concluding panel mahmassani comments vancouver 10.09

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Incorporating Reliability Performance M i E l ti T lMeasures in Evaluation Tools: Physics, Psychology and Economists

International Conference on Travel Time Reliability

Vancouver, BC

October 15‐16, 2009,

Reliability and Project EvaluationReliability and Project Evaluation

• People care about reliabilityPeople care about reliability

• Reliability affected by both Design, Operation, and Managementand Management

• Reliability affected by user behavior: in h lresponse to management, over the long run

• Challenges for project evaluation: reference for comparison

3

Reliability and System ManagementReliability and System Management

• Traffic physics: human behavior causesTraffic physics: human behavior causes unreliability– inherent randomness, collective effectseffects

4

Flow Breakdown

• Flow breakdown is a collective phenomenon resulting from many individual decisionsindividual decisions

• While some of its aspects are predictable and systematic, flow breakdown remains an inherently stochastic phenomenon

• Empirical studies have documented that breakdown might occur with some probability at various flow rates.

80

100

120

1500

2000

2500

mph

)

(vph

pl)

Pre-breakdown Breakdown Recovery Breakdown

0

20

40

60

0

500

1000

1500Sp

eed

(m

Flow

rate

(

5

5:00

5:30

6:00

6:30

7:00

7:30

8:00

8:30

9:00

9:30

10:0

0

10:3

0

11:0

0

Time (AM)

Flow

Speed

Flow Breakdown and Travel Time Reliability

• Pre‐breakdown and breakdown flow rates are viewed as random variables

Flow Breakdown and Travel Time Reliability

• The difference between two distributions indicates “capacity drop” during flow breakdown (Banks, 1991; Cassidy and Bertini, 1999).

• During flow breakdown extra delay is encounteredg y

0.91

tion Pre-breakdown 25

0.40.50.60.70.8

dist

ribut

ion

func

t

Breakdown

Extra d l ′

10

15

20

congested

uncongested

00.10.20.3

1000 1500 2000 2500 3000

Cum

ulat

ive

d delay t′

0

5

0 1000 2000

Flow rate (vphpl)

uncongested

Flow rate (vphpl)

6

Flow rate (vphpl)

Probabilistic Description of Flow BreakdownProbabilistic Description of Flow Breakdown

• Pre‐breakdown flow rate is viewed as a random variable

• MLE of the pre‐breakdown flow rate distribution function based on censored observations

• Kaplan‐Meier estimate provides the empirical distribution

I-405N Jeffrey section I-405N Red Hill section

0 80.9

1

nctio

n

0 80.9

1

unct

ion

0 30.40.50.60.70.8

e di

strib

utio

n fu

n

0 30.40.50.60.70.8

ve d

istri

butio

n fu

EmpiricalWeibullLogistic

00.10.20.3

1000 1500 2000 2500 3000

Cum

ulat

iv

00.10.20.3

1000 1500 2000 2500 3000

Cum

ulat

iv LogisticNormal

Pre-breakdown flow rate (vphpl) Pre-breakdown flow rate (vphpl)

7

A Markov Chain Approach to Model kd b bili f i iBreakdown ‐ Probability of Transition

• The transition probability pij pertains to the probability of moving from state i to state j.

• The transition probability matrix, P=[pij], is estimated by MLE.

Sjipij ∈∀≥ ,,0 Sipij ∈∀=∑ ,1Sjipij ,,0 SipSj

ij ∈∀∑∈

,1

8

Travel Time DistributionTravel Time Distribution

20

25

10

15

20

rave

l tim

e in

dex

0

5

0 500 1000 1500 2000 2500

Tr

Flow rate (vphpl) 80Flow rate (vphpl)

23456

10

20

30

40

50

abili

ty d

ensi

ty

func

tion

Freq

uenc

y

0.40.60.811.21.4

20304050607080

babi

lity

dens

ity

func

tion

Freq

uenc

y

01

0

10

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Prob

a

Travel time index1

1.5

2

40

60

80

lity

dens

ity

nctio

n

requ

ency

00.2

010

00.

5 11.

5 22.

5 33.

5 44.

