only helps to rank the performance of bus routes and investigate

the internal factors affecting their performance efficiency, but cannot explain the influences

of external factors on efficiency levels of DMUs. This section uses the Simar and Wilson

(2007) double bootstrap approach to examine the impact that external variables (EVs)

have on the efficiency scores obtained in model 2 (the service effectiveness measure)



for a working day (21st Aug 2013). Bus route performance of a working day is opted for

measure because it typically presents the actual demand of residents within the service

corridor of bus routes.

Seven EVs related to population density (PODC, PODYA, PODOA, and PODP),

individual income (LI, MI, and HI), and car ownership (CO) are used in this section, which

potentially affect the bus ridership. To account for the influences of routes’ characteristics on

efficiency levels of routes, this research employs three more independent variables including

signalised intersection spacing (SIS), lane priority (LAP), and frequency (FR). SIS and LAP

may affect the delay time of buses on each route, which possibly affects the attraction of bus

service to passengers. FR is a dummy variable, which accounts for the high or low service

frequency of bus routes. Here, FR equals 1 for high frequency bus routes (headway during

peak periods for one direction is equal to or less than 15 minutes) and 0 for low frequency

bus routes (headway is greater than 15 minutes).

Table 5-2 presents the results obtained from the correlation analysis of external

variables. There is a high correlation between PODOA and PODYA (correlation coefficient

equals to 0.82), and between HI and LI (correlation coefficient is -0.86). Therefore, PODOA

and HI are rejected from the sample of EVs.

Note:

PODC: population density of people with age under 18 within service areas of bus

route

PODYA: population density of young adults with age from 18 to 34 within service

areas of bus route

PODOA: population density of people with age from 35 to 64 within service areas of

bus route

PODP: population density of old people with age 65 and older within service areas of

bus route

LI: percent of low-income group (<400 AUD/week)

MI: percent of medium income group (400-1500 AUD/week)

HI: percent of high-income group (>1500 AUD/week)

SIS: route length per total number of signalised intersections on the route

LAP: percent of Busway travel length to route length

The model can be expressed as follows:



��𝒊 = 𝜷𝟎 + 𝜷𝟏𝑷𝑶𝑫𝑪 + 𝜷𝟐𝑷𝑶𝑷𝒀𝑨 + 𝜷𝟑𝑷𝑶𝑫𝑷 + 𝜷𝟒𝑳𝑰 + 𝜷𝟓𝑴𝑰 + 𝜷𝟔𝑪𝑶 + 𝜷𝟕𝑺𝑰𝑺 +

𝜷𝟖𝑳𝑨𝑷 + 𝜷𝟗𝑭𝑹 + 𝜺𝒊 Equation 7-5

Where: 𝛿𝑖 is the bootstrapped bias-corrected efficiency scores.

Table 7-24a presents the original and bias-corrected efficiency scores on average.

The bias-corrected estimates are less than the original estimates, suggesting that without

correcting for bias, the results would overestimate the actual efficiency of bus routes. The

results also indicate that eight of the nine given EVs have a significant impact on the efficiency

of given routes (see Table 7-24b). The output-oriented efficiency score is the dependent

variable in this model, which varies from 0 to infinity. Therefore, a positive (negative)

coefficient of EV indicates a negative (positive) marginal effect on efficiency.

The results show that PODC with an estimated negative coefficient has a positive

impact on efficiency, while PODP on the contrary negatively affects efficiency of bus routes.

This indicates that a young group of Pop (PODC) contributes to an increase in efficiency,

while older groups of Pop (PODP) contribute negatively to efficiency. This result coincides

with the comparative analysis between routes 115 and 220 in section 7.3 that route 220 is

less efficient than 115 because it crosses areas with higher density of retirees. PODYA is the

only EV that is insignificantly correlated with efficiency scores of DMUs. This suggests that

young adults may use different means for daily travelling such as bus, rail, and private car.

Bus mode seems to be an irregular choice for commuting.

Regarding individual income, the results indicate that LI negatively affects efficiency

whereas MI contributes to an increase in efficiency of DMUs. This indicates that low-income

earners may tend to use bus services less than medium-income earners. The medium-

income group may have stable jobs at fixed work places, so they may use bus services

regularly for travelling between home and the work place. On the contrary, the actual travel

demand of the low-income group for daily work may be less than the medium-income group.

Additionally, CO negatively affects the efficiency of bus routes, highlighting the finding

elsewhere that car ownership possibly has an adverse effect on transit consumption (Taylor,

Miller et al. 2009). In South East Queensland, the mode share of private motor vehicles is

significantly high (accounting for 83% in 2006), and the Queensland Government aims to

reduce the share of trips taken by private motor vehicles to 66% in 2031 (Government 2011).

