book review: muhammad faishal ibrahim and peter j. goldrick

European Journal of Transport and Infrastructure Research Volume 3, no. 3 DUP Science / 2003

Contents EJTIR, 3, no. 3 (2003) Hossain Poorzahedy and Sayed Nader Shetab Bushehri 241 Project Selection in Traffic Accident Prevention and Mitigation Aurelia Bengochea Morancho and Salvador del Saz Salazar 263 Valuing a Road Network Improvement using Stated Preferences Methods Zhenlong Li and Songquan Shi 281 A Differential Game Modeling Approach to Dynamic Traffic Assignment and Signal Control Lars Lundqvist 299 Land-Use and Travel Behaviour. A Survey of Some Analysis and Policy Perspectives Harry Timmermans 315 Book Review: Muhammad Faishal Ibrahim and Peter J. Goldrick. Shopping Choices with Public Transport Options European Perspectives 317 Dominic Stead The External Costs of Transport and Electricity Generation

Project Selection in Traffic Accident Prevention and Mitigation

Hossain Poorzahedy and Sayed Nader Shetab Bushehri Department of Civil Engineering Sharif University of Technology Tehran Iran E-mail: [email protected]

EJTIR, 3, no. 3 (2003), pp. 241 - 261

Received: March 2003 Accepted: August 2003

This paper deals with two problems in relation to the accident treatment of urban street networks, i.e. accident prevention (AP) and accident mitigation (MP). These two problems are defined based on the concepts of suitable remaining trip-hours, link importance, and k-link connectedness of node-destinations in the network. The objective of problem (AP) is to upgrade the important links so as to maximize a measure of the performance of the network. This is a before-accident treatment of the network. The objective of problem (MP) is to mitigate the accident effects in the network so as to maximize a measure of network connectedness. This is an after-accident treatment of the network, which is done by equipping auxiliary links in the network to join the available set of links, in order to make important 1-link connected node-destination pairs, k-link connected )( 2≥k . Two algorithms have been proposed to solve these two problems. The reasonability of the solution results has been shown by applying these two algorithms on a small-sized (6 nodes, 10 links) example network. The feasibility of the application of these algorithms on larger networks has been investigated by applying them on the network of Sioux Falls (24 nodes and 76 links).

Keywords: traffic accident, accident prevention, link importance, accident mitigation, network connectedness

1. Introduction

Accidents are events in transportation networks which hinder normal flows of traffic in the links, or halt some parts of the network for a short period of time (say, 10-15 minutes) or even longer. These events cost money, materials, take lives and even affect the environment, proportional to the severity of the events. Moreover, the delay caused by the accidents to

242 Project Selection in Traffic Accident Prevention and Mitigation

those passengers not being involved in such events may be significant. The traffic in the accident-hit link backs up and the moment the drivers are informed of the event they are tempted to change their routes. Where there is no suitable alternative route, their detours would become unsuitable. Attention has been recently paid to analysing such events from the perspective of network performance. Wakabayashi and Iida (1994), noting the importance of transportation networks in everyday life, emphasize the significance of having a reliable network that functions suitably despite the failure of parts of the network due to accidents, natural disasters, congestion, or closure of roads for maintenance. Asakura (1996) proposes to use a reliability measure defined as the probability of having the ratio of an origin-destination (O/D) travel time after the event over that time before it which is below a certain acceptable level. Du and Nicholson (1997a, 1997b), referring to transportation network as lifeline, define critical links as important yet weak links. An �important� link means that the link failure causes economic and social costs and by �weak� link is meant that the link is vulnerable to natural disaster. They propose identification of critical links by making a sensitivity analysis in the process of network performance improvement. Sanso and Soumis (1991) present a method for evaluating the performance of networks under uncertainties. As for transportation networks, they present a 3T model for the analysis of traffic accidents which considers three periods of time for this analysis, i.e. before the accident, just after the accident, and after the information of accident occurrence has reached the users of the network. Sanso and Milot (1994) have used the EMME/2 package to show the implementation of the 3T model. Literature reveals the need for more research to explore the effect of accidents upon the performance of the networks (Iida, 1999). This paper makes an attempt in this respect. First, as a preventive strategy this paper aims at solving a problem to identify a set of links which, when upgraded by certain actions under limited resources, would increase the network performance most. As a remedial strategy the paper then considers the problem of identifying a resource feasible subset of local access links in the network which, when equipped with certain means and introduced to the network, would create alternative routes for the users of accident-struck links and decrease the negative implications of weak connections of the network best. Section 2 of the paper presents the definitions and assumptions made in this paper. Section 3 discusses the models and is followed by section 4, which presents applications of the models for two test networks. The paper is concluded with section 5.

2. Definitions, Assumptions, and Notations

Assume that, without loss of generality, accidents occur in network links. At any time, the state of the network may be represented by a state vector, ,...),(... ijcc = , where ijc shows the state of link ),( ji of the network at that time: 10 /=ijc , if an accident does/does not occur in link ),( ji (or, link ),( ji is not /is functioning). For example, ),...,,...,( 111=oc shows that no link of the network is involved in an accident (or, that all links are functioning). This state is called a prevalent one. Define remaining trip )( esrt of a trip of a trip-maker in a new state c, is a trip with its origin being the point of the network where that trip-maker is, at the time state c starts, e, and its

Hossain Poorzahedy and Sayed Nader Shetab Busherhi 243

destination being the original destination of the trip, s. We call )( esrt suitable if its travel time does not exceed that of the respective prevalent state beyond a certain level esθ . Let

)(ct es represent the esrt travel time at state c. Let also )(ct esρ be the )( esrt travel time through

path ρ when the state of the network is c. Then, )( esrt is suitable in state c if eses

es

ctct θ≤

)()(o

,

and path ρ from e to s is a suitable path in state c if eses

es

ct

ctθρ ≤

)(

)(o

.

Node-destination (N/D) (j,s) is said to be suitable in state c , if there exists at least one suitable path from j to s in state c . N/D (j,s) is called k-link connected if destination s could be reached from j by k suitable paths with no links in common (see also Pierre and Elgibaout, 1997). Fig 1 shows 5 paths from node j to destination s, of which one path is longer than others and is not suitable. So, there are 4 suitable paths from j to s, but the N/D (j,s) is 2-link connected.

Fig.1. Suitable / not suitable paths, and k-link connected N/D (k=2)

Now let us turn to the assumptions made in this paper. For a street network, it is assumed that:

1. The probability of accident occurrence in a link during the analysis period (say, morning peak period) is known;

2. Accidents only occur in the links of the network (intersections may be represented by a set of links);

3. All network users will be informed of the accident immediately after the occurrence of an accident (say, by radio stations or variable sign messages);

4. Those travellers who have the accident-struck link on their paths to their respective destinations tend to change their paths to avoid that link, regardless of the severity of the accident;

5. What is important to the users of the network after the occurrence of the accident is to reach their destinations in a suitable time period;

6. The change of paths in (4) has a negligible effect upon the level of service offered to other travellers (because of the extent of the network or short duration of accident effect), so that they keep on using their usual paths and that their trips remain suitable;

7. Travellers who have to pass through the accident-struck link will experience unsuitable rt; 8. Accidents only affect the travellers who have already started their trips and those who have

not started their trips would only do so if their trips become suitable.


Thus, the travellers in the network may be divided into three groups when an accident occurs in a link of the network: the first group are those travellers who do not have the accident-struck link on their paths from the origin to the destination. These travellers would, according to assumption (6), continue using their usual path to reach their respective destination and finish their trips suitably. The second group are those travellers who at the time of accident occurrence, are travelling within the accident-struck link and, if the accident is ahead of them, they have to pass through it and their rt�s become unsuitable by assumption (7). Otherwise, if they are travelling past the accident point, they continue their trips and finish them suitably. The third group are those travellers who have the accident-struck link on their path from O to D and are informed right after the accident of its occurrence. Until they reach the link, they have time to change their paths to avoid the accident-hit link to finish their trips suitably. If there is no such alternative path from where they are to their destinations, then their rt�s become unsuitable. To present the models formally, let ),( AVN be a network with V as the set of nodes and A as the set of links. Let n be the number of nodes, Vn = , k and s represent the origin and destination respectively with O and D as the respective sets. Let also, P denote the set of

DO / pairs, ),( sk , with demand ksd from k to s . The (shortest) travel time from k to s is denoted by kst . Moreover, let ρ denote a path in the network, and ksρ the set of paths from k to s . ksxρ is the (user equilibrium) flow in path ρ from k to s in a prevalent (no-accident) situation, and ijx one such flow in link ),( ji , which experiences the travel time ijt . Now let ijp be the probability of non-occurrence of accident in link ),( ji . c represents the state of the network and oc the prevalent state. o

ijc− is the state of the network in which only link ),( ji is hit by an accident. Finally, let )(ct js denote the ),(/ sjDN travel time when the network

is in state c . We are now in a position to state the problem formally.

3. The Proposed Models

3.1 Choice of Accident Preventive Actions

This section is devoted to a model for choosing among a set of accident preventive actions under limited resources. First a link-importance index is introduced. The importance of a link in a network is related to its contribution to the performance of the network. The objective of this study is to improve the level of service offered to the travellers who are using the network at the time of accident event (assumption 8). It is appealing to use the number of suitable rt�s after an accident event relative to that before this event as a measure of network performance. However, it is clear that, in order to differentiate between long rt�s and short ones, the remaining trip-hour (rt-hr) is a better measure. Another appealing measure for network performance could have been suitable trip-hour. However, this measure fails to appropriately express the performance of the network in some cases. For example, consider a trip which usually takes one hour. Suppose this trip becomes involved in an accident 2 minutes just


before it ends. How would the trip-maker express his feeling in such occasions? He would most probably say that the trip was fine just before it ends, but he was unfortunate in the last few minutes. That is to say the trip-maker is unsatisfied with the remaining (last few minutes) of the trip. Let )(cE be the sum of rt-hr�s when the network is in state c . Let also )(cPI be the performance index of the network in state c , defined as

)()()(ocE

cEcPI = (1)

Now let us suppose that there are m passengers destined to s travelling in link ),( ji who are uniformly distributed over this link. Also assume that the occurrence of an accident in link

),( ji is uniformly distributed over this link. Then: Proposition 1. The expected suitable rt-hr�s for these travellers when the state of the network is c , )(cE s

ij , is given by:

)()()23

()()2

()( czczttmczt

tmcE js

ij

jsijjsjsijs

ij +−+≈ (2)

where )(czij is a binary variable, which is 1 if an accident occurs in link ),( ji in state c ,

otherwise 0. Also, )(cz js is another binary variable, which is 1 if )(crt js is suitable, 0 otherwise. Now let us suppose that the users of the network are distributed over different portions of a path from origin k to destination s in proportion to the time taken to traverse those portions. In other words, a link that takes more time to travel through contains more travellers at any instant. With this assumption, we now state: Proposition 2. Assume that users of the network are immediately informed of an accident occurrence in the network and that the number of passengers on any portion of the path is proportional to the travel time of that portion. Then we may write:

∑∑∈ ∈

Ψ−Φ=Vj Ds

jsjsjs czccPI )())(()( (3)

where,

∑

∑ ∑ ∑

∈

∈ ∈ ∈

+=Φ

Psk

ksksks

Ok jBi

jsijksijij

ks

js

tdt

tt

txks

),(

)(,

)2

(

)2

(ρρ

ρρ δ

(4)


∑

∑ ∑ ∑

∈

∈ ∈ ∈

+=Ψ

Psk

ksksks

Ok jBiij

jsijks

ijijks

js

tdt

cztttx

cks

),(

)(,

)2

(

)()23

()( ρρ

ρρ δ

(5)

where )( jB is the set of tail nodes of the links of the network with head node j , and ksij ρδ , is a

binary variable which takes the value of 1 if link ),( ji belongs to path ρ from origin k to destination s , and 0 otherwise. It is worth noting that jsΦ is the performance index of the network from node j to the destination s , which is deducted by )(cjsΨ to represent the inefficiency caused by the occurrence of an accident in link ),( ji in this index in state c . Definition. An important link in a network is a link such that reducing the probability of accident occurrence in that link would increase the performance index of the network significantly. Define the importance index of link ,),,( ijIji as the reduction of the performance index of the network without link ),( ji as compared with that of the prevalent state:

)()( ooijij cPIcPII −−=

which is the change in performance of the network when ),( ji is excluded from the network. Clearly, 1=)( ocPI , and according to Proposition 2,

∑∑∈ ∈

−−−− Ψ−Φ=Vj Ds

ijjs

ijjs

ijjsjs

ij czcczcPI )]()()([)( oooo

(6)

Thus, one may write:

∑∑ ∑∑∈ ∈ ∈ ∈

−−− Ψ+Φ−=Vj Ds Vj Ds

ijjs

ijjs

ijjsjs

ij czcczI )()()](1[ ooo

(7)

The first term of the above expression is a measure of the importance of link ),( ji in providing alternative suitable paths in the network, whilst the second term adds an amount to the importance of link ),( ji , which an accident occurrence in link ),( ji would deduct.

3.2 Accident Proofing of the Network

Suppose that several accident preventive (AP) measures or actions may be undertaken for each link in the network. Suppose that for each street (or link), ),( ji there are ijk alternative actions, and that alternative k would reduce the probability of accident occurrence in link

),( ji by kijα percent. Moreover, suppose that there are L types of resources needed to undertake

the projects of interest and that lB is the amount of resource l . Let klije be the amount of

resource l required for implementing alternative k over link ),( ji . The question is, under the limitation of the available resources, which alternative action of each street should be


implemented so as to maximize the performance of the network under study. The following is a model to answer this question:

(8-0)

(8-1)

(8-2)

ijkij

Aji

k

k

lkij

klij

k

k

kij

Aji

k

k

kij

kijijij

kkAjiz

LlBzc

Ajizts

zpIMaxAP

ij

ij

ij

,...,,),(;/)(

,...,;)(

),(;)(:..

])([)(

),(

),(

1103

12

11

1

1

1

1

=∈=

=≤

∈≤

−

∑ ∑

∑

∑ ∑

∈ =

=

∈ =α

(8-3)

In this model, ijp−1 is the probability that an accident occurs in link Aji ∈),( and hence kijijp α)( −1 the reduction of this probability by alternative action k for this link, which is

weighted by the importance of the link to form kijijij pI α)( −1 . This � benefit � of alternative k

of link ),( ji accrues if action k of link ),( ji is chosen )( 1=kijz , otherwise not )( 0=k

ijz , and thus obtaining the expression k

ijkijijij zpI α)( −1 which is summed over all links ),( ji in the

network. The first constraint ensures that at most one alternative is chosen for each link. The second constraint is the resource constraint, and the third constraint limits k

ijz to 0 (rejected) or 1 (accepted). The following algorithm is presented to solve problem (AP).

Algorithm (AP): To identify links to be improved with an ultimate goal of Accident Prevention.

Step 0. Initialization. Prepare the following information: AV & for ),( AVN ; ij

ksij tPskdAjip ;),(,;),(, ∈∀∈∀ function ;),(,;),( SVsjAji js ×∈∀∈∀ θ and ., LlBl ∈∀

Step 1. Equilibrium Flow Computation. Solve a user equilibrium flow problem for the network ),( AVN and demand }),(,{ Pskd ks ∈∀ to find the path flows and link travel times.

Step 2. Finding N/D Information. For all node-destinations DVsj ×∈),( , using the information obtained from step 1 above, compute jsΦ from Eqn. (4), and

)( oij

js c−Ψ from Eqn. (5). For all links Aji ∈),( , exclude link ),( ji and compute the

shortest travel time from j to s , DVsjct ijjs ×∈∀− ),(),( o using the equilibrium link

travel times obtained in step 1 above. Identify the suitability of the shortest path from j

to s ))(.,.( 1=−o

ijjs czei by verifying that for node-destination ),( sj js

jsij

js

ctct

θ≤−

)()(

o

o

, for all

DVsj ×∈),( .


Step 3. Compute Link Importance Index. Compute ijI by Eqn. (7), using the information obtained in step 2.

Step 4. Solve Problem (AP). Solve problem (AP) by a suitable algorithm, using ijI obtained in step 3 above.