5 5

Pro b

Travel time index

9

0

0.5

0

20

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Prob

abi

fun

Fr

Travel time index


• Traffic physics: human behavior causesTraffic physics: human behavior causes unreliability– inherent randomness, collective effects

• Management affects travel time reliability:• INFORMATION affects reliabilityy• PRICING affects reliability• INTEGRATED TRAFFIC MANAGEMENT affects reliability

10

ANTICIPATORY INFORMATION AFFECTS RELIABILITY

4050607080

(mph

)

10001200140016001800

e (v

phpl

)

Travel time information

010203040

Spee

d

0200400600800

Flow

rate

Reliability & Travel time information

• Providing travel reliability information contributes to delaying the

7:00 7:30 8:00 8:30 9:00 9:30 10:00 10:30Time (AM)

7:00 7:30 8:00 8:30 9:00 9:30 10:00 10:30Time (AM)

• Providing travel reliability information contributes to delaying the onset of breakdown and alleviating its extent

• Higher and more stable flow is observed under the reliability scenario, indicating an increase in freeway throughput

11

indicating an increase in freeway throughput

Effectiveness: Average Travel TimeEffectiveness: Average Travel Time

4550

te)

2025303540

avel

tim

e (m

inut

Travel time information

05

101520

Aver

age

tra Reliability & Travel time information

• Scenarios:

7:00 7:30 8:00 8:30 9:00

Departure time (AM)

only anticipatory travel time information is provided

both anticipatory travel time and reliability information is available

• Significant time savings are observed when travel reliability

12

information is provided in addition to travel time information

ANTICIPATORY PRICING AFFECTS RELIABILITY

• Concentrations averaged over links along the congested portion of toll road, weighted by the link length

RELIABILITY

• Throughput measured at downstream of where traffic breaks down in base case (no pricing)

• Anticipatory pricing strategy can provide higher throughput while t c pato y p c g st ategy ca p o de g e t oug put emaintaining lower concentration (steady traffic flow)

Throughput vs ReliabilityThroughput vs. Reliability

reliability

BreakdownBreakdown

throughput


• Traffic physics: human behavior causes a c p ys cs: u a be a o causesunreliability– inherent randomness, collective effects

• Management affects travel time reliabilitySo what are we exactly evaluating? Well managed or poorly managed future systems?

• Psychology: user response and adaptation affects li bilitreliability

15

Behavioral ConsiderationsBehavioral Considerations

• “Indifference band” of arrival times in congested situations:People not only adjust their decisions but also adjust indifference band in response to experienced fluctuations in performance

• In real systems, users cope with complexity using simple rules: buffer time safety margin– confounded with perception/judgmentbuffer time, safety margin confounded with perception/judgment

• Conventional SP exercises limited in uncovering underlying preferences; games, laboratory experiments, experimental economics more promisp

• Strong interactive effects that suggest that system may be in dynamic disequilibrium rather than stationary equilibrium

• Risk attitudes: risk seekers prefer variability– experimental d ( ) h d f h h hevidence (Bogers, 2009) that some drivers prefer routes with high

variability hoping to attain lower travel times…• Assumption of users facing stationary and known (and

understood ) distribution of travel times highly questionableunderstood…) distribution of travel times highly questionable

16

Network Traffic PhysicsNetwork Traffic Physics

• Strong correlation between travel times in different parts of the network

d l k l k l h h d l– Adjacent links are likely to experience high delays in the same general time period than unconnected links

– Difficult to capture these correlation patterns when p ponly link level measurements are available

– Difficult to derive path‐level and OD‐level travel time distributions from the underlying link travel time distributions from the underlying link travel timedistributions

– Link‐level relations not robust

17

Travel Time ReliabilityStandard Deviation vs. Average Travel Timeg(Greater Washington, DC network: OD level variability)

0.9000.9501.000

on

0.7500.8000.850

d de

viat

io

No_buildCorridor I

0.6000.6500.700

Stan

dard Corridor I

0.5000.550

1.500 1.700 1.900 2.100 2.300 2.500

Avg. travel time (min/mile)

Derived from static assignment model results under ergodicity assumptions

1.1000

0.9000

1.0000

iatio

n

N b ild0.8000

dard

dev

i No_buildCorridor ICorridor II

0.6000

0.7000

Stan

d

0.5000

Avg. travel time (min/mile)g ( )

Irvine Network

• Network

Irvine Network

Network– Freeways I‐405, I‐5, state

highway 133

– 326 nodes326 nodes

– 626 links

– 61 TAZs

• Demand• Demand– Two hours morning peak

(7‐9AM)

20

Path Travel Time and Standard Deviation

• Each data point represents the mean and standard

Path Travel Time and Standard Deviation

Each data point represents the mean and standard deviation of travel times for all the vehicles (over the entire planning horizon) traveling on one path.