This statistic for mode share of private cars may support the finding above that private car

ownership has a negative impact on bus routes’ efficiency. Therefore, encouraging residents

to change their weekday trips from private car use to transit use may be an effective solution

for bus routes performance improvement.



Finally, SIS, LAP and FR positively affect efficiency of bus routes, suggesting that bus

routes with high frequency and better conditions for decreasing delay time may be more

efficient. This suggests that the increase of FR for some inefficiency bus routes with

significantly low frequency (such as one hour) may be essential to improve their performance.

Moreover, possible solutions should be made by transit agencies to increase SIS and LAP of

some inefficient routes of the case study. This may help to increase the operating speed of

bus vehicles, OTP, and bus LOS, which makes bus service more attractive to passengers.

These findings significantly demonstrate the contribution of the exogenous operating

environment to the efficiency of bus routes in the given case study, which appeals to transit

regulators and operators for policy making to create a better operating environment for

inefficient bus routes.

Table 7-24: a) Original and bias-corrected efficiency scores; and b) Truncated Regression

a) Original and bias-corrected efficiency scores

Number of DMUs Original DEA estimates Bias-corrected estimates

Mean Standard deviation

52 0.731 0.63 0.101

Bias-corrected estimates are based on the first stage of Algorithm #2 of Simar and Wilson

(2007).

b) Truncated regression

Variable Coefficient Confidence Interval

Lower bound Upper bound

Constant -1.859462 -3.851271 -0.216262

PODC -0.003560* -0.005480 -0.000712

PODYA 0.000054 -0.000131 0.000149

PODP 0.006640** 0.002014 0.010353

LI 0.085844** 0.049474 0.131246

MI -0.044075* -0.084589 -0.004426

CO 4.542467** 1.089310 7.847107

SIS -0.137264* -0.297773 -0.036946

LAP -0.014555** -0.027754 -0.007861

FR -0.366482* -0.517776 -0.119881

** Significant at 1% confidence interval; * Significant at 5% confidence interval;

Total number of iterations = 2000; Bold values present significant variables.



From this investigation of external sources of inefficiency of bus routes and the

identification of internal factors (service duration, space-km, and OTP) significantly

influencing the efficiency level of bus routes in sections 7.2 and 7.3, some recommendations

are provided in Table 7-25.



Table 7-25: Recommendations for performance improvement of inefficient bus routes

Recommendation Rationale Further considerations

Decrease service duration of inefficient bus routes in model 1 (technical efficiency measure) by increasing the operating speed of bus vehicles (or reducing the travel time of trips).

Slack variables in model 1 mainly occur for service duration (see Table 7-3).

Transit agencies need to consider the signalised intersection spacing, stop spacing, and transit priority system. Those factors potentially affect bus service duration.

Reduce the number of bus stops along some routes to ensure the appropriate distance between them (which varies from 0.4 to 0.6 km for urban area (Alterkawi 2006)).

Buses’ delay time at signalised intersections can be reduced by using transit signal priority on arterial roads.

The most inefficient bus routes for model 1 (such as routes 174, 175, 230, and 235) in the sample show that its signalised intersection spacing (less than 0.55) and stop spacing (less than 0.35) are significantly lower than the mean of the sample (which are 0.88 and 0.64 for signalised intersection spacing and stop spacing, respectively).

Reducing the total number of stops will help to decrease the total dwell time at stops, and then reduce the travel time of trips. However, it possibly has adverse effect on the route accessibility of passengers.

The service effectiveness can be improved for the most inefficient routes by reducing space-km and increase OTP.

Slack variables in model 2 mainly occur for space-km and OTP (see Table 7-4).

It is hard to reduce the number of trips per day, so smaller bus size should be applied on those routes to be appropriate to actual demand.

Bus routes on the street (such as routes 184 and 185) can be provided with separate lane on arterial roads by road marking to ensure the operating speed and increase OTP.

LAP positively affects the efficiency of bus routes in model 2 (see Table 7-24b).

Transit agencies need to balance the road space for other modes such as private cars and bicycle.

The timetable of bus routes should be adjusted to accommodate the actual congestion on the road.

Inefficient routes with an hour headway should be considered to increase its frequency to at least two trips per hour. Such as routes 113, 185, 310, 325, and 335.

Bus frequency (FR) was demonstrated to positively contribute the efficiency of bus routes (see Table 7-24b).

Transit agencies need to consider the overlap of these routes with rail and other high frequency bus routes, such as 111, 180, 330, and 333.

The timetable of some routes should be further investigated and modified to be more appropriate to the actual demand of residents within their service areas.

