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DOI: 10.1177/0042098012452324

2013 50: 191 originally published online 19 July 2012Urban StudTufayel A. Chowdhury, Darren M. Scott and Pavlos S. Kanaroglou

SpaceUrban Form and Commuting Efficiency: A Comparative Analysis across Time and

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Urban Form and Commuting Efficiency:A Comparative Analysis acrossTime and SpaceTufayel A. Chowdhury, Darren M. Scott and Pavlos S. Kanaroglou

[Paper first received, June 2011; in final form, May 2012]

Abstract

In this paper, a method is proposed that relates several measures of average com-mute distance (actual, minimum, maximum) explicitly to urban form. Specifically,Brotchies urban triangle is modified to represent the commuting benchmarks (min-imum and maximum commutes) and urban form of a city. By comparing the urbantriangle of a city at different points in time, it is possible to determine whether com-muting behaviour is becoming more or less efficient with respect to urban form.Also, comparisons can be made across multiple cities for a specific point in time.The method is applied empirically to examine the commuting efficiencies of three

Canadian cities (Hamilton, Halifax and Vancouver) for three census years (1996,2001 and 2006). Comparative analyses reveal the drawbacks of the excess commutingand commuting potential utilised approaches and demonstrate that the proposedmethod overcomes these limitations.

1. Introduction

Understanding the relationship between

urban form and travel behaviour has

inspired transport researchers for decades(Badoe and Miller, 2000; Shiftan, 2008;

Ewing and Cervero, 2010). One line ofresearch in this domain concerns excess or

wasteful commuting, which was introduced

by Hamilton in 1982. Since that time, the

literature on excess commuting has grown

considerably, as suggested by a recent

review of the subject by Ma and Bannister(2006). Excess commuting is the difference

between the actual average commute1 andthe theoretical minimum average commute

expressed as a percentage of the actual aver-

age commute.2 The minimum commute is

Tufayel A. Chowdhury, Darren M. Scott (corresponding author) and Pavlos S. Kanaroglou are inthe School of Geography and Earth Sciences, McMaster University, 1280 Main Street West,

Hamilton, Ontario, L8S 4K1, Canada. E-mail: [email protected]; [email protected]; and [email protected].

Urban Studiesat 5050(1) 191207, January 2013

0042-0980 Print/1360-063X Online 2012 Urban Studies Journal Limited

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the average commuting distance (or time)if every worker worked at the nearest joblocation from home. Thus, the minimumcommute represents a perfect jobshousing

balance scenario (Giuliano and Small,1993) and is therefore considered to be ameasure of urban form (Yang and Ferreira,2005).

Comparing the actual commute with theminimum commute is a way to understandthe connection between peoples commutingbehaviour and urban form. Understandingthis connection can help to set urban growthstrategies (Yang, 2008). Although modelling

the relationship between individual com-muting behaviour and urban form mayseem to be more appealing simply becauseof its behavioural robustness, examiningcommuting behaviour from a system per-spective is also beneficial. The advantagehere is that the spatial scope of such analysisis much broader, to the level of a city (Frostet al., 1998) or a region (Murphy, 2009),

and comparisons can be made across citiesand across time for a particular city.Excess commuting is often used to evalu-

ate the commuting efficiency of cities. In theexcess commuting literature, commuting effi-ciency is defined as the degree to whichpeople live near their jobs (Scott et al., 1997,p. 245). Put another way, commuting effi-ciency is a measure of how much actual com-muting deviates from optimal behaviour,

given a citys urban form (defined as the spa-tial arrangement of jobs and workers house-holds). More recently, commuting potentialutilised has also been used to evaluate com-muting efficiency. This method, developed byHorner (2002), is an extension of the excesscommuting framework. Here, the actualcommute is compared with theoretical mini-mum and maximum commutes to determinethe commuting efficiency of a city.

In this paper, an alternative method toassess commuting efficiency is proposedone that relates measures of average

commuting distance (actual, minimum,maximum) explicitly to urban form. A keyfeature of this approach is the point of ref-erence for measuring commuting efficiency.