3.3 A Method for Accident Mitigation

The previous section has dealt with the case of improving the important links so as to increase the performance of the network. In this respect, problem (AP) is a before-accident problem. This section, however, deals with the after-accident problem, i.e. the case of mitigating the negative impacts of accidents in the network. The objective here is to find the best action for each selected link from among a set of candidate links so that they are collectively resource feasible, and when implemented would strengthen the weakness of the network by offering alternative paths to the travellers to reach their destinations after the occurrence of an accident. After an accident occurrence, travellers who have the accident-struck link on their paths to their destinations, would seek alternative paths to avoid this link. For those travellers with no such an alternative path, the rt would become unsuitable. Suppose that some local roads/streets may be equipped in such a way that they become available to the traffic as alternative path creators or bypass streets. These auxiliary streets may make some of the unsuitable rt�s, suitable; however, they are designed in such a way that they are virtually closed to through traffic in case they are not expected to bypass a related troubled zone of the network. In the following a method is presented to choose among investments which aim to prepare auxiliary links for cases of accident occurrence. The objective of the network is to equip those auxiliary links that make the �important� and 1-link connected node-destinations at least 2-link connected. The �importance� of a node-destination pair ),( sj is evident from jsΦ . Referring to Eqn. (4), jsΦ is the proportion of the remaining trip-hours that are destined to s and j is the first node to be reached right after the accident occurrence. Now suppose that there is a set of candidate links proposed to be equipped as auxiliary links, each requiring certain costs to be implemented ( e.g. for meeting safety standards, installing control measures, increasing capacity, regulating speed etc.). A choice of these links is subject to budget constraint. Let ije be the cost of preparing auxiliary link ),( ji for joining the existing network ),( AVN when needed, and B the budget. Let yA be the set of auxiliary links, and y the vector of choice with elements ijy which takes values of 1 or 0 depending on accepting auxiliary link yAji ∈),( or rejecting it, respectively. Let yA′ represent the set of links of a chosen network corresponding to the decision { }1,),(|),(: =∈∪=′ ijyy yAjijiAAy Finally, let js

yz be a binary variable which is equal to 1 if with decision ,y ),(/ sjDN in the network ),( yAVN ′ is 2≥kk -link connected, and 0 otherwise (i.e. if it is 1- link connected). Let us show this variable for the existing network, ),( AVN , by jszo . The following is a network design (ND) problem for choice of accident mitigation (AM) measures:


(9-0)

(9-1)

(9-2)

.,

),(),(,)(

),(,/)(

)(:..

)()(

),(

otherwise

AVNinconnectedlinkkissjifz

Ajiy

Byets

zzMaxAM

ykjsy

yij

Ajiijij

Vj Ds

jsjsy

js

y

013

102

1

2 ′−=

∈∀=

≤

−Φ

≥

∈

∈ ∈

∑

∑∑ o

(9-3)

This problem may be approached by any of the suitable set of existing algorithms to solve ND problem. The following is then a general procedure to solve this problem:

Algorithm (AM): To choose links to be prepared to join the network when needed.

Step 0. Initialization. Prepare the original network, ),( AVN ; set of auxiliary links yA , with cost ije for all yAji ∈),( ; DO / demand ksd for all Psk ∈),( ; volume-delay functions )( ijij xt for all Aji ∈),( ; suitability standards jsθ for all DVsj ×∈),( ; the travel time of auxiliary links ,),,( ijtji for all yAji ∈),( .

Step 1. Assign DO / demand, ksd , to the original network ),( AVN and find the UE path flows and link travel times.

Step 2. For all ),(/ sjDN find jsΦ from Eqn. (4), using the results of step 1.

Step 3. Solve problem (AM) using a method to identify 1-link connected N/D , and any conventional ND algorithm.o

Remark 1. A procedure to identify 2≥kk -link-connected ),(/ sjDN in network ),( AVN is as follows. Let ijA− denote the set of links A excluding link Aji ∈),( . We call ),(/ sjDN , 2≥kk -link connected if it remains suitable for ),( ijAVN − , for all Aji ∈),( . Otherwise, i.e. if it becomes unsuitable for at least one such network, the DN / is called 1-link connected. Remark 2. If we assume that using auxiliary links by some travellers would have a negligible effect on the flows of the rest of the links of the original network, then one may easily find the 1-link connected NDs by the procedure mentioned in remark 1. Moreover, one need not worry about Braess� paradox in such a case and hence use simpler algorithms of ND like Ochoa-Rosso and Silva(1968).


4. Numerical Examples

4.1 AP Problem 1

Consider the Example Network 1 in Fig. 2 with 6 nodes and 10 links. Suppose that link travel time functions are of the usual type: 4

ijijijijij xbaxt +=)( . Table 1 presents the parameters of this function for each link as well as the respective probability of non-occurrence of accident in the link. DO / trips from origins 1 and 4 to destinations 3 and 6 are assumed to be 7 thousands of trips / day. Assume an average occupancy rate of 1 person per vehicle for all O/Ds. Also assume that 31.=jsθ , i.e. any node�destination travel time after the occurrence of an accident which exceeds the respective value of travel time in a prevalent state )( oc by 30% , would be considered unsuitable. Consider 3 alternative actions for reduction of accident rates for each link in the network: (1) police presence to enforce laws more positively, (2) enhancing geometrics, signs, markings etc. of links in addition to the action mentioned in alternative 1 above, and (3) prompt response to accident occurrence to remove disabled vehicles and cleaning up the accident site quickly in addition to alternative 2 above. Let us assume that 1 unit of police would reduce the accident occurrence by 1/2 , 1 unit of police and 1 unit of expenditure in link enhancement would reduce this probability by 1/4 and finally, let us assume that 1 unit of police , plus 1 unit of expenditure in links, plus 1 unit of accident scene management workforce would remove either the probability of accident occurrence or the effect of an accident on the rest of the traffic. Assume that there are 41 =B units of police,

32 =B units of financial resources, and 23 =B units of accident scene clearance workforce. The question is what link should be treated by which alternative to obtain the best result.

Fig.2 . Example Network 1. (node numbers are written on them)


Table 1. Specifications of the links of Example Network 1.

Link ),( ji

Free flow time )( ija

)( hr210−×

Congestion parameter )( ijb

))//(( 44 100010 dayvehhr×−

Prob. of non-occurrence of accident )( ijp

(1,2) 5 0.030 0.96 (1,4) 3 0.090 1.00 (1,5) 18 0.030 1.00 (2,3) 10 0.100 0.96 (2,5) 9 0.070 1.00 (2,6) 2 0.050 0.98 (3,6) 3 0.100 1.00 (4,5) 1 0.050 0.96 (5,2) 4 0.060 0.98 (5,6) 4 0.120 0.98

Applying algorithm AP to the problem resulted in the following. In step 1, at user equilibrium, each of the paths ( ) ( ){ } ( ) ( ){ } ( ) ( ) ( ){ }32255462213221 321 ,,,,,,,,,,,,, === ρρρ , and

( ) ( ){ }65544 ,,,=ρ get a flow of 7 units and the link flows and travel times become as shown in Table 2. In step 2 of the algorithm, using Eqn.(4), one may compute jsΦ for all DVsj ×∈),( . Also, using Eqn. (5), one may compute )( o

ijjs c−Ψ , and thus ∑∑

∈ ∈−Ψ

Vj Dsij

js c )( o , for all Aji ∈),( .

The former quantity is given in Table 3, and the latter in Table 2. Now we are in a position to find the suitability of the remaining trip from j to s , DVsj ×∈),( , and thus determine the values of )( o

ijjs cz − .

Having had jsΦ , )( oij

js c−Ψ and )( oij

js cz − , for all DVsj ×∈),( and all Aji ∈),( , one may then calculate in step 3 the importance of link ),( ji , for all Aji ∈),( , by using Eqn. (7) as shown in Table 2. Step 4 of the algorithm may now be performed by solving problem (AP) using information regarding ijI from step 3, and the input information ijp , k

ijα , and

)),(3,2,1,3,2,1( AjiandlkBl ∈== . This is done here by the effective gradient method as presented by Nazim (1983). The optimal decisions are presented in Table 2, as the chosen alternative for each link.

Table 2. Results of applying algorithm (AP) on Example Network 1.

Link ),( ji ijt (hr) ijx )/( hrveh1000 ∑∑∈ ∈

−ΨVj Ds

ijjs c )( o

ijI #ijz

(1,2) 0.1652 14 0.1131 0.1131 2 (1,4) 0.0300 0 0 0 - (1,5) 0.1800 0 0 0 - (2,3) 0.4842 14 0.1215 0.5050 3 (2,5) 0.0900 0 0 0 - (2,6) 0.0320 7 0.0009 0.1043 - (3,6) 0.0300 0 0 0 - (4,5) 0.2021 14 0.1436 0.1436 3 (5,2) 0.0544 7 0.0199 0.2077 1 (5,6) 0.0688 7 0.0031 0.0031 -

# ijz =k shows that alternative k is chosen for link ),( ji . �-�means do nothing alternative.


Table 3. Quantity jsΦ for Example Network 1.

s

j

3 6

1 0 0 2 0.1957 0.1034 3 0.3646 0 4 0 0 5 0.1878 0.1364 6 0 0.0122

4.2 Discussion

The contribution of the improvement in link ),( ji to the objective function of problem (AP) may be written as:

ijVj Ds

ijjs

ijjs

ijVj Ds

ijjsjs

ijijk

ij pczcpczpIf ∆

Ψ+∆

Φ−=∆= ∑∑∑∑

∈ ∈−−

∈ ∈− )()()(1. ooo

(10)

where ( ) kijijij pp α−=∆ 1 is the percent of reduction by alternative action k in the probability of

accident occurrence in link ),( ji . This improvement in ijp results in an improvement of suitable rt- hr�s of the passengers in the accident-struck link ),( ji by an amount equivalent to the second part of the expression on the right-hand side of Eqn. (10) . The first part of Eqn. (10) regards the rt-hr�s of the network which becomes unsuitable because of the unavailability of an alternative path for the accident-struck link. Improvement in link ),( ji would improve these rt-hr�s by an amount equal to ∑∑

∈ ∈−Φ

Vj Dsij

jsjs cz )( o .

Table 2 shows that link ( )32, has the most importance, because the passengers going from nodes 1 and 4 to node 3 have no other option, except passing through link ( )32, . By accident occurrence in this roadway almost all remaining trips to destination 3 become unsuitable. It is worth noting that link ( )25, is on the one and only path that leads passengers of origin 4 to destination 3 . With an accident in this link, some of the remaining trips in the network become unsuitable. There is an alternative path to replace link ( )65, . Path ( ) ( ){ }6225 ,,,=ρ is such a path. So, passengers destined for node 6 may take this alternative path in case of an accident occurrence in link ( )65, , and keep their rt�s suitable. However, link ( )62, is an important link, because there is no suitable alternative path to replace this link for those passengers who reach node 2 on their way to destination 6. Path ( ) ( ){ }6552 ,,,=ρ is an alternative, but not with suitable travel time. Links ( ) ( ) ( )415121 ,,,,, and ( )54, are links with tail nodes as origins. According to assumption 8, passengers who have not yet started their trips, would not do so in case there is no suitable path. In passing, we note that the second term of Eqn.(10) is the benefit accrued due to the reduction of accident chance for those passengers in link ),( ji , experiencing an accident in this link. This quantity is a function of the number of passengers in this link (which is in turn


a function of the link flow, link length etc.) and their travel times to their respective destinations. Links ( ) ( ),,,, 3254 and ( )21, are links with high values of this quantity.

4.3 AM Problem 1

Consider once again the Example Network 1 in Fig. 2, but this time for an accident mitigation example. Suppose that local streets (links) a, b, and c, with constant travel times 0.60, 0.04, and 0.50 hours may be equipped to bypass links ( ) ( ),,,, 6235 and ( )32, , at a cost of 1 unit each, respectively. Given a budget B , the problem is to identify the (best) projects which increase the objective function (9-0) most. Solving the resulting problem by a suitable algorithm (e.g. a branch-and-bound algorithm similar to Ochoa-Rosso and Silva (1968)), results in the following solution: choose �c� for B=1, and choose �a� and �c� for B=2. It is quite clear why local street �c� has been chosen for B=1. This street may be a suitable alternative for link ( )32, , the failure of which would make a significant number of rt�s in the network unsuitable. Similarly, street �a� may offer an alternative path for those passengers who reach node 5 and intend to go to destination 3.

4.4 Problem 2

To show the applicability of the algorithms presented on large networks, Sioux Falls�network has been chosen as an Example Network 2. This network, with 24 nodes and 76 links, is shown in Fig.3. The network specifications and DO / demands are given in Tables 4 and 5, respectively. Again, for ease of computation, suppose that the average vehicle occupancy is 1 person. The probability of non-occurrence of accident for each link is given in Table 4. Finally, assume that 151.=jsθ for all Vj ∈ and Ds ∈ . Using Algorithm AP to solve problem (AP) results in the importance of links as given in Table 6. For a vector of resources as (30,15,5) = (police, financial resources, accident scene clearance units), the solution of the problem is given in Table 6. Applying Algorithm (AM) on the Example Network 2, proposes the solution given below for various budget levels for the set of candidate local links given in Table 7:

Budget (B) Proposed local streets 1 d 2 d, f 5 c, d, e, f, j

There is an interesting point to note here. Because of the existence of many links in an urban network, like the Example Network 2, it seems that hardly any N/D is 1-link connected; hence, the question arises as to how useful and effective it is to solve an AM problem to implement the actions chosen.. Table 8 is an answer to this question. In this table the ratio of the number of 1-link connected N/Ds to the total number of N/Ds in the Example Network 2 (of Sioux Falls) for various values of jsθ are presented. The ratio in this table shows that it is quite significant for this seemingly connected network. Thus, solution to problem (AM) could be valuable information.


Legend:

________ Main streets _ _ _ _ _ _ local streets

Fig. 3. Example Network 2: The Sioux Falls network.


Table 4. Specifications of the links of Example Network 2.

Link ∗),( ji Free flow time

)( ija )( hr210−× Congestion parameter )( ijb

))//(( 44 100010 dayvehhr×−

Prob. of non-occurrence of accident )( ijp

(1,2) 5.96 0.00023 0.99 (1,3) 4.34 0.00017 0.99 (2,6) 5.17 0.12408 0.98 (3,4) 4.31 0.00069 0.99 (3,12) 4.14 0.00016 0.99 (4,5) 2.16 0.00035 0.99 (4,11) 6.46 0.15504 0.99 (5,6) 4.17 0.10008 0.99 (5,9) 5.03 0.00755 0.98 (7,18) 2.18 0.00008 0.98 (8,9) 9.61 0.23064 0.99 (8,16) 4.82 0.11568 0.98 (10,11) 5.00 0.00750 0.98 (10,15) 5.87 0.00265 0.98 (10,17) 8.04 0.19296 0.98 (11,12) 6.46 0.15504 0.98 (11,14) 4.42 0.10608 0.97 (12,13) 2.98 0.00011 0.99 (14,15) 4.52 0.10848 0.98 (15,19) 3.50 0.00104 0.98 (15,22) 3.50 0.00525 0.98 (16,17) 1.67 0.04008 0.95 (16,18) 2.69 0.00025 0.99 (17,19) 2.31 0.05544 0.96 (18,20) 4.46 0.00017 0.99 (19,20) 3.99 0.09576 0.97 (20,21) 5.72 0.13728 0.98 (20,22) 4.71 0.11304 0.98 (21,22) 1.67 0.04008 0.98 (21,24) 3.29 0.07896 0.97 (22,23) 4.00 0.09600 0.97 (14,23) 4.25 0.10200 0.98 (23,24) 1.88 0.04512 0.98 (9,10) 2.75 0.00124 0.98 (6,8) 2.17 0.05208 0.95 (13,24) 3.72 0.08928 0.96 (7,8) 2.50 0.01185 0.98 (10,16) 4.50 0.10800 0.98

* The information for ),( ij is the same as that of ),( ji


HIER KOMT TABEL 5 (DWARSE PAGINA!)


Table 6. Result of applying algorithm (AP) on Example Network 2.