Route 200 following pattern 4 (see Table 6-5) has the highest efficiency scores at middle noon (which offers 4 trips per hour for a direction) and lower efficiency scores for peak periods. This route offers 7 trips per hour during the morning peak period for inbound and 9 trips per hour during the afternoon peak period for outbound.

Route 200 has a significant overlap with route 222, so further study should be conducted to examine whether this overlap has a negative impact on its inefficient performance, and whether there is a need to reduce the frequency of this route to save resources and make it more efficient during peak periods.



Transit operators are able to consider the recommendations proposed in Table 7-25

with further considerations to achieve the performance improvement of inefficient bus routes.

For example, for the morning peak hour (21st Aug 2013), the service duration that should be

reduced to improve the performance of inefficient bus routes regarding the technical

efficiency (model 1) is presented in Table 7-26. The space-km that should be reduced to

improve the performance of inefficient bus routes regarding the service effectiveness (model

2) is presented in Table 7-27

Table 7-26: Reduction of service duration for inefficient bus routes in model 1 (the morning peak hour)

DMU Efficiency

score

Reduction of service

duration (hour)

Route 112 0.699 0.23

Route 113 0.864 0.535

Route 116 0.754 0.756

Route 120 0.831 0.59

Route 124 0.726 0.536

Route 125 0.807 0.176

Route 155 0.855 0.028

Route 172 0.744 0.001

Route 174 0.742 1.304

Route 175 0.731 0.375

Route 180 0.797 0.413

Route 184 0.758 0.691

Route 185 0.793 1.389

Route 204 0.873 1.452

Route 210 0.722 0.142

Route 222 0.77 0.198

Route 230 0.765 1.144

Route 235 0.823 0.389

Route 310 0.815 0.091

Route 325 0.882 0.086

Route 345 0.888 0.859

Route 353 0.968 0.294



Table 7-27: Reduction of space-km for inefficient bus routes in model 2 (the morning peak hour)

DMU Efficiency score Reduction of

space-km

Route 100 0.913 1935

Route 105 0.5 1414

Route 110 0.843 1290

Route 112 0.54 729

Route 120 0.961 4311

Route 130 0.935 7921

Route 150 0.88 6202

Route 160 0.617 2846

Route 172 0.77 919

Route 184 0.586 880

Route 204 0.778 1975

Route 215 0.5 836

Route 346 0.667 2040

Route 353 0.835 567

Summary of Findings

The sample of the 52 bus routes in the case study of Brisbane was employed for

empirical analysis using proposed framework and NDEA models. The obtained results

indicate that bus routes have fairly good performance regarding the technical efficiency

measure (model 1), while the temporal and spatial performance varies significantly with

regards to the service effectiveness measure (model 2).

NDEA proved to be a good tool for the performance measurement of the bus routes,

including two linked sub-processes (technical efficiency and service effectiveness). Here,

node 2 plays an important role in the network model. Therefore, the performance

improvement of node 2 may significantly lead to the overall bus route performance

improvement.

Based on the efficiency scores obtained from model 1 and model 2 separately, and

for network model, 52 bus routes are ranked for every hour and key periods of time within a

day, as well as a full day. The benchmarks and the least efficient bus routes of the given

sample are identified. Furthermore, the internal factors, significantly affecting the efficiency

levels of bus routes, are identified. The empirical analyses show that, for technical efficiency

measurement (model 1) service duration is statistically associated with inefficient routes,



while for service effectiveness (model 2), space-km and on-time performance (OTP) have a

potential role in improving the performance of ineffective routes.

The comparison between results obtained from model 1 and model 2 indicates that

there is a weak correlation between the service production process and the service

consumption process. This is explained by the significant variations of bus ridership of

different routes, and different periods of time in a day of a single bus route. Thus, it is essential

to investigate the influences of external factors on the performance of bus routes, especially

factors related to the bus ridership.

Based on the data of external factors collected within the service corridor of individual

bus routes, the sensitivity of efficiency scores in model 2 to EVs was examined using the

double bootstrap model of Simar and Wilson (2007). The results demonstrate the significant

effect of eight out of nine selected EVs on the efficiency levels of DMUs. It is notable that

private car ownership (CO) and low-income group (LI) negatively affect the efficiency,

whereas population density of people under 18 (PODC) positively contributes to the efficiency

of DMUs. Those results are similar to the findings of Taylor, Miller et al. (2009). Furthermore,

the characteristics of bus routes (SIS and LAP) and service frequency (FR) are demonstrated

to be positively significant to the efficiency of DMUs. Those findings provide transit policy

makers with additional and useful information for decision making, which helps to improve

the operating environment of inefficient routes.