This point is defined by two conditions:jobshousing balance in spatial units (suchas census tracts or traffic analysis zones)and an observed commute that equals thetheoretical minimum commute.3 The pro-posed method overcomes issues concerningthe use of traditional metrics in compara-tive analyses of commuting efficiency. Forexample, excess commuting should alwaysbe lower in a monocentric city than in a city

where jobs are decentralised. Thus, if twocities have the same observed commute, themonocentric one would have little to noexcess commuting and would seem to bemore efficient. However, the other city,which has a more balanced jobshousingdistribution at the local level and thus abetter chance of lowering the observedcommute, is in fact more efficient than the

monocentric city.As is discussed later in this paper, com-muting potential utilised is biased by citysize. The proposed method overcomes city-size bias. Specifically, it extends Brotchiesurban triangle to accommodate the mini-mum and maximum commutes. Brotchiestriangle was first used by Brotchie (1984) toillustrate how changes in technology wouldimpact work-trip length. In the excess com-

muting literature, Ma and Banister (2007)used the triangle to explain their simulationresults. The study presented in this papermodifies Brotchies original triangle todetermine the commuting efficiency of acity. The method is demonstrated empiri-cally by comparing the commuting efficien-cies of three Canadian cities across timeand by comparing the same cities at a par-ticular point in time.

The contributions of this study to theexcess commuting literature are twofold.First, the study discusses drawbacks of the

192 TUFAYEL A. CHOWDHURY ET AL.

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two commonly used metrics to measure

commuting efficiency and offers ways toovercome these limitations. Secondly, the

study provides an alternative method for

determining the commuting efficiency of acity. The most appealing aspect of this

method is that it does not require addi-tional data other than what are already

needed to compute commuting potential

utilised.In terms of policy, the proposed method

can be used to determine how far a city isfrom achieving jobshousing balance and

optimal commuting behaviour. Policy-

makers can also evaluate policy instruments

(zoning, community redevelopment forjobshousing mix, etc.) adopted in differ-

ent cities by comparing their commuting

efficiencies. In so doing, policy-makers can

discover what measures are effective in pro-

moting efficient commuting.The remainder of the paper is organised

as follows. Section 2 presents a brief review

of the excess commuting literature perti-nent to this study. The proposed method is

explained in section 3 along with a briefaccount of the datasets used in this study.

In the following section, the method is

applied to three Canadian cities and the

results are discussed. In the concluding sec-

tion, the limitations of this study are dis-cussed and avenues for future research are

presented.

2. Literature Review

The concept of excess commuting was first

introduced by Hamilton (1982) who deter-

mined a theoretical minimum commuting

length assuming that jobs were located in

the central business district (CBD) of a cityand housing location was a function of a

consumers trade-off between housing andcommuting costs. Hamilton termed the dif-

ference between the actual and theoretical

minimum commuting distance as wastefulcommuting since the difference between thetwo could be perceived as unnecessary com-muting given the urban form of the city.

Small and Song (1992) referred to the differ-ence as excess commuting. The assumptionof monocentricity of Hamiltons approachwas relaxed by White (1988) who adoptedHitchcocks (1941) transportation problemto determine the minimum commute. Inthis approach, the commuters locations of

jobs and housing were exchanged in a waythat minimised the system-wide travel costgiven the constraint that the total number of

workers and jobs in each zone remained thesame. Most of the later studies adoptedWhites approach to calculate the minimumcommute (Ma and Banister, 2006).

Hamilton (1982) and White (1988) bothcalculated minimum commuting based onlyon travel cost, assuming all workers to beequal in terms of socioeconomic andemployment characteristics. This assump-

tion was challenged by Thurston and Yezer(1991) who modified Hamiltons mono-centric model by introducing householdheterogeneity in terms of employment. Fora sample of US cities, their estimates ofexcess commuting were much lower thanHamiltons estimates. Similarly, Cropperand Gordon (1991) modified Whites(1988) approach of linear programming anddetermined minimum commuting by relo-

cating households to minimise commutingdistance subject to the constraint that nohouseholds utility would be reduced fromthe relocation. The household utility wasbased on housing cost and other housingand neighbourhood attributes. Buliung andKanaroglou (2002) also refined Whitesmethod by segmenting commuters to thosewho could exchange jobhousing locationsand those who could not, based on a set of

socioeconomic characteristics and employ-ment status. Conducted for the GreaterToronto Area, Canada, their findings

URBAN FORM AND COMMUTING EFFICIENCY 193



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suggested that policies seeking to reducework-trip length should target particularcommuter groups.