Link ),( ji ∑∑

∈ ∈−Ψ

Vj Dsij

js c )( o ijI #

ijz Link ),( ji ∑∑

∈ ∈−Ψ

Vj Dsij

js c )( o ijI #

ijz

(1,2) 0.0019 0.0064 - (2,1) 0.0008 0.0143 - (1,3) 0.0026 0.0045 - (3,1) 0.0006 0.0223 - (2,6) 0.0045 0.0081 - (6,2) 0.0012 0.0238 1 (3,4) 0.0041 0.0137 - (4,3) 0.0019 0.0306 -

(3,12) 0.0015 0.0239 - (12,3) 0.0028 0.0152 - (4,5) 0.0036 0.0130 - (5,4) 0.0013 0.0432 -

(4,11) 0.0022 0.0071 - (11,4) 0.0019 0.0093 - (5,6) 0.0055 0.0128 - (6,5) 0.0048 0.0159 - (5,9) 0.0100 0.0209 - (9,5) 0.0072 0.0289 1

(7,18) 0.0021 0.0238 - (18,7) 0.0013 0.0306 - (8,9) 0.0077 0.0136 - (9,8) 0.0062 0.0151 -

(8,16) 0.0056 0.0056 - (16,8) 0.0068 0.0068 - (10,11) 0.0093 0.0332 1 (11,10) 0.0112 0.0267 1 (10,15) 0.0180 0.0367 2 (15,10) 0.0120 0.0506 2 (10,17) 0.0022 0.0155 - (17,10) 0.0044 0.0080 - (11,12) 0.0039 0.0039 - 12,11) 0.0089 0.0089 - (11,14) 0.0084 0.0178 1 (14,11) 0.0070 0.0201 1 (12,13) 0.0017 0.0270 - (13,12) 0.0022 0.0270 - (14,15) 0.0081 0.0138 - (15,14) 0.0058 0.0180 - (15,19) 0.0052 0.0291 1 (19,15) 0.0055 0.0402 2 (15,22) 0.0090 0.0373 2 (22,15) 0.0143 0.0271 1 (16,17) 0.0119 0.0419 3 (17,16) 0.0177 0.0296 3 (16,18) 0.0023 0.0281 - (18,16) 0.0018 0.0275 - (17,19) 0.0114 0.0234 2 (19,17) 0.0091 0.0242 2 (18,20) 0.0042 0.0405 - (20,18) 0.0037 0.0454 1 (19,20) 0.0058 0.0158 1 (20,19) 0.0090 0.0197 1 (20,21) 0.0033 0.0089 - (21,20) 0.0023 0.0186 - (20,22) 0.0029 0.0088 - (22,20) 0.0033 0.0095 - (21,22) 0.0025 0.0078 - (22,21) 0.0019 0.0117 - (21,24) 0.0090 0.0192 1 (24,21) 0.0071 0.0226 1 (22,23) 0.0062 0.0134 - (23,22) 0.0076 0.0106 - (14,23) 0.0042 0.0161 - (23,14) 0.0061 0.0151 - (23,24) 0.0022 0.0129 - (24,23) 0.0017 0.0138 - (9,10) 0.0083 0.0367 2 (10,9) 0.0080 0.0359 2 (6,8) 0.0127 0.0286 3 (8,6) 0.0116 0.0333 3

(13,24) 0.0180 0.0233 2 (24,13) 0.0087 0.0408 3 (7,8) 0.0068 0.0219 - (8,7) 0.0044 0.0351 2

(10,16) 0.0206 0.0206 1 (16,10) 0.0162 0.0162 1

# ijz =k shows that alternative k is chosen for link ),( ji . �-� means do nothing alternative.


Table 7. Candidate local links for problem (AM) for the Example Network 2.

Local street name Link ),( ji ijt (hr) Cost of local st. preparation a (7,16) 0.20 1 b (16,7) 0.20 1 c (13,14) 0.22 1 d (14,13) 0.22 1 e (11,15) 0.24 1 f (15,11) 0.24 1 g (9,11) 0.24 1 h (11,9) 0.24 1 i (19,22) 0.26 1 j (22,19) 0.26 1

Table 8. Ratio of 1-link connected N/Ds to total N/Ds

jsθ Ratio jsθ Ratio 1.10 0.7708 1.50 0.4167 1.15 0.6806 1.70 0.3160 1.20 0.6076 2.00 0.2083 1.30 0.5104

5. Summary and Conclusions

Accident events in transportation networks have three distinct adverse effects: (a) the effects upon those that are directly involved in the accident, which may be a combination of monetary costs, injuries or deaths. These are important and sometimes tragic consequences of traffic accidents that are the primary objectives of most analysts to deal with; (b) the effects upon the users of the network at large, which are usually in the form of traffic delays, opportunity losses and even induced accidents, and (c) the effects upon the environment which may be in the form of air pollution, environmental damages resulting from toxic material spillage, fumes etc. Although great attention has been paid to reducing the adverse effects mentioned above in (a) and (c) , the authors are not aware of any previous work in the area of adverse effects in (b) above (See Iida,1999). This paper endeavours to formulate and solve the design problems of accident prevention and mitigation of (urban) road networks, basically with the objective of reducing the adverse effects of accidents upon the users of the network at large. This is in accordance with upgrading the performance of the network to function properly in cases of accidents or other similar events. In this respect, a network performance index has been defined based on the concept of suitable remaining trip-hours in a network after an accident occurrence in a link. This index led us to a measure of the importance of a link in the network, based on which the problem of accident prevention is defined and an algorithm is presented to solve it. The proposed (AP) algorithm incorporates the following important factors into the decision-making process: the link importance (topology characteristic, flow and length), the probability of accident occurrence in the link (congested and unsuitable traffic behaviour), and the cost of link improvement. A usual approach to select a street for


improvement in accident prevention is based on only some of the above-mentioned factors including congestion, traffic flow and accident probability. The results of this algorithm have been shown for the design of two example networks. The smaller example network has 6 nodes and 10 links and is used to show the reasonability and suitability of the solution results. The second example network with 24 nodes and 76 links is used to show the applicability of the algorithms on large or real-sized networks. In this case, the accident mitigation problem is defined based on the concept of remaining trip-hours and k-link connectedness. The objective of this problem is to make the important 1-link connected node-destination pairs at least 2-link connected. Again, an algorithm has been proposed to solve this problem and the results of this algorithm have been shown for the two example networks mentioned above. Contrary to the general belief that 1-link connected node-destinations are rare in an urban street network, it has been shown in this paper that a seemingly connected Sioux Falls� network has a surprisingly high proportion of 1-link connected node-destinations. Thus, (AM) algorithm may be an effective means for improving network connectivity. Several assumptions have been made in the definition of the problem (AP) and (AM). Some of them are made to avoid undue complexities in the presentation of the problem and may be relaxed. For example, assumption 2 (accidents only occur in the links) may be relaxed by representing an intersection by several links. Research is under way to relax assumption 3 (users are informed about accidents immediately), and assumption 6 (the change of paths has negligible effects upon other users of the network). Moreover, the concept of suitable remaining trip-hours is related to a measure of welfare of the travellers, e.g. consumer surplus.

References

Asakura, Y. (1996). Reliability measures of an origin and destination pair in a deteriorated road network variable flow. In: Bell, M. G.H. (Ed). Transportation Networks: Recent Methodological Advances. Pergamon Press, Oxford.

Du, Z.P. and Nicholson, A.J. (1997,a). Degradable transportation system: an integrated equilibrium model. Transportation Research B, 31, No.3, pp.209-223.

Du, Z.P. and Nicholson, A.J. (1997,b). Degradable transportation systems: sensitivity and reliability. Transportation Research B, 31, NO.3, pp.225-237.

Iida, Y. (1999). Basic concepts and future direction of road network reliability analysis. Journal of Advanced Transportation, Vol.33, No.2, pp.125-134.

Nazim, U.A. (1983). An analytical decision model for resource allocation in highway maintenance, Transportation Research A, Vol.17A, No.2, PP.133-138.

Ochoa-Rosso, F. and Silva, A. (1968). Optimum project addition in urban Transportation networks via descriptive assignment models, Research Report R68-44, Dept. of CE, MIT, Cambridge, Mass..


Pierre, S. and Elgibaout, A. (1997). A tabu-search approach for designing computer-network topologies, with unreliable components. IEEE Transactions on Reliability, Vol.46, No.3, pp.350-359.

Sanso, B. and Soumis, F. (1991). Communication and transportation network reliability using routing models. IEEE Trans. on Reliability. Vol.40, No.1, pp.29-38.

Sanso, B. and Milot, L. (1994). A reliability model for urban transportation planning. Preprint in TRISTAN-II Conference, Capri, Italy, pp.617-622.

Wakabayashi, H. and Iida, Y. (1994). Improvement of road network reliability with traffic management. IFAC Transportation System, pp.603-608.

Appendix

A.1 Proof of Proposition 1

There are dttm

ij)( number of travellers in a dt time interval at a point e in link ),( ji destined to

s , by assumption of uniform distribution of the travellers over links, as shown in Figure A1. If t is the travel time from e to j , the time for these travellers to reach destination s is jstt +

, and the expected suitable rt-hr�s is approximated by )())()()(( czczttttdt

tm js

ijij

js

ij−+ 1 1, where

))(( cztt

ijij

−1 is the probability of having no accident from e to j in state c , and

)(cz js accounts for the rest of the trips from j to s to be suitable. Thus,

∫ −+≈ijt

jsij

ij

js

ij

sij dtczcz

tttt

tmcE

0

1 )())()()(()(

which leads to the stated expression.

Fig.A1. Accident occurrence and determination of expected suitable rt-hr’s.

1 Assuming that

esrt is suitable if and only if there is no accident in link segment ),( je

and jsrt is suitable.


A.2 Proof of Proposition 2

By the proportionality assumption, for ksxρ number of travellers per unit of time on path ρ from k to s , there will be kskstx ρρ travellers on path ρ at any instant of time, with

)( ksijksks

t

ttx

ρρρ being the share of link ),( ji of that path hosting these travellers at that instant. Thus,

in general ksijij

kstx ρρ δ , is the number of travellers in link ),( ji due to those travelling in path ρ from k to s . Then, ks

ijijks

Ok kstx ρρ

ρρ

δ ,∑ ∑∈ ∈

would be the total number of travellers in

link ),( ji heading to destination s . So, according to Proposition 1, the expected rt-hr�s of all travellers in link ),( ji destined to s in state c may be written as:

∑ ∑∈ ∈

+−+=Ok ks

jsij

jsijks

ijijksjsjsijks

ijijkss

ij czcztttxczt

ttxcE

ρρρρρρ δδ )]()()()()([)( ,, 232

Then, this quantity in state c for all links with the head node j , )(cE js , is:

∑∈

=)(

)()(jBi

sij

js cEcE

For the network it is:

∑∑∈ ∈

=Vj Ds

js cEcE )()(

On the other hand, for the prevalent state oc the rt-hr�s of the network may be computed as follows: ksd is the rate of demand per unit of time from k to s , which takes kst unit of time to reach s from k . Then, at any instant, kskstd would be the total number of travellers from k to s . On the average, these travellers are half-way through their path from k to s , so that the

average remaining time for them would be 2

kst , and hence:

∑∈

=Psk

ksksks ttdcE

),(

)()(2

o

Thus,

∑

∑∑

∈

∈ ∈==

Psk

ksksks

Vj Ds

js

ttd

cE

cEcEcPI

),(

)(

)(

)()()(

2

o

which leads to the stated expression.

Valuing a Road Network Improvement using Stated Preferences Methods

Aurelia Bengochea Morancho* and Salvador del Saz Salazar** * Departament d�Economia Universitat Jaume I Castellón Spain E-mail: [email protected] ** Departament d�Economia Aplicada II Universitat de València Valencia Spain E-mail: [email protected]

EJTIR, 3, no. 3 (2003), pp. 263 - 280

Received: July 2003 Accepted: March 2004

In this paper we address, from a double perspective, the social valuation of transport improvements caused by the construction of a new motorway. First, we estimate the value citizens confer on this infrastructure as a whole. Second, we assess the time savings and the reduction in the risk of accidents the new motorway might be expected to bring about in relation to roads used at the moment. To do this, we use two approaches based on individuals’ stated preferences: the contingent valuation method and conjoint analysis. The results show the social benefits of this project to be positive, although to what extent depends on initial assumptions. The information provided in this study will be useful to public managers since it can be incorporated in a cost-benefit analysis on the social profitability of this public investment.

Keywords: Road endowments valuation, Transport improvements appraisal, Stated preferences methods, Contingent valuation, Choice experiments.

1. Introduction

The assessment of improvement in citizens� welfare derived from an increase in public infrastructures, such as the construction of a new motorway, presents certain difficulties.

264 Valuing a Road Network Improvement using Stated Preferences Methods

From an economic point of view, the provision of this type of goods takes on the characteristics of a public good and, consequently, it lacks a market price. This fact has caused the social valuation of certain public projects to be frequently ignored in cost-benefit analysis, hereby seriously impairing the accuracy and relevance of the results. Economic science has developed specific methods that enable us to assess the social welfare changes caused by variations in the quantity or quality of public goods which became part of the individuals' utility function. Although they have no market price, the value of these public goods can be inferred in several ways. In a broad sense, we can distinguish between indirect and direct methods of valuation (Freeman, 1993). The first category includes all those techniques based on demand functions, observed cost functions, changes in commodities or inputs prices, transactions made in the market such as the purchase of housing or the observation of individual behavior related to certain recreational activities. The second category covers those methods where the value of the public good is obtained by directly asking people how much they are willing to pay for the good. The theoretical background of both categories can be found in the neoclassical consumer theory, according to which the value assigned to a good or service is based on the individual preferences. The social benefit is obtained by aggregation of the individual values. From this perspective, the value afforded by the provision of a public good can be inferred from the analysis of revealed preferences (indirect methods) or from stated preferences (direct methods). In this paper we use two approaches from the second category (the contingent valuation method and the choice experiment) to value the social benefits derived from a new motorway in Castellón (Spain). This new road will ease traffic between the ceramic industrial district and the Port of Castellón, an area that currently experiences very high flows of both passenger and commodity transport, with daily average intensities sometimes exceeding the existing capacity of the transport network. Determining the potential benefits of this investment provides useful information for a cost-benefit analysis on its social profitability. The paper is structured as follows: the first sections describe the methodology, section four introduces the scenarios presented and section five sets out the results. Finally, section six summarizes the main conclusions of our study.

2. The contingent valuation method

The theoretical foundations of the contingent valuation method are based on the consumer rational choice theory. This assumes that individuals take consumption decisions which maximize their welfare and that consumers� preferences are defined for private and public goods. Following Braden, Kolstad and Miltz (1991), let us suppose that q is the amount of a public good, v is its quality, Y the personal available income and, finally, x the amount of a combination of private goods. It is also assumed that p is the price of the public good and that the price of the composed good is one. We also suppose p to be a normalized price with respect to the private good. The consumer attempts to maximize the following utility function:

Aurelia Bengochea Morancho and Salvador del Saz Salazar 265

0,..

),,(max,

≥≤+

xqYxpqas

vxquxq

(1)

From a theoretical point of view, the accurate measure of the change in the individual�s welfare is the amount of money that would cause him or her to be indifferent to whether or not there is a variation in the quantity or quality of the public good. Let us suppose that the consumer spends all his or her income. For a certain level of Y and v, the consumer solves the equation (1) obtaining an utility u* and an optimum consumption basket (q*,x*) depending on p, Y and v. By totally differentiating the utility function in its optimum values (u* = u (q*, x*, v)] and considering the budget constriction [Y = pq* + x*] we obtain the following expressions:

dxxudv

vudq

qudu

∂∂

∂∂

∂∂ ++=

(2)

dxdqpdpqdY ++= (3)

If we attempt to see how the changes in the variables q and v can be compensated by changes in the variable Y, then du = 0 and, at the same time, if we suppose prices to be fixed, then dp = 0 and this term disappears from the equation (3). If we reorder the two previous equations, we have:

dvxuvudq

xuqudx

∂∂∂∂

∂∂∂∂ +=− (4)

dYdqpdx −=− (5)

Let us now suppose v to be the attribute for which a change is contemplated. By equaling terms and reordering equations (4) and (5), we obtain

dYdqpdvxuvudq

xuqu −=−+

∂∂∂∂

∂∂∂∂

(6)

This equation shows that the payment should equal the difference between the value the individual places on the change in the quantity and quality (the first two terms of the left hand side in the previous equation) and the change in the money spent in q (the last term of the left hand side). A fundamental condition in consumer theory is that individuals, to maximize their welfare, equal the substitution marginal relation to the products prices relation, which means that

pxuqu =

∂∂∂∂ (7)

Now, by replacing (7) in (6) we obtain the following equation:


dvdY

xuvu −=

∂∂∂∂ (8)

This expression indicates that the substitution marginal relation between the quality of the public good (v) and the private good (x) should equal the change in the individual�s income (the amount he or she would be willing to pay) to maintain the utility constant when v is changing. Hence, if the change in quality is positive, then the consumer would be willing to reduce his level of income to keep the utility constant and vice versa if the change is negative. Thus, the substitution marginal relation coincides with the monetary variation that would cause the consumer to be indifferent to whether or not there is a change in the quality of the public good.