Based on the investigation of both internal and external sources of inefficiency,

several recommendations are also proposed to improve the performance of bus routes in the

case study. Here, the operating environment of bus routes should be improved by bus priority

systems (lane priority and signal priority) and appropriate distance between stops. This helps

to reduce service duration and increase OTP. Additionally, FR should be increased for

several routes with only an hour headway.

Conclusion and Recommendations


8 Conclusion and Recommendations

This chapter summarises the findings and contributions of this research; and provides

potential directions for future research. The main results obtained are summarised in section

8.1. Significant contributions are presented in section 8.2. Section 8.3 identifies the practical

implications and section 8.4 discusses the limitations of this research. Finally, section 8.5

provides recommendations for future research on this topic.

Summary of Research Findings

This research is carried out to evaluate the spatial and temporal performance of

individual bus routes composing a bus network, and investigate its sources of operational

inefficiency. Therefore, it is organised coherently to achieve the four research objectives

outlined in Section 1.6, Chapter 1:

Research objective 1: ‘Build up a framework to measure the operational

effectiveness of key bus routes within a bus network.’

Research objective 2: ‘Measure the temporal and spatial performance of key bus

routes within a bus network using the proposed framework in objective 1.’

Research objective 3: ‘Examine the influence of external variables on the efficiency

scores estimated in objective 2.’

Research objective 4: ‘Provide recommendations to transit agencies and policy

makers to improve bus route performance considering the knowledge generated

through the case study conducted.’

The first research objective was fulfilled by Chapter 2 (Literature review), Chapter

3 (Methodology), and Chapter 4 (Framework for bus routes performance measurement). The

role of each chapter is as follows:

o Chapter 2 first reviewed the approaches used for performance measurement of

bus systems in the literature (Section 2.1). This found that there are three main

approaches to measure the performance of a bus system, including (1)

Comparative Analysis (CA); (2) Stochastic Frontier Analysis (SFA); and (3) Data

Envelopment Analysis (DEA). Compared with CA, an approach using different

single productive ratios (an output/ an input) to compare bus route performance,

SFA and DEA are superior in dealing with DMUs with multiple inputs and outputs.

Both SFA (a parametric approach) and DEA (a non-parametric approach) are able

to generate an overall efficiency score of a given DMU based on the frontier



production function (the best DMUs within a set of DMUs). Therefore, most recent

studies that were reviewed have employed SFA and/or DEA for performance

measurement of bus systems. Although both SFA and DEA have their own

advantages and disadvantages, it is proven by Michaelides et al. (2010) that those

two approaches generate consistent results in general terms. The DEA model

requires no specific functional form for the production function, and the sensitivity

of DEA scores to data errors can be addressed by using AFC data, a fairly

accurate data source. Furthermore, Coelli et al. (1998) indicated that the SFA

approach is only well-developed for single-output technologies, and that in the

non-profit service area where multiple-output production is important and prices

are difficult to define, the DEA approach should be applicable. Thus, DEA is

employed for empirical analysis in this research.

Second, Chapter 2 reviewed bus performance evaluation using the DEA

models (in Section 2.2). The results indicated that bus performance is measured

at both system (DMUs are bus systems) and route levels (DMUs are bus routes

within a system). However, a limited number of studies focused on measurement

at the route level. Additionally, the performance measurement is separately

performed for two major bus performance concepts defined by Fielding et al.

(1985): (1) Technical efficiency; and (2) Service effectiveness. Those

performance concepts are coincided with the definitions of ‘productivity’ and

‘utilisation’ of Vuchic (2007), respectively. Therefore, there is a need to develop

a comprehensive framework for bus route performance measurement, which

considers both of these bus route performance concepts.

o Chapter 3 provided details about the CCR-DEA model (developed by Charnes,

Cooper, and Rhodes (CCR) in 1978) and the BCC-DEA model (developed by

Banker, Charnes and Cooper in 1984), and the network DEA model (NDEA)

developed by Färe and Grosskopf (2000). NDEA illustrates its ability to look into

the internal structure of a production process consisting of several linked sub-

processes, and generates a single overall efficiency score of DMUs. Therefore, a

NDEA model was selected for the development of framework for the examination

of bus routes’ performance.

o Chapter 4 developed the framework for bus routes’ performance evaluation with

appropriate inputs and outputs. This framework, consisting of two linked nodes (1

and 2), enables one to either evaluate the performance of bus routes for each



node separately (models 1 and 2 for nodes 1 and 2, respectively) or for the whole

network model. Particularly, ‘transit work’ was used to present the service

consumption in this model. This offers a more accurate output compared to the

definition of ‘passenger-km’ in preceding studies. The first research objective

was fully achieved by the development of the NDEA-based framework for bus

route performance evaluation in this chapter.