The excess commuting framework was

extended by Horner (2002) who introduceda theoretical maximum commute for agiven jobshousing distribution in a city.He termed the range between the mini-mum and maximum commute as the com-mute potential or carrying capacity of a cityin terms of commuting. He argued that theobserved level of commuting with respectto the commuting potential offered a betterassessment of commuting efficiency over

the concept of excess commuting. Whencomparing two cities, A and B, if city A hasa lower excess commute compared withcity B, but the observed commute of A ismuch closer to its theoretical maximumcommute compared with that of B, then Bwould be more efficient in terms of com-muting since A, albeit having a lower excesscommute, has consumed most of its com-

muting carrying capacity. More recently,Yang and Ferreira (2008) provided an alter-native method to calculate the maximumcommuting benchmark, called proportion-ally matched commuting. In this method,the probability of a worker living in zone iand working in zone j is proportional tozone js share of jobs in the region. Thus,interzonal flows are assigned irrespective ofthe zones locations and the average com-

muting distance is equivalent to the maxi-mum commute of Horner (2002).

At the core of the excess commutingliterature, the commuting efficiency ofcities is measured by comparing actualcommuting with commuting bench-marksnamely, the theoretical minimumand maximum commutes. Such bench-marking is animplicitway of representing acitys urban form in terms of commuting

distance or time.Ma and Banister (2007) first attempted

explicitly to relate commuting behaviour

to urban form. Conducting a simple simu-lation study, and citing the findings ofFrost et al. (1998), they concluded that asingle measure of excess commuting to

assess the commuting efficiency of a citycould be misleading. Based on six simula-tions of a hypothetical city of 19 equal-sizehexagonal zones, they concluded that thecommuting efficiency of a city should bebased on excess commuting along with thetype of urban form (dispersal of land use)and the theoretical maximum commute ofthe city.

Like Ma and Banister (2007), many

recent studies have focused on representingurban form by means other than only min-imum and maximum commutes. Forexample, Charron (2007) proposed a newapproach called the commuting possibili-ties framework. He argued that the theore-tical minimum and maximum commuteswere highly improbable outcomes of thestatistical distribution of commuting possi-

bilities. Based on Monte Carlo simulations,he developed statistical distributions ofcommuting possibilities for different typesof urban forms. For a city, the average ofthose possible commuting distances wascompared with the actual commute, whichgives its commuting efficiency.

More recently, OKelly and Niedzielski(2008, 2009) used an interesting way of rep-resenting the urban form of a city. Based on

the spatial interaction literature, theyexpressed urban form in terms of entropy.Entropy is the degree of disorder in asystem, which depends on the relative loca-tion of workers jobs and housing in thecity. If a city has plenty of cross-commuting,the entropy (as well as the observed com-mute) will be high. Conversely, if workersare employed close to their homes, thesystem is orderly, thus the entropy (also, the

observed commute) will be low. OKellyand Niedzielski (2008) measured the changein entropy if the citys observed commuting




6/18

is lowered by 3 per cent and termed the

change in entropy as effort or difficulty toattain more efficient commuting. They

compared a sample of US cities, based on

how difficult it is to reduce observed com-muting to a certain level.

It is evident from the literature thatseveral methods have been proposed to

evaluate the commuting efficiency of a

city. The purpose of such methods is to

provide policy-makers with some knowl-

edge as to how a city is performing withrespect to commuting across time, or in

comparison with other cities at a particu-

lar time. The current study proposes a

new method and overcomes the draw-backs of two commonly used methods

excess commuting and commuting poten-

tial utilised.

3. Data and Method

3.1 Method

The method proposed in this study is based

on a graphical presentation of urban form

and commuting measures known as

Brotchies triangle. Brotchie (1984) illu-

strated the relation between land use dis-persal and work-trip length to explain the

impact of technological change on trans-

port. Ma and Banister (2007) used

Brotchies triangle in the excess commutingliterature. They designed six different types

of population and employment distribu-

tions for a hexagon-shaped, hypothetical

city and explained what would be the

excess commuting when the citys urbanform changed from one scenario to

another. They used Brotchies triangle to

explain the scenarios. The current studymodifies the original triangle to accommo-

date different commuting measures (mini-mum, maximum, observed) at a given

urban form of a city.