3. The choice experiment technique

The choice experiment is an approach based on conjoint analysis, another stated preferences method. Its purpose is to obtain an indirect utility function in which the utility yielded by the consumption of a good depends on the level of its attributes. The first applications of this technique appeared in the seventies, mainly in transport economics (Louviere et al., 1974; Norman and Louviere, 1974), but over recent decades its use has been extended to other fields such as marketing, health economics and environmental economics. As stated by Louviere (1988), the decision process followed by consumers of comparing available alternatives until they make their final choice is a complicated one, due to the high number of factors that influence their assessments. The individual observes the actual situation and devices certain psycho-physical trials that will lead him or her, depending on his or her beliefs and perceptions, to value the characteristics of the good being considered in a certain way. By evaluating the total set of attributes, the individual comes up with an overall valuation on which the final decision will be based. This choice can be modelled as follows: Let us start from a situation in which there are J complete profile alternatives (X1, X2, ..., XJ). The researcher selects M of these profiles to form a choice set C = {j1, j2, ..., jM} which is presented to the respondents. They are asked to select one of the profiles in the set. Following Laitila (2001), the decision problem that the respondent faces can be formulated as an optimizing problem within the consumer�s utility theory framework.

mi

mmZ

cYZPas

XZUi

−≤..

),(*max,

(9)

where Ui* is the utility function, Yi is the income of individual i, Z is a set of goods he or she consumes with a corresponding price vector P, Xm is the attribute vector of profile m where cost cm is also included. The indirect utility function, conditional on choosing the profile m can be specified as:

),,( mmiim XcYPU − (10)


Assuming that the respondent chooses the profile yielding the highest utility, we can state that

mjCjUU ijim ≠∈∀> KK (11)

If the utility function is linear, then

imimimim cYXPU εαγβλ ++−++= )( (12)

where λ and β are parameter vectors, γ is the marginal utility of income, αi is an individual specific component and εim is a unknown individual specific component corresponding to profile m. Since Pλ, γYi and αi are constant over the alternatives in the choice set C, they do not affect the decision the respondent eventually made, therefore the decisional rule can be restated as: The respondent chooses profile m if

mjCjcXcX ijjjimmm ≠∈∀+−>+− KKεγβεγβ (13)

Assuming respondents are randomly chosen, the unknown individual component corresponding to profile m can be interpreted as a random disturbance term. The probability of obtaining a respondent choosing profile m is

mjCjcXcXPCmP ijjjimmm ≠∈∀+−>+−= KK)(),,:( εγβεγβγβ (14)

If the disturbances εi1, εi2, ..., εiM are independent and identically distributed with density function g(ε), then

ducXuGcXugCmPjj

Mmjmm

)()(),,:( γβγβγβ +−+−= ∏∫ ≠

∞+

∞−

(15)

In the case that disturbances are extreme value distributed, we obtain

∑ ∈

−

−

=Cj

cX

cX

jj

mm

eeCmP γβ

γβ

γβ );,:( (16)

Parameters β and γ can be estimated using the maximum likelihood procedure and the willingness to pay for a certain profile can be obtained with the following formula:

γβj

jprofile

XWTP =L (17)

The marginal value of a change in an attribute can be measured in terms of compensating variation, as stated by Roe et al. (1996), according to the following expression:

γβ s (18)

where βs is the coefficient corresponding to attribute s and γ is the cost coefficient.


4. Scenarios presented

As mentioned above, direct valuation methods are based on stated individual preferences and the value of the public good is inferred from the choice respondents made when facing different hypothetical alternatives designed by the researcher. Therefore, an essential element in empirical applications is the questionnaire presented to the respondents. The survey used in this study was structured in four parts. The first one introduced the individual to the valuation, it outlined the fact that the questionnaire was both anonymous and voluntary, in order to put respondents at ease for providing truthful answers. A verbal description of the current situation and the proposed project was illustrated with pictures, maps and a plan of the layout of the new road. The first questions picked up the respondents� previous knowledge on the projected motorway and their personal opinion related to the need for and the potential advantages of this communication infrastructure. The advantages considered referred to the level of noise, number of traffic accidents, atmospheric pollution, time savings on journeys and, finally, the expected use of this new infrastructure by the interviewee. Once the public good to be valued had been defined, the second part of the questionnaire contained the elements needed in a hypothetical market simulation: the amount of the public good, the mean of provision, the payment vehicle and the elicitation question. The payment vehicle consisted of a voluntary contribution to a special fund for carrying out the works over the foreseen period of execution (2002-2005)1 until the project was complete. This payment vehicle was chosen because it appeared the most neutral for the valuation of this kind of goods in Spain. On the elicitation question, we followed the recommendations suggested by the Blue Ribbon Panel (NOAA, 1993). It was formulated in a closed-ended format and in terms of willingness to pay (equivalent variation), not in terms of required compensation. First, the interviewee was asked whether or not he or she would be willing to contribute to the financing of the project. With this we hope to discover whether or not the respondent was in the market for this public good2. Next, a dichotomous question was formulated in which the respondent had to accept or reject a bid amount proposed as the payment for the provision of the new road. Finally, in an open question, respondents were asked about their maximum willingness to pay (WTP) for the good. If respondents stated that they were not willing to pay anything, they were asked to explain the reason for this position. The aim was to differentiate the �actual zero answers� from the �protest answers� (Portney, 1994)3. To avoid an overestimation of the WTP, the interviewee was reminded of his budgetary restriction as well as the fact that other

1 As Azjen et al. (1996) suggest, it is important to remind the interviewee of the time period in which the public

good will became available, since this reinforces the credibility of the hypothetical market. At the same time, the interviewee can judge whether or not this period of time is relevant to him or her.

2 This question, together with the dichotomous enabled us to apply a Spike model (Kriström, 1997) to estimate the expected WTP.

3 In the contingent valuation context, "protest answers" are understood as unwillingness to pay which in fact does not mean that the respondent places zero value on the good, but rather the rejection has to do with fair-play in the hypothetical market. In contrast, when the refusal to pay reflects true preferences (because the respondent is not interested in the good valued) or it is the result of a low income, the answer is called "actual zero" as opposed to "protest zero".


public projects might also require monetary contribution. The simulation of the market was drafted as follows:

As you will be aware, it is increasingly important for public administration to take into account the opinion of citizens affected by certain public investment projects. Although the new motorway described will be financed through public funds, in order to find out the extent to which you value the project, we would like you to imagine that it had to be funded by the public through a special compulsory payment used to carry out the project within its execution period (two and a half years).

Q 9. In the light of your personal income and of the fact that there are other public projects for which financial contribution could be requested, would you be willing to pay any amount of money during the two and a half years the new road was being built?

□ Yes □ No (Go to Q11)

Q 10. Given that you are willing to pay a certain amount of money, would you be willing to pay X euros per year?

□ Yes (Go to Q10a) □ No (Go to Q10b)

Q 10a. Given that you would pay at least X euros, what is the maximum amount you would be willing to pay? (Go to Q12)

Q 10b. Given that you would not pay X euros, what is the minimum amount you would be willing to pay? (Go to Q12)

In the dichotomous question, five different bids were used: 6, 30, 60, 100 and 150 euros. Diversification of bids is a strategy to avoid the possible �starting point� bias. There is no universally accepted viewpoint in the literature on the number of different bids offered4; in our case, the choice of these bids was based on the amounts declared in the valuation open question formulated in the pilot survey. The third part of the survey presented the choice experiment questions. As mentioned above, this method enables us to capture individual preferences referring to the characteristics that define certain goods and to express in monetary units the welfare variations associated to changes in the levels of the attributes that configure the evaluated profiles. In our case, following focus group discussions, the attributes considered were the reduction in the risk of accidents, journey time savings and the toll to be paid for using the new motorway5. Clearly, other aspects could have been considered but we tried to reduce the number of attributes to a minimum for avoiding inaccuracy in the estimation since, according to DeShazo and Fermo (2002), the inclusion of more attributes leads to an increase in the utility function error term variance. These authors also find that there is a quadratic relationship between the error variance and the number of profiles evaluated; in the first stage the variance falls and later it

4 See Alberini (1995) for an in-depth analysis on this subject. 5 Since the toll payment is expressed in monetary units, its inclusion among the attributes will allow us to deduce

the monetary value of reducing the risk of accidents and also the value of the journey time savings.


increases as new attributes are added. In order to obtain the minimum variance, we included a moderate number of profiles in each subset presented to the respondents. With regard to the levels of the attributes, we considered four levels, including the �status quo�. This gave us 4x4x4 = 64 different combinations, 16 of which were evaluated through a distribution in subsets of four profiles with no dominant options in any subset. With respect to the range of the levels� values, as far as possible, we tried to adjust the scenarios to the information picked up in the focus groups and to be realistic in order to make the situation credible. Thus, the intervals of time savings are not too long (from 0 to 15 minutes) since much greater savings cannot be expected over a distance of 11.5 kilometres. We were equally cautious when establishing the reduction in the risk of accidents (0% to 30%). As far as the toll payment was concerned, values range from a heavy toll to a light one (0.15 to 0.03 euros per kilometre respectively). The scenarios constructed and the profiles evaluated are set out below. The interviewer read the following text:

We are particularly interested in finding out public opinion on the design of this new motorway, since we think that citizens know better than anybody else what their needs are. We would like you to imagine that it was possible to choose the characteristics of this new road concerning the risk of accidents, journey time savings and the toll cost. Bear in mind that as the risk of accidents decreases and journey time savings increase, the cost of the construction of the new road will also increase; therefore, the potential payment requested to use this motorway would also be higher. Next, we will show four possible alternatives with different combinations of these improvements. The amount in euros represents the toll we would have to pay to use the road6.

Subsequently a selection of four profiles was shown to each interviewee. As explained above, a set of 16 different orthogonal profiles were evaluated, grouped into four subsets, each of them containing the current status quo7. Each respondent valued only one subset of options where the levels of the attributes were combined in such a way that no one profile dominated another in the same subset. The valuation scenario was designed in this manner because eliminating the dominant alternatives improves the efficiency of the estimation, as Allenby and Arora (1995) demonstrated. The subsets evaluated were structured as follows:

6 In order to make the scenario credible, we stressed the fact that the potential payment requested to use the new

motorway would increase as the risk of accidents decreases and time savings increase. However, this correlation do not appear in the hypothetical alternatives submitted to the respondents since their construction is based on a experimental design and we have selected an orthogonal subset from the possible combinations.

7 As an anonymous referee has pointed out, in fact they are not 16 profiles but only 13 since each of the four choice set includes three alternatives and one base alternative, which does not vary across the choice sets. The profiles were grouped in such a way that no one profile was �dominating� among the other profiles placed in the same subset.


SUBSET A

A1 A2

Time saving: 0 minutes

Accident reduction: 0%

Toll: 0 euros



Toll: 1 euro

A3 A4



Toll: 0.60 euros



Toll: 1.5 euros

SUBSET B

B1 B2



Toll: 0 euros



Toll: 1 euro

B3 B4



Toll: 1 euro



Toll: 1.5 euros


SUBSET C

C1 C2



Toll: 0 euros



Toll: 0.60 euro

C3 C4



Toll: 1 euro



Toll: 1.5 euro

SUBSET D

D1 D2



Toll: 0 euros



Toll: 0.60 euro

D3 D4



Toll: 0.60 euros



Toll: 1.5 euro


Finally, the fourth part of the questionnaire was made up of a group of questions on respondents� socio-economic characteristics with the purpose of later estimating a validity function where the stated willingness to pay would be explained by these variables. The survey process began in October 2002 with a pilot survey previously discussed in focus groups. After a few changes, the final surveys were carried out in December 2002. A sample of 405 respondents living near the future road were personally interviewed in their homes. The addresses were selected following random routes and matching the reference population�s age and sex quotas to ensure the sample was representative of the citizens potentially affected by this new road. The interviews were conducted by professionals to avoid any interviewer bias caused by lack of training8.

5. Social benefits estimation

5.1 Overall valuation of the motorway provision

From the data gathered in the valuation questions, we estimated the social benefits derived from the provision of this new public infrastructure. The respondents faced a binary question, a bid they should accept or reject depending on whether the payment suggested was higher or lower than their willingness to pay. An open question was then asked to find out their maximum WTP. In the contingent valuation studies with a binary or referendum format, the WTP is usually obtained from the parameters estimated in a logit or probit model. These formulations presuppose that the WTP is distributed following a logistic or a normal function and that all the respondents have a positive WTP for the public good being valued. Other distributions frequently used, such as the log-logistic, lognormal and the Weibull, also assume the WTP to be positive. However, it is possible that some people would not be willing to pay for the good; a discontinuity might then appear in the distribution of the WTP. Halvorsen and Saelensminde (1998) stated that when this fact is ignored, the model is heteroscedastic and the estimators are biased. Therefore, when there is a high percentage of �zero answers�, other more appropriate empirical models should be used. The model developed by Kriström (1997) allows individuals to have a WTP=0 for the public good. It is then possible that a �spike� might occur in the WTP distribution function, i.e., a discontinuity or a jump at zero value9. Yoo and Kwak (2002) state that the Spike model, by taking into account these possible zero answers, significantly improves on the approaches based on conventional models. In this study the percentage of �zeros� was 72%, of which 35.8% were protest answers. Thus, the most suitable approach was to apply a Spike model. This model requires two valuation questions. The first determines whether the respondent is willing to contribute to the provision of the public good, in other words, it attempts to discover whether or not this 8 The survey was administered by Metra-Seis, a market consulting firm, and was made as a stratified probability

sample by establishing quotas according to the population demographic structure. 9 A "spike" means that the empirical survival function does not have a smooth path along the whole range of

probabilities, from zero to one. The fact of having a discontinuity, a spike, at zero value indicates that some individuals do not want to pay for the good, regardless of the price they would have to pay for it.


consumer is in the market for the good. If the individual agrees, a bid A is put forward in a second question. For each individual i, an indicator Ei is defined which reflects whether or not he or she is in the market:

Ei = 1 if WTP > 0 (0 otherwise) (19)

and another indicator Di which shows whether or not the respondent is willing to pay the suggested bid A:

Di = 1 if WTP > A (0 otherwise) (20)

The probability that an individual�s WTP does not exceed an amount A is given by

)()( AFAWTPprob WTP≤ (21)

where FWTP (A) is a right, continous, non-decreasing function. If we assume that WTP is distributed as a logistic on the positive axis, FWTP(A) can take the folowing values:

]]

00)(0)exp(1[)(0)exp(1[)(

1

1

<==+=>−+=

−

−

AifAFAifAFAifAAF

WTP

WTP

WTP

LLLLLLLL

LLL

L

αβα (22)

where α can be interpreted as the marginal utility of environmental improvements and β as the marginal utility of income. The log-likelihood function to be maximized is:

[ ] [ ] [ ])0(ln)1()0()(ln)1()(1ln1

WTPiWTPWTPiiWTPi

N

i FEFAFDEAFDEl −+−−+−=∑ (23)

After estimating the relevant parameters, the expected WTP is obtained by solving the integral:

∫∞

−+−=

0 )exp(1)exp()(A

AWTPEβα

βα (24)

or solving the following equation if β is positive:

[ ])exp(1ln1)( αβ

+=WTPE (25)

The spike is defined as the value for which FWTP (A) = 0, which means the probability of the WTP equalling zero. Kriström (1997) demonstrates how this value can be obtained with the following formula:

[ ])exp(111

α+−=spike (26)

We estimated the log-likelihood function (equation 23) using the econometric package LIMDEP. The mean of the WTP is 48.04 euros over the whole sample or 70.36 euros if the protest answers are excluded to leave only actual zeros. Exclusion of the protest zeros is normal practice in contingent valuation studies (Freeman, 1993), since otherwise, the valuation would be underestimated because zero values would be attributed to individuals


who value the good positively but do not accept the outlined hypothetical market. Table 1 presents the coefficients estimated and the WTP in each case. Table 1. Spike model estimation

α β Mean (euros)

Median (euros)

Protest zeros included

-0.975412 (-17.497)

0.006658 (11.156)

48.04 0

Protest zeros excluded

-0.298059 (-4.747)

0.007890 (11.533)

70.36 0

t-statistic in brackets. To deal with the aggregation, the population considered was made up of inhabitants living in the municipalities nearest to the new infrastructure, as these citizens are the most immediate potential beneficiaries10. The aggregation of the individual valuations yields a social benefit of around the 37 million euros (specifically, 37,083,062 euros). Although this figure is lower than the budget for to the motorway construction, it must be borne in mind that this amount only picks up the valuation citizens make in their role as future users of the infrastructure. However, this new road will be heavily used by vans and trucks coming from the ceramic industrial district to the Port since it will provide them with a new quicker and less congested route. The incorporation of the benefits this new motorway provides to these stakeholders would increase the benefits obtained.