Research objective 2 was performed by Chapter 5 (data collection), Chapter 6

(Data analysis for individual bus routes of the case study), and Chapter 7 (Empirical analysis

for bus system of the case study). The achievement of this objective was established through

two stages of empirical analysis. The first stage was to understand the temporal performance

of individual bus routes (Chapter 6), and the second stage was to measure the spatial and

temporal performance of several bus routes of the case study (Chapter 7). Details are as

follows:

o Chapter 5 provided the methods for data collection of both internal (Section 5.2)

and external variables (Section 5.3). Regarding internal variables, a dataset of

52 key bus routes of the case study were collected for a period of one working

week, from Monday 19th to Friday 23rd August 2013. Bus performance indicators

were drawn from AFC data supplied by TransLink Division of Queensland

Department of Transport and Main Roads, Australia. Relevant variables such as

route length, section length between stops, and timetable were obtained from the

TransLink website (http://translink.com.au).

External variables (EVs) were collected for the sample of 52 bus routes

using ArcGIS and ABS 2011 Census. For a single bus route, the service corridor

was first created using a stop buffering method. The EVs’ data were then

calculated within the service corridor of corresponding route using ABS 2011

Census at the Statistical Areas Level 1 (SA1), which is the most detailed level of

demographic and socio-economic data. Therefore, this method offered the

opportunity to obtain the best EVs for each route.

o Chapter 6 illustrated the results obtained from the temporal performance of

individual bus routes. Here, the DMUs are the performance of a single bus route

for different hours across all working days of a week. This chapter examined the

temporal performance of Route 111 across 19th August 2013 and compared the

results obtained from DEA models (CRS and VRS model) for inbound direction

with two basic transit productiveness indexes (Transit work load factor and Transit




passenger transmission efficiency). It was found that DEA provides additional

advantages in dealing with DMUs consisting of multiple input and output variables,

and that for one direction of a bus route, CRS-DEA efficiency score is closer to

basic transit productiveness indexes than VRS-DEA efficiency score. Additionally,

bus route performance is more efficient during peak periods than off-peak periods

across a day.

This chapter also examined the temporal performance of individual bus

routes using a CRS model. A total of 52 bus routes are categorised into three

clusters: (1) high frequency; (2) low frequency for a long service period; and (3)

low frequency for a short service period. The results indicated that cluster 1

achieves stable efficiency scores of a given hour over different days, while clusters

2 and 3 experience significant variations in efficiency scores of DMUs across

different weekdays. Thus, bus frequency possibly affects the service

consumption of each bus route, and should be examined in the second stage of

analysis. Finally, six different patterns of the changes of efficiency scores of each

route across the daytime were identified on the basis of the results.

o Chapter 7 presented the results obtained from the temporal and spatial

performance analysis of 52 bus routes. An output-oriented NDEA model was

employed for empirical analysis with DMUs being the performance of different bus

routes during a given period of time (an hour, peak/off-peak periods within a day,

and a day). The NDEA model was proven to be a good tool for bus routes’

performance measurement.

Based on the efficiency scores obtained from model 1 and model 2

separately, and from the network model, 52 bus routes were ranked for each

model for different periods of time, especially for a day. The benchmarks and the

least efficient bus routes of the given sample were identified.

Furthermore, the internal factors, significantly affecting the efficiency levels

of bus routes, were identified. The analyses showed that, for technical efficiency

(model 1), service duration is statistically associated with inefficient routes, while

for service effectiveness (model 2), space-km and on-time performance (OTP)

have a potential role in improving the performance of ineffective routes.

Research objective 3 was fulfilled by Chapter 5 (data collection) and Chapter 7

(Data analysis for bus system of the case study). Based on the data of external factors



collected within the service corridor of individual bus routes in Chapter 5, the sensitivity of

efficiency scores in model 2 to EVs was examined using the double bootstrap model of Simar

and Wilson (2007) in Chapter 7. The results demonstrated the significant effect of eight

out of nine selected EVs on the efficiency levels of DMUs. It was observed that private

car ownership (CO) and low-income group (LI) negatively affected the efficiency levels,

whereas population density of people under 18 (PODC) positively contributed to the efficiency

of DMUs. These results coincide with the findings in literature. Furthermore, the

characteristics of bus routes (SIS and LAP) and service frequency (FR) were demonstrated

to be positively significant to the efficiency of DMUs. This result clarified the hypothesis in

Chapter 6 that high frequency routes attract more regular passengers than low frequency

bus routes.