As can be seen in Figure 1A, the measureof land use dispersal ranges from 0 to 1, 0being a monocentric city while 1 representsa city with a perfectly uniform distribution

of activities. A city could be located any-where within the triangle. On the triangle,A represents the concentration of activitieswhere the average commuting distancewould be the average distance of workershouseholds from the CBD (Brotchie, 1984).An extremely improved radial transportnetwork and transit-oriented developmentreinforces such development. Point B rep-resents perfect jobshousing balance but an

extreme level of cross-commuting. Cheaptransport and highest vehicle speed can giverise to such commuting. Point C representspre-World-War-II citiesthat is, perfect

jobshousing balance and every workerliving close to their workplace. A city likethis is characterised by pedestrian or bicycletrips, with telecommuting (nowadays)replacing longer-distance commuting

(Brotchie, 1984, p. 587).A citys excess commuting tends towardszero when one moves closer to point A inBrotchies triangle (Ma and Banister, 2007).It also means that, given the distribution ofland use, it is not possible to lower theobserved commuting distance. When a citybecomes more and more dispersed, there isa chance of cross-commuting (along lineAB) or efficient commuting behaviour

(along line AC).For the purpose of the current study,

Brotchies triangle was modified to includethe commuting benchmarksminimumand maximum commutes (Figure 1B). The

Xaxis represents the level of jobs dispersalrelative to workers housing dispersal andthe commuting distances are plotted alongthe Y axis. Using Whites (1988) andHorners (2002) approaches respectively,

the minimum (Cmin) and maximum (Cmax)possible commuting distances are calculatedfor a given level of jobshousing dispersal x.




7/18

The vertical Cmax Cmin line represents the

commuting potential or carrying capacity of

a city at the given jobshousing dispersal

level. The observed commuting distance

(Cobs) lies on this line. While the triangle ren-

ders the urban system, Cobs represents the

commuting behaviour. Therefore, like the

traditional approach, we also compare com-

muting behaviour with urban form, but in amore explicit manner.

The jobshousing dispersal index (x) is

the ratio of the average distance of jobs from

the CBD (jobs dispersal) to the average dis-

tance of workers households from the CBD

(housing dispersal) (Brotchie et al., 1996).

Mathematically

x= 1EX

j

djej !,

1HX

j

djhj !

Figure 1. A. Brotchies urban triangle; B. Brotchies triangle modified to include minimum

(Cmin), maximum (Cmax) and actual commutes (Cobs).




8/18

where, E and H are the total number ofmetropolitan jobs and workers households

respectively; ej and hj are respectively the

number of jobs and workers households in

zone j; and dj is the network distance fromthe CBD to zonej.

For a perfectly monocentric city, the

jobs dispersal (i.e. the numerator of theequation) is zero, thus the indexx is zero.

If each zone has an equal number of jobs

and workers households, the index is 1.The index could be greater than 1 if more

households are located near the CBD while

jobs are mostly located in the suburbs

which are very unlikely scenarios.In this study, the average actual commute

was calculated following Whites (1988)

approach

Cobs= 1

N

Xi

Xj

cijnij

where,Nis the total number of commuters;

cij is the network distance between zone i

and zonej; andnijis the number of workersliving in zonei and employed in zonej.

In this study, distance is preferred overtravel time as the measure of commuting

cost because distance is a constant metric,

whereas travel time depends on traffic con-

gestion and travel mode. Thus, travel time is

not always proportional to distance (Ma and

Banister, 2007). If computed based on traveltime, the measure of urban form, jobshousing dispersal index, would be biased

towards traffic conditions. The intrazonal

distance,ciiwas calculated by assuming each

zone as a circle and calculating its radius

from this formula:radius =ffiffiffiffiffiffiffiffiffiffiffiffiffiffi

area=pp

(Frost

et al., 1998). Using Hitchcocks (1941) trans-

port problem, commuters were reassigned(that is, a new flow matrix was obtained,

which isnij) to minimise the total transportcost (i.e. the network distance)

minX

i

Xj

cijnij

!

subject toX

jnij= Oi,

Xi

nij= Dj, nij 0

whereOi is the number of workers living inzone i; and Dj is the number of workersemployed in zonej.