5.2 Benefits of the improvements in transport conditions

Respondents were questioned on the possible advantages of the ring roads on easing traffic congestion, the reduction of traffic accidents and lower pollution. The valuation scale for all these aspects was : a great deal, fairly high, not very high and none. Table 2 summarizes the answers obtained. Most interviewees considered ring roads can reduce the noise and lower the number of accidents but they were quite skeptical about cutting pollution levels down. Table 2. Assessment of potential advantages of the by-pass

Assessment Noise reduction Accidents reduction Reduction in pollution frequency % frequency % frequency % A great deal 113 27.9 70 17.3 84 20.7 Fairly high 167 41.2 110 27.2 102 25.2 Not very high 72 17.8 114 28.1 78 19.3 None 37 9.1 62 15.3 116 28.6 No response 16 4,0 49 12.1 25 6.2 Total 405 100.0 405 100.0 405 100.0 Modal value �Fairly high� �Not very high� �Not very high�

10 A population of 256,159 was considered, although for the aggregation we only considered individuals over 18

(210,819) since they have the right to vote and, legally, they are able to decide.


A choice experiment was designed to estimate the benefits of journey time savings and reduced risk of accidents. The interviewees indicated their first choice option from four hypothetical alternatives that differed in their attributes levels. As mentioned in section 3, if the consumer�s preferences function is assumed to be linear and the price is one of the attributes, then the marginal value of a change in a certain attribute can be expressed in terms of compensating variation. Equation (16) was estimated and the results are shown in Table 3. The signs of the coefficients are as expected, positive for the variables corresponding to time savings and accidents reduction, negative for the variable cost. When formula (18) is applied, the WTP for reducing journey time by one minute would be 0.03 euros and the WTP for reducing the risk of accidents by one percentage point would be 0.06 euros. According to these figures, we estimate the WTP for various profiles by applying formula (17) (Table 4). Table 3. Choice experiment: Coefficient estimates

Variable Coefficient t-statistic P-value Journey time reduction 0.099205 2.00 0.045 Risk of accidents reduction 0.189814 5.16 0.000 Cost -3.310607 -4.65 0.000 Log L N11

-434.05261 812

Table 4. Appraisal of a subset of four profiles (euros)

Profile 1 Profile 2 Profile 3 Profile 4

0 minutes 0% risk reduction




WTP 0 0.84 1.2 1.86

Our results concerning time value are similar to those obtained in previous research. Calfee and Winston (1998) conducted a study on the value of automobile travel time in the major U.S. metropolitan areas. They focused on commuters who spend 40-60 minutes driving to work and usually face some congestion. The respondents did not perceive all time to be onerous since they were only willing to pay to reduce congested time (3.84 dollars per hour on average) and did not place value on uncongested time. In our study we estimate a lower value (1.8 euros per hour) but there are no distinctions between congested and uncongested time. This figure is more similar to those obtained by Bergkvist and Westin (1998) referred to the value of travel time in the Swedish road freight. The sample was made up of transport companies. The mean value for all transports was found to be 14 SEK per hour and transport (1.54 euros12). With respect to the risk reduction, our figures are lower than those reported by Persson (2003) concerning traffic safety valuation on Sweden. The studies quoted used the CV approach: the

11 There were 405 surveys but they gave rise to 1620 theoretical observations since each respondent had to

choose from four alternatives. After eliminating the incomplete answers, 812 observations remained. 12 According to the exchanges rates on 2004, 18th January.


subjects were asked about their WTP for 50, 25 and 10 per cent reductions respectively. The marginal WTP was found to be a decreasing function of the size of risk reduction, hence the amount the respondents were willing to pay for one percentage point ranges from 3.07 euros to 1.99 euros. To calculate the aggregated value of both improvements, time savings and accident reduction, we considered different scenarios. For time savings we established a range from 8 to 12 minutes. This is a conservative estimate adjusted exclusively to the new section of 11.5 kilometers. Net savings will probably be closer to 20 or 30 minutes since the new road will bring improved transport fluency within the area under study. Regarding accidents, we assumed the reduction could range from 10% to 25%. We then took into account the transport flows on the A and B roads connecting the Port with the municipalities near the new motorway (Table 5). Multiplying the daily average vehicle intensity on these roads by the monetary value of time savings and the accident reduction assumed, we obtained an estimation of the aggregate value of these improvements. Table 6 summarizes the social benefits corresponding to the different scenarios. The first columns shown in Table 6 have been obtained by multiplying the last column of Table 5 (annual transport flow) by the monetary value of the time savings (0.24 euros for 8 minutes, 0.30 euros for 10 minutes and 0.36 for 12 minutes). The same applies to the figures related concerning the monetary value of safety gains (the last three columns). The last row summarizes the total benefits by adding the partial benefits of the roads connecting the ceramic industrial district to the Port: 4,144 thousands of euros per year (for 8 minutes saved); 7,401 for 10 minutes and so on. It is worthy to notice that figures concerning accident reduction are higher than those concerning time savings, which may indicate that people value more safety than time savings. To infer the social benefits yield by the new motorway, several scenarios can be considered. If we supposed, for instance, that the new motorway would save 10 minutes on average with respect to the current spending and that it would reduce the risk of accidents by 15%, then the social benefits would be 29.6 million euros. This amount is the result of adding the value of both time savings (7,401 thousands of euros) and accidents reduction (22,202 thousands of euros). Similarly, the appraisal of the improvements described in profiles 2 and 4 can be obtained (18,945,121 euros and 45,883,456 euros respectively). Table 5. Transport flows on the A and B roads near the new motorway

Road DAVI Annual transport flow

CN-225 9.592 3.501.080 C-01801 16.741 6.110.465 C-18301 4.800 1.752.000 CN-340 (i) 16.173 5.903.145 CN-340 (ii) 20.279 7.401.835

DAVI: daily average vehicle intensity Source: Own calculations


Table 6. Social benefits yielded by time savings and accidents reduction (thousands of euros per year)

Roads Time savings Accident reduction 8 min 10 min 12 min 10% 15% 25%

N-225 840 1,050 1,260 2,101 3,151 5,252 C-01801 1,467 1,833 2,200 3,666 5,499 9,166 C-18301 421 526 631 1,051 1,577 2,628 CN-340a 1,417 1,771 2,125 3,542 5,313 8,855 CN-340b 1,776 2,221 2,665 4,441 6,662 11,103

4,144 7,401 8,881 14,801 22,202 37,003

6. Conclusions

In this paper we have estimated the social benefits derived from the construction of a 11,5 kilometers stretch of motorway. This new road will improve the connections between the ceramic industrial district and the Port in the province of Castellón (Spain). The analysis was carried out from a double perspective. First, we considered the social value the affected population places on the provision of this infrastructure seen as a whole. Second, we appraised the potential improvements the new road could bring in relation to the decrease in the accident rate and the time stakeholders could save in their current journeys within the affected area. The methodological approaches used were the contingent valuation method and the choice experiment, two direct valuation methods based on individuals� stated preferences. Both are extremely versatile and allow ex-ante valuations to be obtained before the provision of the public good takes place, as in the present case. To carry out the study, 405 citizens living in the town of Castellón were interviewed. The analysis of the first questions in the survey showed that most citizens were unaware of this project, with 62% of the respondents claiming not to have heard about it. Nevertheless, there is a clear social perception of the advantages the construction of ring roads has, since most people consider these infrastructures to be very necessary. In particular, they stated that the new motorway would contribute to making journeys through the Castellón metropolitan area easier and faster. Our estimation of the social value of this new transport provision gives us a figure of over 37 million euros. The appraisal of potential improvements in transport by means of the choice experiment resulted in 0.03 euros for one minute of time saved and 0.06 euros for a 1% reduction in the risk of accidents. The figure concerning time value is similar to those obtained by Calfee and Winston (1998) in U.S. metropolitan areas and it is also similar to the amount Bergkvist and Westin (1998) estimated referring the Swedish road freight. With respect to the risk reduction, our figures are lower than those reported by Persson (2003) concerning traffic safety valuation in Sweden. To infer the social benefits yield by the new motorway, several scenarios can be considered. Thus, if we suppose that the new road will reduce journey time by 12 minutes and the risk of accidents by 25%, its social benefits would amount to 45.8 million euros. When considering


more modest scenarios, the social value of the improvements is lower, at around 19 million euros. In general, the figures concerning accident reduction are higher than those concerning time savings, which may indicate that people value more safety than time savings. Although the decision of whether or not to build the motorway requires other factors to be taken into account, the information provided in this study will be useful to the professionals in the public sector responsible for managing financial and territorial resources that belong to society as a whole. In particular, the social benefits estimated here can be incorporated into a cost-benefit analysis on the social profitability of this public infrastructure. Cities and their surrounding areas are undergoing continuous evolution and transformation, which poses a constant challenge to public managers who must provide immediate answers to citizens� needs. New investment projects planned, when they affect the potential welfare of thousands of citizens, should incorporate a serious and rigorous assessment of the social benefits they generate. Stated preference methods, despite their limitations, pick the information up directly from citizens and can help to achieve this goal.

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A Differential Game Modeling Approach to Dynamic Traffic Assignment and Signal Control

Zhenlong Li and Songquan Shi The Laboratory of Complex Systems and Intelligence Science Institute of Automation Chinese Academy of Sciences Beijing China

EJTIR, 3, no. 3 (2003), pp. 281 - 297

Received: June 2003 Accepted: March 2004

This paper addresses a theoretical issue related to combined dynamic traffic assignment and signal control under conditions of congestion through a brief review of previous research and the discussion on interaction between dynamic traffic assignment and signal control. The dynamic characteristics of the interaction are approached using a differential game modeling approach here to formulate the decision-making process for solving the problem inherent in this combination. Specifically, the combined dynamic traffic assignment and signal control problem is formulated as a leader−follower differential game, where a leader and multiple followers engage interactively to finding optimal strategies under the assumption of an open-loop information structure. Discretization in time is used to find a numerical solution for the proposed game model, and a simulated annealing algorithm is applied to obtain optimal strategies. Finally, a simulation study is conducted on a simple traffic network in which numerical results demonstrate the effectiveness of the proposed approach.

Keywords: dynamic traffic assignment, signal control, differential game theory

1. Introduction

Congestion is a daily occurrence on many stretches of traffic networks in urban areas. Building new roadways is no longer a feasible option due to the high costs, as well as the environmental and geographical limitations. Traditional traffic engineering technology is proving unequal to the rapidly growing traffic demand. Therefore, the focus is on developing Intelligent Transportation Systems (ITS) which apply emerging hard and soft information systems technologies to alleviate transportation congestion problems. Two important components of ITS are the Advanced Traffic Management Systems (ATMS) and the

282 A Differential Game Modeling Approach to Dynamic Traffic Assignment

Advanced Traveler Information Systems (ATIS). The success of ATMS and ATIS will depend on the availability and dissemination of current traffic network conditions. The most important problems in ATMS and ATIS occur in Dynamic Traffic Assignment and Signal Control. Dynamic traffic assignment systems are suites of software tools designed to support traffic management systems. Using current and historical data, dynamic traffic assignment systems estimate traffic flow patterns and determine appropriate signal control and route guidance strategies. Traffic signal control systems are designed to foster real-time sensing, communication, and control of urban networks. The primary objective of traffic signal control systems is to reduce congestion effects. Conventional methods for setting traffic signals assume given flow patterns, and traffic flows are assigned to networks assuming fixed signal settings. This method is not fully satisfactory in the normal case in which traffic flows and signal settings are mutually interdependent (Yang and Yagar, 1995). This interdependence between assignment and control is more evident in a real-time dynamic situation. This interdependence forms a serious challenge to the deployment of ATMS and ATIS (Chen and Ben-Akiva, 1998). The combined traffic assignment and signal control problem has been a topic of substantial research. Allsop (1974) was the first to address the interaction between traffic control and traffic assignment; he suggested that the effects of signal settings on the traffic flow patterns should be taken into explicit account by combining traffic control and route choice. There have been two approaches offered to address this problem: 1) the global optimization models, and 2) the iterative optimization and assignment procedure (Cantarella et al., 1991). The global optimization models seek the global optimality of the control policies when travelers adjust their route selections to the changes in signal settings. Sheffi and Powell (1983) formulated the optimal signal-setting problem as a mathematical program, in which traffic flow is constrained to become user equilibrium. Fisk (1984) described the global optimal signal-setting problem as a Stackelberg game between network users and a traffic agency. Smith et al. (1990) combined traffic assignment with responsive signal control into a static case. Yang and Yagar (1995) formulated the problem as a bi-level program, in which the optimal traffic control represents one level and the user equilibrium assignment, another level. The iterative optimization assignment procedure is to update the signal-setting for fixed flows by alternating the signal setting for fixed flows with solving the traffic equilibrium problem for fixed signal-setting until the individual solutions to the two problems are considered to be mutually compatible (Cantarella et al., 1991; Smith and Van Vuuren, 1993). Smith (1979) proposed a consistent control policy that ensures the existence of traffic equilibrium. Al-Malik (1991) investigated the Wardrop equilibrium under Webster control. Taale and Van Zuylen (2001) gave an extensive overview of the available literature. All the studies in the literature considered only the static traffic case, with three exceptions. The first is found in Gartner and Stamatiadis (1996), who proposed a framework to integrate dynamic traffic assignment with real-time control, but did not give any analytical model formulation. The second is Chen and Hsueh (1997), who formulated one particular model for the traffic-responsive signal timing scheme with user-optimal route choice. The third is Chen and Ben-Akiva (1998), who formulated the combined dynamic traffic assignment and dynamic traffic control as a one-level Cournot game between traffic authority and users. He also formulated the dynamic traffic assignment and dynamic traffic control as a Stackelberg game between the traffic authority and users. In his PhD thesis (Chen, 1998), Chen fashioned a set of

Zhenlong Li and Songquan Shi 283

analytical models for the combined problem and developed new control strategies and new solution algorithms. It is well-known that dynamic traffic assignment and signal control are two processes that influence each other. The two processes have different 'players' who may have different goals. The traffic manager will try to achieve a network optimum, while the road users will search for their own optimum, e.g. the fastest way to travel from origin to destination. Decisions taken by the traffic manager in controlling traffic in a certain way have an influence on the possibilities which travelers have to choose their route and time of departure. A change in traffic control may have as impact, changing traffic volumes. The influence of the type of control on route choice was the essence of the research carried out by Taale and Van Zuylen (2000). They extended it with more examples and showed that route choice did indeed depend strongly on the type of control used. At the same time, it is possible to follow an interactive approach, where the control scheme should be adjusted after each shift in traffic volume to achieve equilibrium. However, it can be shown that the process of traffic control adjustment, followed by a shift in traffic volumes, does not necessarily lead to a system optimum. The system optimum is good for the network as a whole, but may be disadvantageous for some of the travelers in the network. Decision-makers, traffic managers and travelers strive to maximize their utility and each player's final utility will depend not merely on his/her own action but on the actions of others as well. It is obvious that the fundamental characteristic of the combined problem is formed by the dynamic characteristics of the interaction. The key problem posed is related to how traffic assignment and signal control interact dynamically when embedded within the same traffic network. Game theory provides a framework for modeling a decision-making process in which more players than one are involved. However, game theory is not congenial to problems involving dynamic phenomena because of the static nature in conventional game theory. Therefore, we need a dynamic game approach to study the interaction between dynamic traffic assignment and signal control. Differential game theory, one branch of this game theory (Isaacs, 1965; Lewin, 1994; Thoma and Wyner, 1991), provides a good framework for the combined problem, where it is assumed that the behavior of the system can be modeled as a system of ordinary differential equations. Differential game theory can be used to model situations where several interacting agents make strategic dynamic decisions. Differential game theory, which frequently deals with multiple performance indices, has been found applicable to the multi-objective control problem. The application of differential game theory to the combined dynamic traffic assignment and signal control problem are considered here, with the focus on the dynamic characteristics of the interaction between dynamic traffic assignment and signal control. Inspired by the adaptability of Complex Adaptive Systems (CAS), We regard signal controllers as being at the intersections as the adaptive agents and model the combined problem on the basic idea that traffic flows are assigned in the proper road network by the traffic manager; these are then adapted by signal controllers by changing the signal settings. The traffic manager acts as the leader and signal controllers at the intersections act as the followers. A leader−follower differential game model of dynamic traffic assignment and signal control is then proposed. Discretization in time is used to find a numerical solution for the proposed game model, and a simulated annealing algorithm is applied to obtain optimal strategies. Finally, a simulation is conducted on a simple traffic network, with numerical results of this simulation demonstrating the effectiveness of the proposed approach.


This paper begins with an analysis of the interaction between dynamic traffic assignment and signal control, after which a differential game model of the combined problem is specified. The solution algorithm is then given, followed by an outline of a sample network and its characteristics. Analysis results, conclusions and a brief mention of further research round off the paper.