• Only paths with more than 10 vehicles are considered

14

8

10

12

14

Deviation

0

2

4

6

Stan

dard

0 5 10 15 20 25

Path Travel Time (minute)

21

OD Travel Time and Standard Deviation


OD Travel Time and Standard Deviation

Each data point represents the mean and standard deviation of travel times for all the vehicles (over the entire planning horizon) traveling between one OD pair.

10

12

4

6

8

10

dard Deviation

0

2

4

0 5 10 15 20

Stan

OD Travel Time (minute)

22

Network Travel Time per Unit Distance and d d ( l)


Standard Deviation (5 minute interval)

Each data point represents the mean and standard deviation of travel times per mile for all vehicles departing in 5‐minute interval.

• 24 data points for 2‐hour demand

1.82

0 60.81

1.21.41.6

dard Deviation

00.20.40.6

1 1.2 1.4 1.6 1.8 2

Stan

Network Travel Time per Distance (minute/mile)

23

Network Travel Time per Distance and d d ( l)


Standard Deviation (1 minute interval)



1.82

0 60.81

1.21.41.6

dard Deviation

00.20.40.6

1 1.2 1.4 1.6 1.8 2

Stan


24

Network Travel Time per Distance withl h l


Sampling Vehicles



1 82

0.81

1.21.41.61.8

ard Deviation

100% Sample

10% Sample

00.20.40.6

1 1.2 1.4 1.6 1.8 2

Stan

d


25

CHART Network

• Network

CHART Network

Network– I‐95 corridor between

Washington, DC and Baltimore, MD, US

– 2241 nodes

– 3459 links

– 111 TAZ zones

• Demand– Two hours morning peak

(7 9AM)(7‐9AM)

26

OD Travel Time per Unit Distance and d d


Standard Deviation

Each data point represents the mean and standard deviation of travel times per mile for all the vehicles (over the entire planning horizon) traveling between one OD pair.

6

3

4

5

ard Deviation

0

1

2

0 2 4 6 8 10

Stan

da

0 2 4 6 8 10

OD Travel Time per Distance (minute/mile)

27

Network Travel Time per Unit Distance h l h l


with Sampling Vehicles



1 82

0 81

1.21.41.61.8

ard Deviation

100% Sample

00.20.40.60.8

1 1 2 1 4 1 6 1 8 2

Stan

da

100% Sample

10% sample

1 1.2 1.4 1.6 1.8 2


28

Network Travel Time per Unit Distance with iff d l (C i l)

• Low demand: 80% of the peak hour demand

Different Demand Level (Congestion Level)

Low demand: 80% of the peak hour demand

• High demand: 100% of the peak hour demand

1.4

1.6

1.8

2

on

0 4

0.6

0.8

1

1.2

Stan

dard Deviati

High demand

Low demand

0

0.2

0.4

1 1.2 1.4 1.6 1.8 2


29

Network Travel Time per Unit Distance h ff k

• The mean travel time per mile range is comparable,

with Different Networks

The mean travel time per mile range is comparable, which indicates similar congestion level

• CHART network shows lower variation in travel times

1 4

1.6

1.8

2

n

0.6

0.8

1

1.2

1.4

Stan

dard Deviatio

CHART

Irvine

0

0.2

0.4

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

Network Travel Time per Distance (minute/mile)p ( / )

30

Concluding CommentsConcluding Comments

• Many things could be done in the short termMany things could be done in the short term to reflect reliability considerations; robust relation between SD and Mean of trip timerelation between SD and Mean of trip time PER MILE

• DTA plus robust analytical relations on supply• DTA plus robust analytical relations on supply side, w. Vovsha’s approaches to utility valuation provide low hanging fruitvaluation provide low hanging fruit

31

Concluding CommentsConcluding Comments

• Required: a more fundamental perspective on project and system evaluation that recognizes:

• Traffic physics and role of system management:• Traffic physics and role of system management: controllability and opportunities for intervention

• Short and long term dynamics of user judgment and behaviorbehavior

• Network spatial and temporal dynamics• Relevance of “external” events (accidents, weather) to evaluation frame of referenceevaluation frame of reference

• Connection between individual attitudes towards risk and social preferences

32

concluding panel mahmassani comments vancouver 10.09

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