The first two constraints mean that thetotal number of workers residing and work-

ing in each zone should remain the same in

the optimised flow matrix, n

ij. The mini-mum average commute is

Cmin= 1

N

Xi

Xj

cijnij

Excess commuting is the differencebetween the actual and minimum commute

expressed as a percentage of the actualcommute

E=Cobs Cmin

Cobs3100

To obtain the maximum commuting dis-tance, the commuters were reassigned (nij )

in such a way that the total commuting costwas maximised

maxX

i

Xj

cijnij

!

subject toX

j

nij= Oi,X

i

nij= Dj, nij 0:

The maximum commute is

Cmax= 1N

Xi

Xj

cijnij




9/18

Horner (2002) demonstrated that themaximisation problem is equivalent to theminimisation one when the elements ofthe cost matrix are negative. The absolute

value of the equivalent minimisation prob-lem gives the solution to the maximisationproblem

maxX

i

Xj

cijnij

![ min

Xi

Xj

cijnij

!

The commuting potential or carryingcapacity, as discussed by Horner (2002), isthe difference between the minimum and

maximum commutes,R = Cmax Cmin, andcapacity utilisation (U) is

U=Cobs Cmin

R 3100

Whereas the excess commute is, in essence,the difference between a citys actual com-

muting distance and the minimum com-mute, capacity utilisation is this difference

compared with the commute potential. Ascan be seen from Figure 1B, commutepotential is proportional to the dispersionof land use.

3.2 Data and Study Area

The data used for this study are journey-to-

work data, collected by Statistics Canada aspart of the 2006 Census of Canada, for

three census metropolitan areas (CMAs)Hamilton, Halifax and Vancouver. Thetemporal comparison was made for thethree CMAs for the years 1996, 2001 and2006. These were the latest census yearsavailable for the analysis. The three cities

were also compared with one another for2006, which was the latest census year for

the analysis. The cities were selected to rep-resent three different regions of Canada: the

Atlantic region, the Central region and the

Pacific region. Only three cities were usedin this study because the purpose of thisstudy is to propose a new method and todemonstrate how the method would work

empirically. Future studies could apply themethod to a larger sample of cities and

years.The flow matrix (nij) of a CMA is given

at the census-tract level. The flow matrixdoes not include commuting into or out-side the CMA. As mentioned earlier, thecost matrix (cij) is the interzonal shortestdistance along the road network. The short-est path calculations and transport optimi-sation were carried out using TransCAD,

a powerful GIS for transport applications(Caliper Corporation, 2000).

For comparisons across census years, the2001 and 2006 zoning systems of each CMAwere aggregated to the 1996 system. Thenumber of census tracts for Hamilton,Halifax and Vancouver in 1996 are respec-tively, 163, 75 and 299.

3.3 Definitions of Commuting Efficiency

The excess commuting literature examinesurban commuting from a system perspec-tive. Individuals in a city make travel deci-sions to optimise their utilities based ontheir choices of residence and worklocationsnot to optimise (or minimise)the average travel distance in the city. The

behaviour of people is measured by theobserved average commuting distance and

the system optimum is gauged by the theo-retical minimum commuting distance. Thedifference between these two relative to theobserved commute is the excess commute.Thus, the excess commute is a measure ofcommuting efficiency of a city (Scott et al.,1997). In Horners (2002) extendedapproach, efficiency is measured by the

commuting potential utilised. In this study,another dimension is added to define

commuting efficiency. While previous




10/18

definitions of commuting efficiency were

along the Yaxis of Brotchies triangle only(Figure 1B), the new approach also consid-

ers the Xaxisthat is, urban form. Under

this approach, a city is considered to bemost efficient if two conditions are met:

urban form is such that the jobs and hous-ing are perfectly balanced within spatial

units (local level)that is, the minimum

commute is the least; and the actual average

commute is equal to the theoretical mini-

mum. Therefore, the most commuting-

efficient city would be located at point C in

Figure 1A.

4. Results

4.1 Commuting Efficiency across Time

Table 1 and Figure 2 show that jobs not only

decentralised in all three CMAs over the 10-

year period, they also became less clustered

as indicated by decreasing values of Morans

I. In contrast, households became more clus-tered as they moved away from their urban

cores.In Halifax, proximity between jobs and

households, as indicated by the minimum

commute, decreased slightly between 1996and 2001. This was followed by an increase

between 2001 and 2006. The observed com-

mute increased over the 10-year period

despite the fact that jobs moved somewhatcloser to households. Thus, looking at theurban triangles for Halifax (Figure 2A), it

appears that, over the 10-year period, com-muting has become less efficient. Values of

excess commuting (Table 1) correspond to

this observation while commuting potential

utilised suggests the opposite.The urban triangles of Vancouver

(Figure 2B) suggest a positive trend of

commute change. As jobs and householdsmoved away from the CBD during the 10-

year period (Table 1), proximity between

them increased while average commutingdistance decreased. Such changes suggestthat Vancouver is moving towards jobshousing balance. Interestingly, commuting

potential utilised supports this assessmentwhile excess commuting does not.