2. Model formulation

As mentioned above, dynamic traffic assignment and signal control are mutually interdependent. Because signal settings are usually determined by the flow patterns, these should be considered in the signal settings. Since flow patterns, described by the flow on each link, are influenced by signal settings, traffic assignment should take signal settings into account. Traffic assignment can cause a change in traffic flows, and the changed flows will subsequently make the signal settings non-optimum and thus require a corresponding change in signal settings. Of course, signal control can cause a change in travel time and the changed travel time will subsequently make the traffic assignment non-optimum and also require a corresponding change in traffic assignment. Traffic assignment can change the flow patterns from the macroscopic level, and signal control can change the flow patterns from the microscopic level. These two process are simultaneously carried out and are highly interdependent, as shown in Figure 1.

Figure 1. Interaction between traffic assignment and signal control

Before presenting the combined dynamic traffic assignment and signal control problem, let us first address each dynamic traffic assignment and signal control individually.


2.1 Dynamic traffic assignment problem

Dynamic traffic assignment was a subject of recent studies in which various traffic assignment models were developed (Merchant and Nemhauser,1978; Carey,1992; Wie, Friesz and Tobin, 1990; Lu, 1996). Of these models, the dynamic system optimal model is usually employed for the criterion, its significance found in its provision of an upper limit in systematic search procedures for the optimal network design problem. This is why the dynamic system optimal model is used here. A traffic network is made up of different links and nodes. One OD pair can have different routes, with each route including different links and nodes. Let a directed graph G ( N, A) denote the road network and

N be the set of nodes in the network;

A be the set of links in the network;

A(k) be the set of links whose tail node is k;

B(k) be the set of links whose head node is k;

)(txa be the number of vehicles on link a at time t;

)(txna be the number of vehicles arriving at destination n on link a at time t;

)(tua be the entry flow into link a at time t;

)(tu na be the entry flow into link a arriving at destination n at time t;

)(tva be the exit flow from link a at time t;

)(tvna be the exit flow from link a arriving at destination n at time t;

)(tqkn be the flow generated at the node k arriving at destination n at time t;

)(tmλ be the green ratio for the phase m at time t;

))(( txt aa be the travel time on link a ;

))(),(( ttxd maa λ be the signal delay and queuing delay at the intersection.

The travel time between the OD pair should be considered as a sum of the travel time and travel delay in a signaled network. Travel delay should be divided into two kinds, signal delay and queuing delay, the former being due to interruption of traffic by the traffic signal, and the latter to limited capacity (Yang and Yagar, 1995). Therefore the total travel time spent on the network, ))(),(( ttxt maa λ , is the sum of flow-dependent running time, ))(( txt aa ,and delay due to the signal and queuing delay at the intersection, ))(),(( ttxd maa λ :


))(),(())(())(),(( ttxdtxtttxt amaaamaa λλ += (1)

Friesz et al. (1989) modeled the dynamic traffic assignment problem as an optimal control formulation. A standard-system optimal control formulation that seeks to minimize the total system travel time can be represented as:

dtdtddttutxtdttuttxtJAa

txma

Aaaaa

AaamaaG

aωλωλ ∑∫ ∫∑∫∑∫

∈∈∈

+==T

0

)(

0

T

0

T

0))(,()())(()())(),((min (2-a)

s.t.

)()()( tvtutx na

na

na −=& (2-b)

∑∑∈∈

+=)()(

)()()(kBa

nakn

kAa

na tvtqtu (2-c)

[ ]),0,,(,0)(,0)( TtNnAatutx na

na ∈∈∈≥≥ (2-d)

2.2 Traffic signal control problem

Let us assume that each signal controller phase has been determined and the cycle length given. The problem for a signal controller is to find an optimal signal timing strategy, i.e. allocating green time to each signal phase during a time period. Consider the intersection shown in Figure 2, with the time period [0,T]. Let )(1 tl denote the number of queuing vehicles at time t, and )(1 tu w the entry rate into the waiting area of link 1.

Figure 2. The intersection

In the congested situation, the equation for traffic flow state is:

.)4,3,2,1()()()()()()( =−=−= iSttuS

tCtGtutl m

wi

mwii λ& (3)

where C(t) is the cycle length, S the capacity of the intersection, and Gm(t) the green time for the phase m. The objective of the intersection is to minimize the queuing delay, and the problem is to allocate green time to each signal phase during a cycle period to minimize the queuing delay (Jing,1995). The objective function is then:


∫=T

0)())((minmin dttQltlJ T

C (4)

))(),(),(),(()( 4321 tltltltltl = (5)

s.t.

maxmin )( GtGG m ≤≤ (6)

.4,3,2,1,0)0(,)(0 max ==≤≤ illtl ii (7)

∑ −=m

m LtCtG )()( (8)

where Q is weighting matrix. Gmin,Gmax is the respective minimum and maximum green times, lmax the maximum queuing length, and L the lost time per cycle. According to Equation (8), the summation of green time over all phases and total lost time equals the cycle time. The traffic signal control model can be obtained by extending the above-mentioned traffic state equation, constraints and objective function to the k intersection, as shown in Equation (9), with the model meant to make total delay of each intersection minimal.

∫=T

0)())((minmin dttQltlJ kTkk

C (9-a)

s.t.

))(,,,())(,),(),(()( 2121kAaaatltltltl n

ka

ka

ka

kn

∈⋅⋅⋅⋅⋅⋅= (9-b)

)0)0(()()()( , ≥−= ka

km

wka

ka lSttutl λ& (9-c)

[ ]TtNkGtGGLtCtG km

m

km ,0,,))(0()()( maxmin ∈∈≤≤≤−=∑ (9-d)

where

k is the index of the intersection;

)(tG km the green time for phase m at intersection k at time t;

)(tkmλ the green ratio for phase m at intersection k at time t;

)(tl ka the number of queuing vehicle on link a at intersection k at time t;

)(, tu wka the entry flow into the waiting area of link a at intersection k at time t;.

If the attraction of links to vehicle is not considered and the distance between intersections is not too great, the entry rate into the waiting area of link is equal to the delay of the entry rate into link (Ma, 1999):

)()(, τ−= tutu ka

wka (10)


where τ is the travel time of freedom flow.

2.3 A model formulation for the combined problem

Traffic manager pursues the minimal total cost; in other words, it wants to minimize the total travel time. Each intersection aims at finding green time for each phase that minimizes its queuing delay. Traffic manager and intersections have different objectives. The goal of the manager is to find an optimal assignment strategy that drives the traffic flows to the system optimum. The optimal assignment strategy achieves the minimal total cost and leads to the most efficient utilization of system resources. Each intersection is mandated by the desire to minimize an individual cost function, namely, its queuing delay. The traffic manager and signal controllers at the intersection are regarded as the adaptive agents. We assume that the manager can guide travelers by disseminating information or providing route guidance, and most travelers take up the manager's suggestion. The travelers' routing and departure times are assumed to be fixed. Accordingly, traffic flows are assigned to the proper road network by the traffic manager, after which the flows are adapted by signal controllers at the intersections by changing the signal settings. Traffic manager and intersections are considered the participants in the game, with the traffic manager acting as the leader (has the first mover advantage) and the intersections as followers. Using differential game theories, we consider a continuous time model. In this way dynamic traffic assignment and signal control can be formulated as a leader−follower differential game under the open-loop information structure, where )(tu n

a is the control variable of traffic manager, and )(tk

mλ is the control variable of intersection k. JG is the payoff function of traffic manager, and k

CJ is the payoff function of intersection k. The leader−follower differential game model of dynamic traffic assignment and signal control follows:

The aims of players, manager and intersections are to make their utility maximal by selecting strategies, i.e. control variables.

3. The solution algorithm

Discretization in time is used here to find a numerical solution for the proposed game model.


∑∑∈ =

=Aa

M

imaaaG iixtixJ

1

))(),(()(min λ

)()()()1( iviuixix na

na

na

na −+=+

∑∑∈∈

+=)()(

)()()(kBa

nakn

kAa

na iviqiu

1,,2,1,0,,,0)(,0)( −⋅⋅⋅=∈∈≥≥ MiNnAaixiu na

na

∑=

=M

i

kkC eiliCJ

1

)()(min

))(,),(),(()(21

ilililil ka

ka

ka

kn

⋅⋅⋅=

Siiuilil km

wka

ka

ka )()()()1( , λ−+=+

∑ −=m

km LiCiG )()(

1,,2,1,0,,,2,1,0)0( −⋅⋅⋅=⋅⋅⋅=≥ MiNkl ka

where e is unit column vector. In this game, there are many decision-makers at the lower level and one decision-maker at the upper level. The game is played as follows: the leader chooses a strategy that will affect the followers' restraint-set and objective function, so as to achieve system optimum with respect to the distribution of the traffic flows in the network. The followers then react by modifying their behavior. The aim of each player is to minimize his/her own objective function which will depend on players' strategies. Both the leader's and the followers' strategies will affect the overall system performance. The strategy ))(),(( ** kku λ makes the overall system performance optimal; )(* ku and )(* kλ can be obtained by solving the model. The simulated annealing algorithm (SA) presents an optimization technique that can process objective functions possessing quite arbitrary degrees of nonlinearities, discontinuities and process quite arbitrary boundary conditions and constraints imposed on these objective functions. Simulated annealing is an optimization strategy invented by Kirkpatrick et al.(1983). The SA algorithm does not require derivative information, but merely needs to be supplied with an objective function for each trial solution it generates. Compared with conventional, iterative search techniques, the SA algorithm is robust. Compared with genetic algorithms (GA), the SA is, according to some suggestions in the literature, a �quick starter�, arriving at good solutions in a short time. However, the SA is not able to improve on that given more time. Furthermore GA algorithm is reported to be a �slow starter�, i.e. able to improve the solution consistently when given more time. In comparing SA and GA for a traffic routing problem, Mann and Smith (1996) reported GA to give slightly better solutions than SA, but also noted that the SA achieved its solutions much quicker. Lahtinen et al. (1996) provided a good discussion on how a meaningful empirical comparison should be


done. Lahtinen et al.(1996) compared several algorithms, including SA and GA ; their results indicated that given the same amount of time, SA consistently gave better solutions than GA. For this reason, the simulated annealing algorithm is applied here to obtain optimal strategies. Consider an analysis period divided into equal intervals j =1,2,�,H. here, we can implement the simulated annealing algorithm to the model at the start of each interval. The algorithm for solving the model can be summarized as follows:

Step 1: Determine an initial temperature T1 and the initial solution 0))(( ju na . Solve the

lower problem for a given 0))(( ju na to obtain 0))(( jk

mλ . Set the iteration counter at p=1.

Step 2: New trial solutions can be generated according to: ujuju pn

apn

a ∆+= −1))(())(( where ∆u is a random number in neighbourhood of 1))(( −pn

a ju . Compute the new objective function value )))((( pn

a juF and the change ∆F in the objective function, )))((()))((( 1−−=∆ pn

apn

a juFjuFF .

Step 3: If 0≤∆F , then ujuju pna

pna ∆+= −1))(())(( ; if 0>∆F , compute the

probability of accepting new trial solutions )

Texp()(

ppFFp

⋅∆−=∆

and generate a random number r, 0 < r < 1. If the Metropolis criterion is satisfied, i.e. rFp ≥∆ )( , then

ujuju pna

pna ∆+= −1))(())(( . Otherwise 1))(())(( −= pn

apn

a juju .

Step 4: If a stopping criterion is satisfied, then pna ju ))(( is the optimal solution of the

upper problem and solves the lower problem for given pna ju ))(( , yielding

pkm j))((λ .

)))((,))((( pkm

pna jju λ is the approximate global optimal solution. Otherwise, go

to Step 5.

Step 5: A new temperature is generated according to: pp TT 1 α=+

Let p=p+1 and go to Step 2.

4. A numerical example

In this section, a numerical example is presented to illustrate the application of the model and algorithm above. The test network is indicated in Figure 3 with seven nodes and eight links. Detailed link characteristics are shown in Table 1.


Figure 3. Simulation network

Table 1. Information on links

Link number Start−End node

Length (m) Capacity (# of Vehicle)

No. of lanes Speed of freedom flows (km/h)

a1 1-2 500 600 1 80 a2 1-3 400 600 1 80 a3 3-4 300 600 1 80 a4 2-4 400 400 1 60 a5 4-5 300 600 1 80 a6 4-6 400 600 1 80 a7 6-7 400 400 1 60 a8 5-7 300 600 1 80

Figure 4. The OD demand

Figure 5. Two-phase signal


One origin−destination pair from node 1 to node 7 is assumed. The OD pair has four alternative routes available: Route1(a1/a4/a5/a8), with a length of 1500 m, Route 2 (a1/a4/a6/a7), with a length of 1700 m, Route 3 (a2/a3/a5/a8), with a length of 1300 m and Route 4 (a2/a3/a6/a7), with a length of 1500 m. The OD demand is shown in Figure 4. During the simulation, it is necessary to specify the link travel-time function, also known as the link performance function. A widely used link travel-time function is the formulation suggested by the US Bureau of Public Roads (BPR) and used in the paper. Both assignment cycle and control cycle are equal to 100s. The sample time is 50s. We assume that the obedience rate, the percentage of drivers following the manager's route guidance, to be 80%. The signal phases used in the paper are shown in Figure 5. It is important to note that a high initial temperature will be necessary to find a global minimum and reduce the possibility of being trapped in a local optimum. Therefore the number of iterations will have to be very large and too much computation time will have to be spent. In a practical situation, however, there is a trade-off between finding the global minimum and a point near the global minimum, depending on the time one is prepared to wait until a global minimum has been found. Therefore, it may be more efficient to use a stopping criterion after a certain number of iterations with only minor changes of the energy function or even without any improvements of the energy function (Salomons et al.,1995). The stopping criterion greatly affects the SA's performance. For reasons of efficiency, our implementation uses the following parameters:

! initial temperature T1 = 1000 ! final temperature Tf = 0.1 ! cooling factor α = 0.98

The stopping criterion used in the paper represents only minor changes in the objective function or the current temperature less than the final temperature. Simulation is conducted using the proposed approach of this paper. CPU times are measured on PII366, and the run time is about 6.8 seconds on average, which is far less than the cycle of assignment and control, indicating that the solution algorithm is available and the algorithm performance acceptable. A fixed-time control policy based on the Webster method is also carried out for comparison. The route travel time and the number of vehicles on the route can be obtained through two cases at the sample time. The results of the simulation are shown in Figures 6 and 7.


(6-a) In the case of fixed-time control

(6-b) In the case of the proposed approach

Figure 6. Travel time


(7-a) In the case of fixed-time control

(7-b) In the case of the proposed approach

Figure 7. The number of vehicles

In the case of �fixed-time control�, the average travel times for the four routes are 101.38s, 103.25s, 174.46s, 129.27s, respectively, and total average travel time is 127.09s. In the case of �the proposed approach�, the average travel time of the four routes are 107.47s, 108.12s, 147.36s, 101.15s, respectively, and total average travel time is 116.03s, a reduction of 8.70%. In Figures 6 and 7, we see that the vehicles on Route 3 increase sharply in the �fixed-time control� case, since most of drivers choose Route 3, which is the shortest route in a static situation. Consequently, congestion occurs on Route 3 and the network performances decline. While, in the case of �the proposed approach�, the flows are adjusted by the traffic manager and the signal timing is correspondingly changed when the flows on Route 3 increase. Therefore congestion can be alleviated to a certain extent. However, it is important to note that the global optimum can not always be obtained; sometimes, a point may be found that is near the global optimum.


5. Conclusions and future research

In this paper, differential game theory has been applied to the modeling of the combined dynamic traffic assignment and signal control problem. The simulation was conducted on a simple sample network using two cases: the fixed-time control and the approach proposed in this paper. The numerical results demonstrate the validity and effectiveness of the proposed approach. There is a great need for future research on this topic. Firstly, demand is assumed to be fixed in the model of this paper, while the demand for transportation is, in practice, variable. A subsequent study will deal with the elastic demand in the traffic-assignment problem. In a practical situation, the assumption that traffic manager can assign routes to travelers is not practical, the dynamic user-equilibrium would be more realistic. Secondly, the paper proposes a differential game modeling approach to the combined problem, but differential game theory is not used for solving and analysing the problem. How the differential game theory can be used to solve the combined problem needs further study. Finally, there are plans to perform parallel simulated annealing to improve the performance of algorithm.

Acknowledgements

This research was supported by The Outstanding Young Scientist Research Fund of China (No.60125310).