Research objective 4 was given by Chapter 7. Here, both internal and external

factors contributed to the performance of bus routes. Reducing service duration of inefficient

routes is one of the solutions to improve the technical efficiency of the bus route. The increase

of on-time performance (OTP) and decrease of space-km may be solutions to improve the

service effectiveness. Regarding the operating environment of bus routes, the increase of

SIS and LAP for some inefficient bus routes should be considered to reduce the delay time

and offer better LOS. Another solution is that the timetable of some inefficient routes should

be modified with the careful consideration of travel behaviour of local residents.

Research Contributions

The principal contribution of this research is that it has developed a comprehensive

approach to provide insight into the temporal and spatial performance of bus transit,

considering the influences of external factors on bus routes’ performance. Through a logical

process, the achievement of the four research objectives has made several contributions to

transit knowledge in the course of conducting. Those contributions are as below:

o This research developed a network DEA-based framework for performance

evaluation of bus routes. As indicated in the literature review chapter, bus route

performance was explicitly examined for a particular performance concept

(technical efficiency or service effectiveness). The proposed network

framework, thus, provides transit professionals with an overall and single measure

for bus route performance evaluation (operational effectiveness). It allows one

to evaluate the operational effectiveness of individual bus routes, accounting for

both linked sub-production processes: technical efficiency and service

effectiveness. Thus, the results obtained from the NDEA model were



demonstrated in section 7.3 to be superior to those obtained from traditional

method (aggregate model).

o This research has addressed research gaps identified in Chapter 2 by employing

AFC data and 2011 ABS Census Data at SA1. AFC data was used for extracting

actual bus performance indicators such as travel time, OTP, space-km, and

transit work. Those actual bus performance indicators were then utilised as

inputs and outputs in DEA models to generate the most reliable results. ABS

Census Data at SA1 was used to calculate EVs (socioeconomic and demographic

characteristics) within the service corridor of a single bus route. Those EVs were

used in the truncated regression model (the Bootstrap model) to investigate the

impact of EVs on the efficiency levels of bus routes (refer to table 7-24).

o This research is the first of its kind that has investigated the temporal performance

of 52 individual bus routes using the case study in Brisbane, Australia, across a

working week (from 19th to 23rd August 2013). The results provided further

understanding of the temporal performance of those bus routes as follows: the

performance of bus routes are more stable during the daytime than the evening

time; high frequency routes attract more regular passengers than low frequency

routes; the changes of efficiency scores across the daytime of given bus routes

may follow six different patterns (refer to Table 6-5); and pattern 1 is the most

popular pattern for high frequency bus routes.

o The temporal and spatial performance of 52 bus routes of the case study in

Brisbane was sufficiently evaluated in this research using a NDEA model. Those

bus routes were examined for model 1 and model 2 separately, and for the

network model across different periods of time (every hour, key periods of time

within a day, and a full day). Bus routes were ranked to identify the benchmarks

and the most inefficient routes. Furthermore, through the values of slack variables,

this model helped to identify the internal sources of inefficiency and the

quantitative reduction of inputs/increase of outputs for the performance

improvement of those bus routes (refer to tables 7-26 and 7-27).

o Using the case study in Brisbane, Australia, this research is the first of its kind that

investigated the sources of inefficiency of given bus routes related to

socioeconomic and demographic characteristics within the service corridor of a

single bus route. It identified the significant influence of eights EVs on efficiency

of bus routes. Some EVs, such as CO, PODC, and LI, illustrated the coincided



results with findings in preceding studies, that were implemented at the urban area

level (EVs are collected for different urban areas). Thus, the knowledge gained

help to substantiate the existing findings in literature. Moreover, the results of

other EVs, like PODP, LAP, and FR, presented the additional findings for this case

study.

o This research has provided transit agencies and regulators in Brisbane with

additional information for policy making, which helps to optimise the performance

of the current transit system of this area (refer to section 8.3).

Practical Implications

The approach developed in this research can be used by transit professionals for

developing more practical and appropriate policies, which may help to improve the

performance of the current transit system, as well as support the planning of new routes.

Figure 8-1 presents the process in which regulatory rules and policies are made based on

additional information provided by the efficiency analysis process. The regulatory rules and

socio-economic policies made by regulators have an impact on the transit operating

environment: the external factors (such as private car ownership, parking facility, transit

accessibility, road system, traffic condition, and employment distribution) and the

management behaviour of transit agencies. Within a transit agency, decision making and

actions are made to offer better services for a community, which directly relate to the internal

factors (schedule, stops, priority lane, route length, and service coverage). Both internal and

external factors then significantly affect the service consumption of a target community.

Finally, analysing the performance efficiency of routes is useful to identify the benchmarking

routes, the most inefficient routes, and sources of inefficiency, and then effectively assist

transit operators and regulators in policy making.

This approach was developed for the bus mode of the case study in Brisbane. It is

transferable to bus networks of other cities. Furthermore, this approach could be applied to

other transit modes such as ferry and rail with the availability of AFC data.