Hamiltons trend is opposite to that ofVancouver (Figure 2C). As jobs and house-holds decentralised, they clustered awayfrom one other (thus the increase in mini-mum commute) and the observed commuteincreased. Since urban form and commutingbehaviour have moved away from jobshousing balance, Hamilton has become lesscommuting efficient over time. However,

the traditional indices of commuting effi-ciency, excess commuting and commuting

potential utilised, suggest otherwise. Excesscommuting has declined during the decadebecause the rate of change of the minimumcommute (11.3 per cent) was higher thanthat of the observed commute (5.7 per cent).As for commuting potential utilised, the

commuting range (Cmax Cmin) increasedat a higher rate (6.6 per cent) than that of theobserved commute (5.7 per cent). The com-muting range, an indirect measure of urban

form, is related to the level of job and house-hold decentralisation. As jobs and house-

holds become more dispersed spatially,commuting range increases.

This discussion clearly reveals that bothexcess commuting and commuting potential

utilised fail to accurately assess commutingefficiency. Inclusion of an additional dimen-sion, urban form, in the commuting analysis

provides a better understanding of commut-ing phenomena, while it requires no addi-

tional data.

4.2 Commuting Efficiency across Cities

The proposed method is also applied to a

cross-sectional analysis for the year 2006.Different measures of urban form and

commuting are displayed in Table 1 and




11/18

Table

1.

Urbanform

andcommutin

gefficiencystatisticsforHalifax,

VancouverandHamilton,

19962006

Year

N

umber

ofworkers

Jobdispersal

(km)

H

ousehold

dispersa

lCCBD

(km)

Jobshousing

dispersal

index

MoransIa

Cmin(km)Cmax

(km)Cobs

(km)

Excess

commuting

(percentage)

Commuting

potential

utilised

(percentage)

J

ob

Household

Halifax

1996

135685

6.49

12.46

0.52

0

.22

0.18

7.71

17.31

11.62

33.60

40.69

2001

147910

7.43

12.61

0.59

0

.21

0.16

7.39

18.44

11.83

37.52

40.17

2006

159675

7.71

13.29

0.58

0

.13

0.20

7.65

19.33

12.30

37.81

39.82

Vancouver

1996

715285

14.55

19.33

0.75

0

.27

0.13

6.01

29.66

12.78

53.02

28.65

2001

790770

15.19

19.62

0.77

0

.24

0.18

5.80

30.12

12.74

54.50

28.55

2006

833010

15.67

19.76

0.79

0

.23

0.23

5.52

30.57

12.43

55.63

27.61

Hamilton

1996

196360

10.19

11.80

0.86

0

.24

0.17

3.82

18.88

9.27

58.76

36.17

2001

210125

10.71

12.03

0.89

0

.21

0.20

4.17

19.63

9.74

57.16

36.00

2006

211840

11.29

12.25

0.92

0

.19

0.18

4.25

20.31

9.80

56.58

34.54

aAllp-va

luesarebelow0.01.




12/18

Figure 3A. When compared in terms of

excess commuting, Halifax seems to have

the most efficient system; Vancouver is

intermediate; and Hamilton is the worst.

The reason Halifax has the lowest excess

commuting is because its urban form tends

to be more monocentric than the other

cities. In Halifax, jobs are mostly clustered

in the downtown area (lowest jobs dispersal

value and the highest global Morans I forjobs). In Vancouver, there are some decen-

tralised concentrations of jobs, while in

Hamilton jobs are more distributed

throughout the city (lowest global Morans

I). Since Halifax is more monocentric thanthe other cities, its jobshousing dispersal

index is the lowest, which is why it has the

highest minimum commuting distance and

therefore the lowest excess commute. As is

evident from Brotchies urban triangle

(Figure 1A), a perfect monocentric city

(jobshousing dispersal index = 0) wouldhave no excess commuting. Thus, the

fact that Halifax has the lowest excess

Figure 2. Change in urban form and commuting in three CMAs, 19962006.