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Land-Use and Travel Behaviour. A Survey of Some Analysis and Policy Perspectives

Lars Lundqvist Unit for Transport and Location Analysis Department of Infrastructure, Teknikringen 78B KTH - Royal Institute of Technology Stockholm Sweden E-mail: [email protected]

EJTIR, 3, no. 3 (2003), pp. 299 - 313

Received: June 20021 Accepted: May 2004

This paper discusses interactions between land-use and travel behaviour in the light of recent developments on the policy arena, in particular the increasing emphasis on sustainable development of urban and regional systems. Schemes for integrated analyses of land-use and transport and for comparing urban structures in terms of land-use dispersion and travel behaviour are presented. The new national transport policy of Sweden has a strong emphasis on environmental and safety objectives. However, increasing vehicle kilometres of travel (VKT) and decreasing transit shares are characteristic for the projected development of Stockholm until the year 2030. Only very drastic integrated policies can reduce VKT to a level consistent with long-term environmental targets. Land-use policies play a small role in this context. A transit-oriented settlement structure on the sub-regional scale tends to be more important than increased density on the regional scale. Compact cities and local job-housing balance may provide the potential for sustainable transport behaviour, but other policies and strong incentives are needed to reverse current urban development trends. With current trends other urban forms (e.g. “decentralised concentration” or “corridor development”) are likely to be more efficient in terms of VKT.

1. Introduction

The discussion of linkages between land-use and transport on the urban level and between regional development and transport on the interregional level has been intensive in many

1 This paper was initially submitted and accepted for the Special Issue Land Use and Sustainable Mobility.

EJTIR, vol. 3, no. 1 (2003).

300 Land-Use and Travel Behaviour

countries during the recent decades. The increasing importance of environmental issues has been confronted with rapidly growing volumes of person transport and freight. The growth of the globalising economy and the deregulations and reductions of barriers in the European context have resulted in increasing transport of goods and people over longer distances. On the urban scale consistent trends towards higher volumes of car traffic and decreasing transit shares have emerged. From partial equilibrium models of simple mono-centric urban economies we learn that increased income, a growing population and more efficient means of transport all lead to expanding urban areas, lower densities and longer transport distances. Other factors like increased specialisation on the labour market and increasing labour participation rates tend to reinforce the observed tendencies towards increased volumes of car traffic. The interest in policies for a sustainable development during the 1990s has focussed on the need for systematic and system-wide measures that reconcile ambitions concerning economic growth, social equity and environmental protection. Hence, the interactions between spatial development and transport behaviour should be seen in the light of emerging policies for sustainability. Part of this paper is based on sections in Lundqvist (2000) and Lundqvist (2003). This paper is organised in the following way. First a short review of land-use/transport interactions is provided in Section 2 together with some observations on the development of the policy context (mainly in Sweden) and on implications for modelling. Results from applications of transport models and land-use/transport models in Stockholm are summarised in Section 3. The focus is on illuminating relations between land-use and travel behaviour. In Section 4 results from similar studies in other spatial contexts are presented. Section 5 contains Swedish and international perspectives on interactions between transport, land-use and regional development. Finally, the main conclusions from the paper are outlined in Section 6.

2. Interactions between land-use and travel behaviour in the light of policy developments: some implications for modelling

Land-use and transport systems are, in principle, interdependent. Strong arguments support the proposition that different urban forms and different land-use patterns (density, mix) influence the conditions for various transport systems and lead to different transport and travel patterns. Similarly, strong reasons can be stated for the potential influence of transport supply on location decisions of firms and individuals and in the long term also on the settlement structure. However, it should be emphasised that these seemingly natural and mutual interactions do occur with different speeds and with various delays. Land-use/transport interactions are also masked by many other mega trends and socio-economic developments (e.g. demographic, economic, social, policy-making) with potential (stronger or weaker) linkages to the land-use/transport systems. Wegener (1996) summarises these mutual interactions in �the land-use transport feedback cycle�. Another way of illustrating the linkages between land-use and transport is shown in Figure 1. It should be clear that the time scales of various impacts in Figure 1 are widely different: from more or less daily route and mode choices, to intermediate time horizon changes of location

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(moves), car ownership, travel patterns, traffic management and transit supply to very long term changes of transport network design, urban form and settlement structure. There are obvious feedback loops within and between the land-use and transport markets providing strong reasons for integrated modelling and policy analysis of land-use/transport systems.

Figure 1. Linkages between the transportation market and the land-use market (dotted arrow: medium to long-term impacts; solid arrow: short to medium-term impacts).

Another way of illustrating some fundamental relationships between land-use and transport behaviour is the �Brotchie triangle�. A simplified version is shown in Figure 2. In a very stylised way, any urban structure is characterised in two dimensions: one indicator of spatial interaction (e.g. average trip length or travel time) and one indicator of dispersal of non-residential land-use (e.g. degree of decentralisation of working places). After defining proper indicators for these two dimensions, any urban region can be represented as a point in the diagram at any point of time (e.g. D). Different urban regions can be compared with each other at any point of time and the development over time of any urban region can be represented as a trajectory in the diagram (e.g. D → E). It is instructive to think of a circular and symmetric city with residents distributed around the geographical centre. Spatial interaction is measured in terms of the average trip length for commuting. Point A in Figure 2 represents the case where all employment activities are located in the city centre. All commuters have to travel to the centre (many-to-one interaction) and the average trip length can be uniquely defined. Radial transport systems and mass transit constitute relevant options in such a context. At the other extreme, along the axis B-C employment has the same spatial


distribution as residential location (i.e. �complete� decentralisation). In this case, the trip length depends heavily on travel behaviour: if residents choose the nearest employment opportunity, point C would be the result with very short local trip length, while if residents choose employment opportunities at random, point B would be the result with very long average trip length. Point C would reflect one-to-one interaction on local networks while point B corresponds to many-to-many interactions with dispersed traffic flows on complete networks. Different kinds of socio-economic scenario assumptions and technological developments can be related to various parts of the diagram. A few examples are indicated in Figure 2. The prevailing development trend can be represented as a trajectory in the �eastern� or �north-eastern� directions (like D → E): towards more decentralisation of employment, more car traffic and tendencies towards longer trip lengths in more dispersed travel patterns.

Figure 2. Main features of the “Brotchie triangle” on land-use and travel behaviour. For a more complete original figure and discussion, see Brotchie (1984).

Land-use/transport modelling has developed since the 1960s but mainly in research environments or pilot projects. The criticism of Lee (1973) had strong influences both on the modelling field and on attitudes of practitioners towards modelling. Large-scale urban models were accused for e.g. being data hungry, non-transparent and computer intensive. Some of these objections have become less relevant due to developments of theories, modelling techniques, statistical estimation methods, computing capability, etc (see Lee (1994) and other articles in the same journal issue). On the policy arena a renewed interest in integrated land-use/transport models has emerged from the growing importance of environmental issues. In the US, the Clean Air Act of 1990 and the Intermodal Surface Transportation Efficiency Act of 1991 provide new challenges for development of policy responsive and integrated land-use and transport modelling. The focus on sustainable development and Agenda 21 during the 1990s has also led to a demand for integrated analyses of social, economic and

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environmental urban and regional problems. A few examples of policy discussions related to sustainability will be provided but a thorough treatment of sustainable development is outside the scope of this paper. In Sweden a new national transport policy was adopted in 1998: Transport Policy for a Sustainable Development. Its main objective is to provide citizens and firms in all parts of the country with a transport supply that is socio-economically efficient and sustainable in the long term. Six sub-goals are formulated: an accessible transport system, high transport quality, safe traffic, good environment, positive regional development and equality between genders. Two of these have very precise and rather far-reaching short term objectives: the number of persons killed in traffic accidents should be reduced by 50% 1996-2007, the emission of CO2 from transport should not increase 1990-2010 and the emissions of NOx, S and VOC from transport should be reduced by 40%, 15% and 60% respectively in the period 1995-2005. In the committee report preceding the new national transport policy (Communication Committee, 1997), one chapter was devoted to �a less transport intensive society�. In addition to the economic incentives and regulations for internalising the external costs of transport, the committee emphasises that a better co-ordination between the planning of settlements, infrastructure and traffic is needed. In particular, a public transit oriented development of land-use is discussed. A stronger position for regional planning is required which may develop from a stronger regional role in the distribution of resources for infrastructure investments. It is also noted that Agenda 21 requires an integrated land-use and transport planning. Guidelines for such an integration have been adopted in Norway, in the UK and in the Netherlands. These principles are said to be applicable also in Sweden. However, the committee proposes no formal guidelines, partly because of differences in the planning system with a stronger role for local governments in physical planning in Sweden. The existing Planning and Building Code is containing guidelines that can be given similar interpretations as the guidelines in Norway and in the UK. Also in the area of external locations of shopping centres, the committee considers the existing planning regulations to be sufficient for the time being. Local governments should be restrictive in permitting new external centres that can weaken the position for city centres and local services. The emphasis on sustainable development during the 1990s has lead to a discussion of integrated policies (e.g. land-use/transport policies) in many countries. At the European level, an EU Directive on Strategic Environmental Assessments (SEAs) of certain plans and programmes was adopted in 2001, EU (2001), in order to take environmental issues into account at an early planning and programming stage. Similar strategic economic and social impact assessments are also emerging. The message from many policy discussions on sustainable urban development has been clear: increase densities, promote a mix of land-uses, cluster high density, walking scale settlements along public transport lines. Peter Hall (1997) has noted the similarity between these principles and the ones underlying the General Plan of Stockholm in 1952 with its satellites located on underground transit lines. Economic developments and behavioural changes (income, car ownership, commuting patterns, modal choices, housing demand, etc) have resulted in a less sustainable urban region than initially intended, although in relative terms Stockholm is considered to be sustainable in a European or, even more so, in an American context. It can be concluded that a proper account of the interplay between socio-economic mega trends, land-use and transport planning and developments on urban markets are essential for achieving a sustainable development. There is a wide range of options for reorganising the use of existing land-use/transport systems


without major rebuilding of urban infrastructures. However, in order to study such options a comprehensive systems view of urban interactions is needed. Land-use/transport models may have a role to play in assessing the impact of package policies for urban management on indicators of urban sustainability.

3. Some results from studies of land-use and travel behaviour in the Stockholm region during the last decade

In this Section some long-term results from the early preparatory stages of the work on the Regional Development Plan 2001 for the Stockholm region are reported. A related study conducted by the City of Stockholm illustrates the kind of planning and management measures that are likely to be needed in order to achieve long term environmental goals. Finally, some projections related to the consultation proposal in connection with the Regional Development Plan 2001 are presented. During 1995 a number of interrelated long-term studies were carried out in the Stockholm region. They were based on an integrated traffic forecasting system (traffic demand model T/RIM and traffic assignment model EMME/2) and on a related land-use/transport model system (IMREL). The studies were commissioned by the County Council Office of Regional Planning and Urban Transportation and the Stockholm City Planning Office. In the report �Traffic and Environment � Studies of Regional Structures�, the County Council Office of Regional Planning and Urban Transportation (1995) analysed five scenarios for the land-use/transport system until the year 2020. The scenarios differ with respect to investments in the public transport and road networks and with respect to the pattern of land-use development. Four of these scenarios are subject to more detailed comparisons in Table 3. One of the five scenarios is representing the adopted Regional Plan 1991. In Table 1 the results for the Regional Plan scenario and the intervals obtained for the five scenarios are reported. The results for 1993 are also produced by the model. Table 1. Regional structures: long-term projections of traffic and environment

Scenario 1993 RP91/2020 Five scenarios/2020

Traffica: Person kilometresb 4712 5877 5862-6852 VKTc, County 1916 2839 2666-2862 VKTc, Inner city 139 141 128-145 Transit share (%) 39 34 34-38 Emissions (tons): Carbon dioxide 503 758 716-768 Nitrogen oxides 5.72 2.58 2.44-2.63 Hydrocarbons 5.78 0.78 0.74-0.79

a Morning peak hour indicators b Thousands c Vehicle kilometres of travel (thousands)

Source: Office of Regional Planning and Urban Transportation (1995)

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The projected traffic volumes for the county imply a traffic growth of around 50% during 1993-2020. For the inner city the traffic volume is stabilised on the 1993 level by the introduction of a cordon toll system that was part of the transport system according to the Regional Plan 1991. The RP91 scenario leads to a growth of vehicle traffic that is on the high side as compared to the other four scenarios. This is due to the long-term drop in the transit share by 5% in the RP91 scenario, while in the transit oriented scenario the transit share remains almost stable. The emission forecasts show good improvements in terms of nitrogen oxides (about 55%) and hydrocarbons (about 87%). However the emissions of carbon dioxide are projected to increase by about 50%, which should be compared to the intermediary transport policy target of �15% (1990-2020). The assumptions concerning increased fuel efficiency seem to have been very modest. These conclusions are reinforced by another long-term land-use/transport scenario study conducted by the Stockholm City Planning Office (1995), �A Sustainable Transport System for the Stockholm Region � Scenario Studies�. The impacts of combined scenarios for economic growth, vehicle technology and land-use/transport policies were studied for the period 1993-2020. The base scenario is identical to the adopted Regional Plan of 1991. Additional scenarios are formed by accumulated changes: 1. Extensive increase in transit supply, 2. No eastern and western by-passes (i.e. elimination of two major road investments), 3. Higher land-use density (i.e. more development in the central part of the region), 4. Doubled cordon tolls, 5. Doubled fuel prices. The results are summarised in Table 2. A comparison is made between the reference scenario, the accumulated impacts of changes in transport networks and land-use (Scenario 3) and the accumulated impacts of infrastructure and pricing policies (Scenario 5). The ranges are reflecting economic growth and vehicle technology scenarios. Table 2. A sustainable traffic system for the Stockholm region: scenario studies

Scenario 1993 RP91/2020 Scenario 3/2020 Scenario 5/2020

Traffic: VKTa, County 100 120-150 108-136 86-108 Emissions: Carbon dioxide 100 30-129 27-116 21-91 Nitrogen oxides 100 28-52 25-47 20-37 Hydrocarbons 100 11-22 10-21 8-15

a Vehicle kilometres of travel

Source: Stockholm City Planning Office (1995) Obviously, the most optimistic vehicle technology assumption together with moderate economic growth will make possible drastic reductions of emissions (70-90% in comparison with 1993). As can be seen by the difference between Scenario 3 and the reference scenario (RP91), only a minor part of these reductions is related to land-use/transport policies (12-14 index points, or about 35%, in terms of VKT and similar shares in terms of emissions). User charges are more important (compare Scenario 5 with RP91). However the assumptions on vehicle technology are by far the most influential factor for the level of emissions, followed by the assumptions on economic growth. For meeting the strict long-term objective


concerning the reduction of carbon dioxide (80% reduction of the 1993 level), a very optimistic scenario for vehicle technology is required (in combination with moderate economic growth and implementation of all infrastructure and pricing policies). This also leads to fulfilment of the other environmental targets. The influence of land-use and transport systems on traffic indicators can be further illustrated by some results from �Traffic and Environment � Studies of Regional Structures�. In Table 3 three land-use/transport scenarios for 2020 are compared to the reference scenario, i.e. the adopted Regional Plan 1991: 1. A regional structure with higher density, transport systems according to the Regional Plan (Dense/RP91); 2. A dispersed but transit-oriented settlement pattern, doubled transit supply, no eastern and western ring road by-passes (Corridor/Road min); 3. Very dispersed settlement pattern, doubled transit supply, no eastern and western ring road by-passes (Dispersed/Road min). The land-use differences between the scenarios are shown in Table 3 in terms of sub-regional shares of new housing developments 1990-2020 as compared to the total shares of the housing stock in 1990. Table 3. Regional structures: impact of land-use/transport systems 2020

Scenario 1993 RP91 RP91

Dense RP91

Corridor Road min

Dispersed Road min

Housing (share of new development): Inner city 57a 38 52 21 13 Inner suburb 18a 22 35 17 12 Outer suburb 15a 24 6 39 51 Periphery 10a 15 5 25 25 Trafficb: VKTc, County 1916 2839 2799 2666 2862 VKTc, Inner city 139 141 145 131 134 Person kilometresd 4712 5877 5862 6681 6852 Transit share (%) 39 34 34 38 37 Average trip lengthe 13.3 12.5 12.4 13.9 14.3

a Share of total housing in 1990 b Morning peak hour indicators c Vehicle kilometres of travel (thousands) d Thousands e Kilometres

Source: Office of Regional Planning and Urban Transportation (1995) Higher density of urban development does not have any major impact on the traffic indicators as compared to the Regional Plan (which is already fairly dense). On the other hand, for a very transit oriented transport system the difference between land-use alternatives oriented towards transit corridors or dispersal is considerable. One may conclude that the land-use distribution within sub-regions tends to be more important for the traffic conditions than the land-use distribution between sub-regions. The studies reported above have shed some light on how land-use changes might impact on transport behaviour. The reverse impact on land-use of an extensive transport policy proposal was subject to analysis in Stockholm in the beginning of the 1990s, see Johansson and