Making decision is always a complicated process in transit sector, as it belongs to

public services and relevant to political, social and economic aspects. Therefore, based on

the empirical analysis, this study proposes some possible ways to addressed operational

problems of bus routes in the case study of Brisbane. Applicable policies should be made by

each transit agency based on different information and tools. To achieve the performance

improvement of the bus network in Brisbane, transit operators are able to consider the

recommendations provided in Table 7-25, including:



• Decrease service duration of inefficient bus routes in model 1 (Routes 174, 175,

230, and 235) by reducing travel time of trips. The travel time of trips could be

reduced by increasing the stop spacing by increasing the stop spacing (reduce

the stops) and/or providing transit signal priority at signalised intersections on

arterial roads.

• Ensure the appropriate distance between stops from 0.4 to 0.6 km for some bus

routes crossing urban areas (Routes 174, 175, 230, and 235) to reduce the travel

time of trips.

• Use transit signal priority on arterial roads to reduce delay time at signalised

intersections of some bus routes, such as routes 184 and 185 (refer to variable

SIS in table 7-24).

• Reduce space-km and increase OTP for inefficient routes in model 2 (Routes

155, 184, 185, 200, 325, and 335).

• Provide a separate lane for buses on arterial roads by road marking (such as

routes 174 and 175).

• Increase FR of some routes (such as 113, 185, 310, 325, and 335).

• Further investigate and modify the timetable of some routes (such as route 200)

to be more appropriate to the actual demand (overlap with rail or express bus).

Figure 8-1: Policy implications of transit routes performance analysis

Regulators

Policies and

regulatory rules

Transit operating

environment(external variables)

Service

consumption

Transit

agencies

Decision making

and actions

Service outputs(internal variables)

Efficiency

analysis

DEA

models

Truncated

regression

models



Limitations

Below is the list of limitations for the current research, largely due to data availability

and limited resources:

o The bus network of the case study in Brisbane consists of more than 250 bus

routes, while this research only employed a sample of 52 radial bus routes of this

case study for empirical analysis. Thus, the results achieved only introduce the

performance of several key routes within the network. With the availability of data

from other routes, the research can be extended to other routes for a

comprehensive analysis of the entire Brisbane network.

o Data in this research is collected from AFC data for only one working week

(Monday to Friday) in August 2013. Thus, it excluded weekends and public

holidays, where actual bus demand may change significantly because of many

public events. The timeframe of one week could not provide a longitudinal

performance evaluation of given bus routes.

o Regarding internal variables used in the proposed framework, some service

inputs, such as fuel consumption, operating cost, and maintenance cost, were

unavailable at the route level of the case study. Therefore, this research uses

proxies to refer to those service inputs. Additionally, this research estimates the

OTP at the destination of bus routes only because of the lack of arrival time at all

intermediate stops when extracting this indicator from AFC data.

o In terms of external variables, this research employed a number of variables

related to population, individual income, car ownership, and route characteristics

only. Other factors, such as weather, employment structure, and travel behaviour

of users were not considered. Moreover, external variables are calculated by

using information from ABS 2011 Census Data while AFC data in August 2013

were employed to generate inputs and outputs for DEA models. This two-year

delay of data collection may lead to bias on the obtained results of the sensitivity

analysis of efficiency scores. To demonstrate the applicability of the proposed

methodology, it is assumed that the changes of those external variables over the

period of two years are not significant.

o This research examined the performance of bus routes without considering the

impacts of other transit modes (such as ferry and especially rail) on bus demand.

Additionally, the linkage between bus routes was not considered.



o There are several ‘Park and Ride’ facilities in the case study, which may influence

the ridership of some nearby bus routes. In this research, ‘Park and Ride’ near the

service corridor of some bus routes was not taken into account.

o This research provides the performance evaluation of an entire bus route based

on data of complete trips. It represents the macro level of the average

performance along the route. The micro level of performance over different

segments of a route is not considered.