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commuting is not because of efficient com-

muting, but because of its urban form.According to commuting potential uti-

lised, Vancouver seems to have the bestsystem and Halifax the worst, with

Hamilton in between. Figure 3A indicates

that the observed commute in Vancouver is

the farthest from the maximum commute,

indicating an efficient commuting beha-

viour. As discussed earlier, the theoreticalminimum and maximum commutes are

the commuting benchmarks given the

Figure 3. A. Urban form and commuting across three Canadian cities, 2006; B. commutingmeasures after maximum commute is adjusted for city size.




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distribution of jobs and householdsthatis, urban form. Conceptually, if a city hadall of its jobs concentrated in its CBD, theobserved commuting distance would be

equal to the theoretical minimum andmaximum commutes. The commutingpotential would be zero for such a city. Atthe other extreme, a city with a perfectmixing of jobs and workers housing(X-axis value equals 1 in Brotchies trian-gle) would display the highest value ofcommuting potential. The commutingpotential of Vancouver does not complywith this idea. Its commuting potential is

higher than that of Hamilton, although itsdegree of jobshousing proximity is lower.

This anomaly can be explained by thebias of the maximum commute towards citysize.4 For two cities with the same degree of

jobshousing proximity, the city with thelarger geographical area will have the highestmaximum commute. For this reason, inFigure 3A, the vertical side of the urban tri-

angle of Vancouver is longer than that ofHamilton, although it is located to the left ofHamiltons vertical side.5 Thus, it would notbe appropriate to use commuting potentialutilised as a metric to compare differentcities at a particular point in time unless thecity size effect is controlled for. However, itcan be applied to compare the commutingof a city at different time-periods.

The bias of the maximum commute

towards city size can be eliminated in twosteps. First, a size factor is calculated foreach city (Table 2). It is computed by divid-ing the CCBD (commuting distance if all

jobs were in the CBD) of each city by thelowest value of CCBD.

6 CCBD refers to thedispersal of workers households from theCBD. One could argue to use simply theradius of each city (assuming the city is acircle and computing the radius from its

area) instead of workers household disper-sal. While this argument is legitimate, a citycould have a large geographical area, but its

settlement could be concentrated in oneplace, leaving the rest mostly vacant.

Secondly, the maximum commute and

CCBDof each city are divided by the respec-

tive size factor. Table 2 displays the originaland adjusted values of commuting poten-tial utilised. The adjusted commutingpotential utilised suggests quite a differentpicture from what was produced by theoriginal metric. As city size is taken intoaccount, Vancouver seems to have theworst system in terms of commuting(Figure 3B). Previously, Vancouver had thelowest commuting potential utilisedbecause the maximum commuting distance

was overestimated due to city size.Removing the size bias is a novel addi-

tion to the excess commuting literature.Brotchie et al. (1996) divided all the valuesin the Y axis byCCBD to take city size intoaccount. However, city size does not influ-

ence the minimum commute, which simplydepends on the relative location of jobs and

houses. Similarly, the observed commutedoes not depend on city sizeit representspeoples behaviour. While it is a valid argu-ment that people in bigger cities have moreflexibility in their choices of jobs and resi-dential locations than in smaller cities, it isnot conclusive whether or not city size hasan impact on commuting behaviour. Evenif city size influences commuting behaviour,it would be almost negligible compared

with the influence it has on the maximumcommute. Thus, only the maximum com-mute is normalised when comparing across

cities. Since Hamilton has the lowest CCBD,the maximum commutes of the cities arestandardised with respect to Hamilton.

4.3 Relationship between CommutingBehaviour and Urban Form

Traditionally, the relationship betweencommuting and urban form is examined

through statistical measures such as the




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commuting behaviour over the other cities.

Thus, from the simple urban triangles, itappears that there is no consistent relation-

ship between commuting behaviour and

urban form.