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Mattsson (1995). The transport policy proposal, containing both road and transit investments and cordon tolls (the so called Dennis agreement), was compared to a do-nothing scenario. The model projection indicated a decentralisation of land-use with about 25000 residents and 25000 workplaces being relocated at a 99-zone subdivision of the Stockholm region. This corresponds to 1.3% and 2.3% of the total activity amounts. The consultation proposal for Regional Development Plan 2001 for the Stockholm region is summarised in Table 4. Two land-use alternatives were presented with various degrees of relative decentralisation until the year 2030. The shares of development (population and employment) in the inner city and the share of population in the inner suburbs are decreasing in both cases. The traffic implications are reported for two economic growth scenarios and for one common transport network scenario. The reduction of the transit share is projected to continue in spite of increased transit supply and shorter average transit travel times. The reduction is somewhat more pronounced in the dispersed settlement pattern. The vehicle kilometres of travel and person kilometres of travel are rapidly expanding. Introduction of a toll system will reduce the total VKT by about 4 index units and the VKT in the inner city by about 15 index units. The emissions of CO2 per capita from transport are projected to increase by 10-15% during 1997-2015, which obviously is in conflict with the adopted national (and regional) targets. Table 4. Regional structures and transport patterns 2030

2030 Concentrated 2030 Dispersed Scenario 1997 2000 Pop

1995 Emp Pop Emp Pop Emp

Inner citya 279 286 315 341 279 275 Inner suburba 627 263 785 406 684 337 Outer suburba 491 151 674 229 752 335 Peripherya 423 139 615 237 675 266

Trafficb: Highe Basee Highe Basee Number of trips: Car 148 260 206 274 212 Transit 168 210 202 197 195 Bike/Walk 84 94 85 93 85 Transit share (%) 42 37 41 35 40

VKTc, County 100 158 135 166 139 VKTc, Inner city 100 136 121 126 115

Person kmc, car 100 161 136 170 140 Person kmc, transit 100 126 118 120 115

Av. tr. timed, car 20,9 20,4 20,2 20,1 20,1 Av. tr. timed, transit 38,0 31,7 31,3 31,9 31,5

a Thousands b Morning peak hour indicators c Index 1997=100 d Minutes e Scenarios for economic development

Source: Office of Regional Planning and Urban Transportation (2000)


In summary, Stockholm is moving in the eastern or north-eastern direction in the Brotchie diagram (Figure 2). This development is characterised by a decreasing transit share, increasing amounts of vehicle kilometres of travel and dispersal of land-uses. Only a very drastic combination of land-use/transport policies, development of vehicle technology and economic incentives can reduce greenhouse gases to the long term target of 20% of the 1990 level and stabilise the total vehicle kilometres of travel (VKT) according to Stockholm City Planning Office (1995), see Table 2. Land-use and transport network changes may reduce VKT by 12-14 index points (about 10%) as compared to the base scenario, while economic incentives (doubling of tolls and petrol prices) is projected to further reduce the VKT by 22-28 index points (about 20%). Of the 10% reduction due to land-use and transport network changes, the higher density of land-use contributes with only 2-3% while increased transit supply and reduced road capacity cause a 7-8% reduction. A bigger land-use effect might have been obtained by using the �corridor� scenario instead of the �dense� scenario, compare Table 3. The impact of lower economic growth rate (0.9% annual growth of the household disposable income instead of 2.0%) is a reduction of VKT by about 20%. Assumptions concerning vehicle technology are most important for the projected level of emissions, in particular for CO2 emissions.

4. Some results from international studies of urban land-use and travel behaviour

In a very interesting paper, Wegener (1996) discusses the conventional wisdom of recommending increased density and mixed land-uses to handle environmental problems of urban areas (see e.g. the Green Paper on the Urban Environment of the European Communities). He refers to research results, which indicate that �decentralised concentration� tend to be the most energy conserving urban form. The famous relationship between urban density and per capita petrol consumption (Newman and Kenworthy, 1989) is reinterpreted in terms of a relationship between normalised petrol price and per capita petrol consumption. The outcome indicates that urban density may be an intermediate variable affected by the more fundamental differences in petrol price. Wegener then proceeds to carry out a case study of the Dortmund region by using an integrated land-use/transport model. A number of future scenarios for travel costs and travel speeds are compared to a base scenario (business-as-usual). In particular two combination scenarios are formulated: �promotion of public transport (PPT)� and �reduction of mobility (RM)�. Very drastic increases of petrol prices (increased four times 1995-2015) and inner-city parking costs (increased five times) are contained in both these combination scenarios. In addition the PPT scenario includes making public transport faster and cars slower, while in the PM scenario both public transport and cars were assumed to be slower and, moreover, public transport fares were assumed to double. The PPT scenario resulted in a reduction of VKT by more than 50% 1995-2015 while the base scenario would result in a 25% increase. The observed decay of the public transport share from about 31% 1970 to about 17% 1995 could be reversed into a projected growth to about 40% 2015. CO2 emissions from transport were projected to decrease by about 65% 1995-2015 and reach a level considerably lower than in 1970. Most scenarios result in moves in the north-eastern direction of the Brotchie

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diagram (more dispersal of land-use and more travel). The PPT scenario leads to increased density (less dispersion of both residences and working places). Working places respond more strongly to transport changes than residences according to the model. The overall conclusion of Wegener (1996) is that there is a wide range of options for reorganising the utilisation of spatial structures that may lead to significant reductions of energy use and CO2 emissions without substantial land-use changes, without unacceptable losses of mobility and without widening social disparities. It should be kept in mind that the simulated price increases are much more drastic than the ones used in the Stockholm scenario study (compare Table 2) and the simulated impact on VKT is also much stronger. In a recent survey of empirical studies of land-use/transport interactions in North America, Badoe and Miller (2000) discuss both the impact of urban form on travel behaviour and transit impacts on urban form. Their summary concluded that the role of residential density as a determining factor for transit usage as well as for the use of non-motorised modes is unclear. The impact of residential density as a direct explanatory variable declines significantly when other factors (e.g. socio-economic characteristics, accessibility) are introduced. Concentration of employment seems to have a stronger and more consistent influence on transit usage, walking and ride-sharing. More emphasis on employment location and on location of other out-of-home activities in modelling and policy-making seems to be the natural implication. Accessibility is a key factor in analysis of relationships between land-use and transport. Investigations of the impacts of local access to work opportunities (i.e. job-housing balance) on VKT have lead to mixed findings. Finally, studies of impacts of neighbourhood design on travel behaviour also show quite mixed results. Neighbourhood design is important for densities, ease of walking and for provision of transit services, but the complex interaction patterns of modern societies extend far beyond the local neighbourhoods and are related to the overall functioning of the land-use/transportation systems of the urban area. Other examples of recent studies of relations between land-use contexts and travel behaviour are reported in Schwanen et al. (2001, 2002). The impacts of contextual and individual attributes on travel distance and travel time are analysed on the basis of the Dutch national Travel Survey. De-concentration of urban land-uses is found to encourage car travel at the expense of other modes. In terms of average distance travelled, the results of de-concentration are mixed. Reference can once again be made to the Brotchie triangle (see Figure 2) illustrating the ranges of travel behaviour options in a certain urban form (degree of dispersion). Proximity and travel costs are weighted against the utility of interactions in determining travel behaviour. Complex labour markets and high evaluation of variety in consumption and activity patterns may lead to longer trips in a city with locally balanced neighbourhoods than in a city with high concentration of employment and services in the city centre. The general conclusion of Badoe and Miller (2000) is a strong plea for integrated land-use/transport models in order to analyse interactions between urban form and travel behaviour and between transit supply and urban form in a comprehensive way. The ambiguities of some of the earlier studies might have been caused by the use of partial approaches, omitting important variables and important linkages. The European Conference of Ministers of Transport (1995) also notes the rather weak effectiveness of land-use planning in limiting car usage and the need for integrating land-use and transport policies. The potential contingency value of urban forms offering possibilities


for shorter trips in a situation with dramatically higher fuel prices is emphasised, even if the current use of such urban forms may lead to diffuse patterns of car journeys (Figure 2 is referred to again).

5. Transport, land-use and regional development – some observations on redistribution and economic development effects

Although the main interest in this analysis is devoted to relations between land-use and travel behaviour on the urban level, we will briefly comment on the relations between transport initiatives on the one hand and land-use or regional development on the other hand. Badoe and Miller (2000) note the difficulty in isolating the effects of transit supply on urban form. Land-use effects materialise slowly and many other changes occur simultaneously, which also affect land-use. For identifying the �true� land-use effects of a transport supply change, an integrated land-use/transport model would be needed in combination with a before-and-after database. Using such an integrated land-use/transport model, large transport policy programmes (e.g. the Dennis proposal in Stockholm and a system of regional trains) have been projected to result in redistribution of less than 5% of the population and working places between 214 zones (mainly in the decentralising direction) in the Mälar Valley, which represents a major extension of the Stockholm region. On a larger interregional scale the corresponding redistributions between counties have been projected to be smaller, below 1%, see Anderstig and Mattsson (1998). The transport networks of developed economies are characterised by high density of links and good accessibility standards. Single transportation improvements tend to have only marginal impacts on the accessibility pattern and hence lead to marginal land-use or regional development effects. Investment programmes or package policies may lead to re-distributions of activities to the extent mentioned above. The net effect (to be distinguished from the re-distributional effects) on economic activities (production or productivity) of infrastructure improvements is an issue that has been subject to much controversy in the recent decade. In developed networks the elasticity of production with respect to transport infrastructure is found to be small (<0.06), corresponding to a normal rate of net return (this would indicate that the transport infrastructure is of the right size). The need to consider productivity effects in addition to the outcome of traditional CBA analysis has also been discussed. In Communication Committee (1997) the potential productivity effect in addition to conventional (�on the road�) CBA analysis was estimated to less than 20%. If the CBA analysis is based on sophisticated regional-economic modelling (e.g. Spatial Computable General Equilibrium Modelling) the need for corrections would be smaller since impacts on transport generation, location and integration of labour markets would have been endogenised. Historically developed relationships between accessibility and the level of economic activities can be observed. It is more difficult to find clear relations between changes in accessibility and changes in the level of economic activities. Due to the �two way road� effect a transport improvement to a region might lead to negative effects depending on the relative competitiveness of the economy of this region as compared to the region(s) at the other end of

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the road. The role of transport supply as a necessary but not sufficient condition for economic development or land-use development has been highlighted in many studies (e.g. Badoe and Miller, 2000). Other policies (e.g. land-use, education, economic climate) need to interact in a mutually reinforcing way for development effects to occur. Such synergies between policies are important to analyse. Combined land-use and transport policies have been advocated strongly (e.g. The European Conference of Ministers of Transport, 1995).

6. Conclusions

The growing importance of policies for a sustainable development of urban areas has lead to a renewed interest in integrated land-use/transport interactions and modelling. Schemes for illustration of interactions between urban land-use and transport behaviour and for comparative analysis of urban systems have been suggested. The conventional wisdom of recommending a high density, mixed land-use �compact city� with a clustering of settlements along transit lines has strong similarities with the principles behind the Stockholm General Plan 1952 with dense satellites located on underground lines. Economic and behavioural changes have lead to a less sustainable use of this structure than initially intended with a high degree of car use and a high degree of out-commuting from the satellites. This is in line with the observation that most cities are moving towards decentralisation of population and employment and increasing VKT. Future scenarios for the Stockholm region show that, in addition to an assumption of moderate economic growth rate, fairly drastic measures have to be taken in order to stabilise VKT over a 30-year period, including public transport investments, land-use policies and strong economic incentives in favour of public transport. The separate impact of higher land-use density only accounts for about 10% of the overall reduction of VKT as a result of infrastructure and pricing policies. In other scenarios it is shown that a sub-regional transit-oriented land-use policy is more important for retaining a high transit share than the overall density on a regional scale. With even more drastic economic incentives and transport policies, model projections for Dortmund show that there is scope for much reorganisation within an urban region implying reversals of the decreasing transit share and of the increasing VKT. The �promotion of public transport� scenario is leading to a somewhat higher density than other scenarios. Employment location and employment densities tend to have stronger impacts on travel behaviour than residential densities. Employment has also shown to be more responsive to transport changes than housing. In highly developed economies the impact of transport infrastructure improvements on land-use and regional economic development can be expected to be small and masked by other simultaneous changes. Due to the �two way road� effect the impact of a transport improvement can even be negative to a region. Transport supply is a necessary but not sufficient condition for development of land-use or of the regional economy.

Acknowledgement

Permission by Shaker Publishing to reproduce parts of Lundqvist (2003) is gratefully acknowledged. Permission by WIT Press to reproduce parts of section 3.4 from �Analysing


transport, land-use and the environment in the Stockholm region� by L. Lundqvist, published in �Urban Transport V: Urban Transport and the Environment in the 21st Century�, edited by L.J. Sucharov, WIT Press, Southampton, UK, 2000, ISBN 1-85312-695-0, is also gratefully acknowledged.

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Book Review:

Muhammad Faishal Ibrahim and Peter J. Goldrick Shopping Choices with Public Transport Options1

Harry Timmermans Eindhoven University of Technology Eindhoven The Netherlands

EJTIR, 3, no. 3 (2003), pp. 315 - 316

Received: July 2003 Accepted: July 2003

This book has been motivated by the observation that by and large studies of spatial shopping behaviour have not taken into account transport mode, while most transport studies ignored the attributes of shopping centres. The study, described in this book represents an attempt to bridge this gap. To that effect, the authors try to identify and analyse the importance of different factors, which are taken into account by shoppers in their shopping centre choice in regions with a wide choice of public transport. In addition, they analyse shoppers� perceptions of transport modes in the context of shopping trips. They start however with a review of trends of retail decentralisation and transport planning. The chapter on retail decentralisation is useful reading, but unfortunately the literature review seems to stop in the mid 1990s. This means that interested readers have to consult other recent books on retail planning to be informed about the most recent trends, which in many European countries diverge from the trends described in the present book. The next chapter on shopping and transport behavioural models is also a little disappointing. Although most approaches are briefly mentioned, this chapter lacks sufficient details for readers less familiar with the various approaches. Given the objective to bridge the gap between the two literatures, a more in-depth discussion would have been useful. The remaining chapters then discuss the findings of the studies, after a very basic and unappealing chapter on principles of qualitative research, sample size, survey administration, data analysis, etcetera. The results of the qualitative study, conducted in Singapore and the 1 Ibrahim, Muhammad Faishal and Peter J. Goldrick

Shopping Choices with Public Transport Options Aldershot: Ashgate Publishing Limited 2003 ISBN 0 7546 1810 2 297 pages

316 Book Review: Shopping Choices with Public Transport Options

UK, suggest that the choice of shopping centre is influenced by the buying situation, socio-economic characteristics, shopping centre attributes and transport mode/travel attributes. Sample sizes however were small and the lack of structure makes it difficult to assess the significance of these findings. This qualitative analysis is completed with a quantitative study involving 1100 questionnaires and the remarkably high response rate of 94.9 percent. Importance ratings suggest that respondents find both transport and shopping centre important. Respondents were also invited to complete part 2 of the questionnaire about their perception of transport modes for shopping purposes. In this case, the response was 61.3 percent; lower, but still many professional marketing firms and national bureaus of statistics would be jealous. Observations of respondents� images of 38 dimensions of the car, bus, MRT, taxi, walking and motorcycle were obtained. Although the evaluation of the practicality and suitability of different modes for shopping was statistically significant between the models, the average scores were more similar than I would expect. This probably reflects the specific transport situation in Singapore. Overall then, this volume reads more like a research report than a balanced academic book. It is useful, interesting and easy reading for those interested in shopping behaviour. One will find basic information about shopping motivations and considerations for people in the UK and in Singapore. Especially information about shopping behaviour in Singapore is scarce, and this might be an important reason for reading this book. The book succeeds in filling the gap between transportation and shopping in that a wide range of variables describing transport modes and shopping environments is taken into account. However, the book has little to offer beyond that. The conceptual framework is developed superficially, there is no attempt to disentangle the specific contributions of the set of variables to shopping centre choice, the analyses are all very basic, implications for the models that were mentioned in the literature review are not discussed, and insightful guidelines for retail and transport planning beyond common intuition are not provided. Thus, although I am inclined to support the basic premise underlying this book that there is a considerable gap between the transport and retailing literatures on shopping behaviour, this book unfortunately does not provide any clues or guidelines, let alone innovative theoretical constructs or modelling approaches how to narrow this gap.

book review: muhammad faishal ibrahim and peter j. goldrick

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