Recommendation for Future Research

This research has focused on the temporal and spatial performance evaluation of bus

routes in Brisbane, Australia. There are still several areas that need to be carried out in future

studies. The most potential areas for future research are as below:

o It would be useful to conduct a similar research in the future using a larger sample

of the case study in Brisbane (greater number of bus routes and longer period of

time). This sample should consist of both radial bus routes and local routes

connecting different suburb areas with each other. Such research would provide

more comprehensive results for this case study.

o This research has considered bus routes as DMUs in the DEA model. It would be

useful to carry out similar research in the future, which considers segments

composing a route as DMUs. The performance evaluation of transit routes at the

segment level would provide insights into the performance of each segment, as

well as identify the least efficient segments along a single route. This will assist

transit agencies effectively in making accurate decisions for system optimisation.

o This research only examined the performance of bus routes across working days

of a week. Future research, thus, can upgrade the approach developed in this

research to investigate the performance of bus routes in Brisbane on weekends

and public holidays to extend the findings.

o This research has employed several EVs to investigate the external sources of

inefficiency. However, a wide range of other EVs, in reality, may affect the

efficiency of bus routes such as employment distribution, the present of railway

on the bus corridor, stops accessibility, parking space availability, and the

presence of attraction points (schools, hospitals, shopping centres, recreation

centres). Therefore, future research can apply the proposed approach to examine

the influence of other EVs on bus efficiency.



o Although bus mode dominates in Brisbane, rail and ferry are important transit

modes in this area. Thus, it would be useful to conduct research on rail or ferry

system using the approach developed in this research with some necessary

adjustments.

o A non-parametric approach, the DEA model, was used in this research for

empirical analysis. However, SFA (a parametric approach) was demonstrated to

be a good tool for efficiency analysis of DMUs. Thus, it would be useful to carry

out research where SFA would be employed to examine bus route performance.

Furthermore, both DEA and SFA can be used in the future research together, and

then the results obtained from those two methods can be compared to explore the

work of each method.

Reference


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Appendix


SPATIAL EFFICIENCY SCORES OF INDIVIDUAL

BUS ROUTES

This appendix provides the spatial performance of remaining individual bus routes within the

given sample (Chapter 6).

Figure A 1: CRS-DEA efficiency score of route 180 (follows pattern 1)


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Appendix


DISCUSSION ON SLACKS

Coelli, Prasada Rao et al. (1998) indicated that the piece-wise linear form of the non-

parametric frontier in DEA can cause a few difficulties in efficiency measurement. The

problem arises because of the sections of the piece-wise linear frontier which run parallel to

the axes (see Figure B 1) which do not occur in most parametric functions. Refer to the Figure

B 1 where the firms use two inputs (x1 and x2) to produce an output y, C and D are the two

efficient firms that define the production frontier (SS’). Firms A and B are inefficient firms

within the production possibility set T. The Farrell (1957) measure of technical efficiency gives

the efficiency level of firms A and B as OA’/OA and OB’/OB, respectively. However, it is

questionable as to whether the point A' is an efficient point since one could reduce the amount

of input x2 used (by the amount CA') and still produce the same output. This is known as

input slack (𝜽𝒙𝒊 − 𝑿𝝀 = 𝒔−) in the literature. Once one considers a case involving more

inputs and/or multiple outputs, the diagrams are no longer as simple, and the possibility of

the related concept of output slack (𝒀𝝀 − 𝒚𝒊 = 𝒔+) also occurs (for the given optimal values

of 𝜽 and 𝝀).

Some authors argue that both the Farrell measure of technical efficiency (θ) and any

non-zero input or output slacks should be reported to provide an accurate indication of

technical efficiency of a firm in a DEA analysis (Tone, Cooper et al. 1999, Cooper, Seiford et

al. 2007). Thus, it can be stated that the i-th firm is completely efficient if its efficiency score

equal 1 and the input and output slacks are equal to zero (𝒔− = 𝟎 𝒂𝒏𝒅 𝒔+ = 𝟎).

Figure B 1: Efficiency Measurement and Input Slacks (Source: Coelli, Prasada Rao et al. (1998))

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Appendix


EXAMPLES FOR DETAILED SAMPLE CALCULATION USING THE DEA MODELS

This appendix presents several examples for detailed empirical analysis of the given sample, using the DEA models. This research uses

Matlab codes and MaxDEA Pro software for data empirical analysis. Here, the slack movement of inputs is presented by negative values.

Table C 1: CCR-DEA efficiency scores of route 111 obtained from temporal performance analysis in Chapter 6 (the date 19th Aug 2013)

Note: PM: proportionate movement; SLM: slack movement; PR: projection

Appendix


Table C 2: BCC-DEA efficiency scores of route 111 obtained from temporal performance analysis in Chapter 6 (the date 19th Aug 2013)


Appendix


Table C 3: BCC-DEA efficiency scores of 52 bus routes obtained from empirical analysis of node 1 (7:00 to 8:00, the date 21st Aug 2013)

Appendix



Appendix


Table C 4: BCC-DEA efficiency scores of 52 bus routes obtained from empirical analysis of node 2 (7:00 to 8:00, the date 21st Aug 2013)

Appendix



Appendix


Table C 5: NDEA efficiency scores of 52 bus routes obtained from empirical analysis (7:00 to 8:00, the date 21st Aug 2013)

Appendix



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