5. Conclusion

An issue with the excess commuting litera-

ture is its inability to capture the dynamic

nature of an urban system. People change

jobs and residences (although perhaps notas often as jobs) and location choice changes

over time. Excess commuting, on the otherhand, only captures a snapshot of this

dynamic process. Regardless of this limita-

tion, the analysis of excess commuting isquite appealing because it embodies the

idea of achieving commuting efficiency

without a change in urban form (Ma and

Banister, 2006). An urban authority could

reduce transport emissions significantly ifcommuting behaviour could be shifted

towards a jobshousing balance scenario

(Scott et al., 1997). Several policies could

work as catalysts for such a behavioural

shiftzoning, community redevelopmentto ensure a blend of various types of jobs

and housing, financial incentives for afford-

able housing, and telecommuting, to name

a few. It is therefore useful to examine the

commuting efficiency of a city over time or

compared with other cities to have an ideaabout how a city is performing. The method

introduced in this research could be a useful

instrument in this regard.As demonstrated in this study, both

excess commuting and commuting poten-

tial utilised are susceptible to misinterpreta-

tion of commuting efficiency in a city as the

commuting benchmarks (minimum andmaximum commutes) represent urban

form indirectly. The method applied in thisstudy provides an explicit way to look at a

citys commuting scenario with respect to

its urban form. The most promising aspectof this method is that it provides additionalinformation, but does not require addi-tional data. However, there is some scope

to improve this method. The jobshousingdispersal index in the X axis in Brotchiestriangle is a simple measure of jobshousingproximity. While it conveys an additionalattribute of metropolitan urban structure(i.e. the level of job decentralisation), it isnot necessarily the best measure of jobshousing proximity. This is why the jobshousing dispersal index of Hamilton from1996 to 2006 has increased while the mini-

mum commute during the period has alsoincreased. Future research could focus ondeveloping a better index of measuring the

jobshousing mix. There has already beenwork on the spatial association between twovariables (Lee, 2001; Anselin et al., 2002;Horner and Marion, 2009), but they allmeasure interzonal association. For exam-ple, bivariate Morans I captures the associ-

ation between two variables across space,but the intrazonal spatial lag or Wii is zero(Anselinet al., 2002). If the inverse distancemethod is applied, one could customise theweight matrix for intrazonal weights (Wii)taking the radius of the zone as intrazonaldistance. In such a case, the diagonal valuesof the weight matrix would be higher thanany other values.

This study assumes that location choice is

only based on the spatial separation of work-place and residence. In order to determine amore realistic measure of excess commuting,it is necessary to incorporate several factors,such as workers heterogeneity based ontheir socio-demographic characteristics,work status (Buliung and Kanaroglou,2002), attributes of residential area(Cropper and Gordon, 1991), job marketflexibility (Ma and Banister, 2006), wage

level, job classification, etc. An urban systemis the outcome of all individual economicdecisions. Although the excess commuting




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literature views cities from a system perspec-tive, controlling for individual economicdecisions during system optimisation wouldmake the excess commuting measures more

pragmatic. Such models would control forjob heterogeneity, number of workers in thehousehold, commute mode choice, etc.With the increasing ease of data collectionand methodological as well as computa-

tional advances, future research should seekmore blends between aggregate system opti-misation and disaggregate individual beha-viour. If data are available, future workcould incorporate non-work travel to con-strain the reassignment of jobhousehold

location to ensure that the jobshousingexchange does not increase overall travel(Ma and Banister, 2006). Future researchcan also make use of the method proposed

in this study to evaluate different growthscenarios in terms of commuting efficiency.

Notes

1. In this paper, the terms actual average com-

mute and observed average commute are

used interchangeably as is often done in the

excess commuting literature (for example,

Horner and Murray, 2002; Ma and Banister,

2007).

2. For ease of presentation, we suppress the word

average when referring to actual (observed)

average commute, minimum average com-

mute and maximum average commute.

3. The definition and explanation of commut-ing efficiency in the context of this method

is expanded upon later in this paper.

4. The alternative measure of maximum com-

mute, proportionally matched commuting

(Yang and Ferreira, 2008), is also prone to

similar bias.

5. Because of the size bias, Horner (2002, p.

557) observed that smaller cities used up

higher commute potential than did larger

cities.

6. When plotting a sample of global cities in

Brotchies triangle, Brotchie et al. (1996) also

normalised the commuting measures in the

Yaxis by the CCBD of respective cities. They

did not compute any size factor by dividing

eachCCBD by the lowest one.

Funding StatementThis research received no specific grant from any

funding agency in the public, commercial or not-

for-profit sectors.

Acknowledgements

The authors would like to thank the US editor

(Professor Andrejs Skaburskis) and three anon-

ymous referees for providing insightful com-

ments to improve this paper.

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