ESTIMATION OF USER BENEFITS OF ROAD INVESTMENT CONSIDER-

ING INDUCED TRAFFIC WITH COMBINED NETWORK EQUILIBRIUM MODEL IN TOKYO AREA

Version, 2002/6/30, 6:16 PM Takuya Maruyama, Noboru Harata, and Katsutoshi Ohta

University of Tokyo 1. Introduction Today, most metropolitan areas are suffering from chronic traffic congestion. Tokyo is one of such areas, and they plan to construct new ring road to allevi-ate the congestion. But there are some questions about the effect of the road investments. Does new road investment really alleviate the traffic congestion? The expanded or improved roads may generate additional traffic, so this in-duced traffic will restrict the effect of road investments. There has been great debate about this issue. Now it is well recognized that new road investment produces induced traffic, so it is necessary to consider the induced traffic in appraisal of road invest-ments. Benefit estimated by fixed OD matrix method will be biased, although the method has been used traditionally. An easiest treatment of induced traffic is elastic OD matrix model, but it is difficult to assume a reliable parameter of elasticity in the model and the result varies largely according to the parameter. In view of drivers’ behavioural side, induced traffic is explained mainly by changes of route, mode, travel destination, and increase of trip frequency when new road is open. In this paper, we use a 4-Level Nested Logit (NL) model, that is, trip making, mode choice, destination choice and route choice models to express these behavioural responses. We assume the level of ser-vices in NL model varies according to network congestion and the present traffic situation is in static equilibrium state. We employ Logit type Stochastic User Equilibrium (SUE) model. We formulate mathematical optimization prob-lem that is equivalent to the whole of 4-level NL model and SUE model. The consistent results are obtained by solving this optimization problem. There are no internally inconsistent problems in our model as those of conventional 4step travel demand model. Our model is similar to Oppenheim (1995) model, but ours differs from his model because we formulate models for each travel-ler’s trip purposes. We apply this combined model to the Tokyo Metropolitan Area. Parameters in NL model are estimated for each trip purposes with travel survey in this area. We use multi-modal and large scaled transport network data using GIS (Geo-graphic Information System) platform. The road network has more than 22,000 links and railway network has more than 4,900 links. The network congestion is expressed by conventional link performance functions in road links and discomfort functions in railway link. The discomfort functions explain the travellers’ discomfort in the crowded train, which is needed to express highly crowded train in peak period in Tokyo area.

We estimated user benefits of Tokyo Outer Ring Road (Tokyo Gaikan Ex-pressway), which is actually planned in Tokyo Area with this model. Some people change their travel mode from railway to automobile because of in-creased accessibility of the road system according to our model. This modal sift worsen the congestion in road network, and it partly relieve the congestion in railway network especially in peak periods. The increased accessibility brings another induced traffic that consists of longer distance trips by chang-ing destination and increased trip frequency. Benefits estimated by our com-bined model considering induced traffic are compared with those by fixed de-mand model. In our case, the benefits by conventional fixed demand model are shown to give overestimated results. This paper is organized as follows. In section 2, we review briefly recent stud-ies on induced traffic. In section 3, we present our model formulation, 4-level NL-SUE model. Then, application of this model to Tokyo Area is shown in Section 4, 5, which is followed by a section of policy evaluation with this model. Section 7 offers conclusion. 2. Review of Issue on Induced Traffic and Modelling Approach There are so many studies on induced traffic issue, and we review briefly re-cent studies. DeCorla-Souza and Cohen (1999) show a hypothetical freeway expansion analysis, and magnitude of travel induced by highway expansion increases significantly as a function of initial congestion levels prior to expan-sion. Abelson and Hensher (2001) describe how to evaluate and model in-duced traffic in the presence of new road infrastructure. They define the vari-ous kinds of induced travel along with some empirical findings about induced travel. They show one of the modelling frameworks of induced traffic. There are many of alternative modelling approaches to detect induced traffic. One framework is aggregate econometric models of VMT (Vehicle Miles of Travel) and lane miles. Noland and Lem (2002) review recent research on this type modelling. These studies have all used aggregate data to test for statisti-cal significance and to derive elasticity values. They say this is common prac-tice in the economic literature, but has been criticized by transportation plan-ners, because they do not capture all the behavioural effects that might occur. The aggregate econometric approach provides information on total system effects. For another approach, Fujii and Kitamura (2000) used a structural equations model system of commuters’ time use and travel for evaluation of trip-inducing effects of new freeways. Activity-based models will one of the al-ternatives (e.g. Bowman and Ben-Akiva, 2001). Coombe (1996) reviews studies in which transportation models have been used in systematic way to give some insight into the relative importance of the induced traffic. Williams, et al. (2001 a,b,c) examine the effect of new roads and highway, applied with and without road pricing, on vehicle emissions and economic user benefits using elastic equilibrium assignment model. The elas-tic equilibrium model is useful simplified appraisal method, but elasticity pa-rameter used in the model is compound elasticities, that is, essentially sub-suming all behavioural mechanisms other than route choice behaviour. It is

difficult to assume reliable parameter of elasticity in the model and the result varies largely according to the parameter. The travellers’ behaviour is treated implicitly in the elastic equilibrium model. On the other hand, our model treats the travellers’ behaviour explicitly. Our model is a regional travel demand model which pays special attention to fore-cast the strict equilibrium point of demand and performance. Another contribu-tion of our model is the careful treatment of consistency among demand fore-casting, benefit estimation and microeconomic theory. The details of our model are shown in next session.

Figure 1 Model Structure

Equilibrium

Railway Flow Road Flow

Congestion disutility

Travel Time

Bi-Modal Network Congestion

Travellers’ Behaviour

Make a trip no trip Trip making

(Generation)

Railway

Destination 1

Car

route k route 2route 1

Destination 2 Destination s Destination choice (Distribution)

Mode choice (Modal split)

Route choice (Assignment)

(mode m)

3. Model Formulation Our modelling framework is shown in Figure 1. This is a combined equilibrium model between traveller’s behaviour and network congestion. We describe each part of this model below. 3.1 Travellers’ Behaviour Following Oppenheim (1995), we use representative traveller approach. We can make logically consistent travel demand forecasting and benefit estima-tion under microeconomic theory with this approach. In addition, we use multi-class type model in order to improve fitness of model to real urban situation. We assume representative traveller’s direct utility function Ui (user class i) as follows.

, *, ,

, , ,

i i rs rsi m k m k i i

r s m kU f t u zτ= − + +∑ (1)

, , , , ,, ,

, , , , ,1 2

,0 0

, 3 4

,

, , ,

1 1ln( ) ln( )

1 1ln( ) ln( ) ln( )

i rs i rs i rs i rs i rs imi m k m k m m m rim im

r s m k r s m

i m im i i i i i i ir r r r r r r r ri i

r m r

i rs im im ir i im s r m r r

r s m r m r

u f f q q q Oθ θ

O O O O O N O O Nθ θq C O C O C

= − −

− − +

− − −

∑ ∑

∑ ∑

∑ ∑ ∑

(2)

Budget constraint of representative traveller is following, ,

, ,, , ,

,rs i rsm k m k i i

r s m kp f z y+ =∑ (3)

and flow conservation constraints, 0

i i ir r rO O N+ = , im i

r rm

O O=∑ , ,i rs imm r

sq O=∑ , , ,

,i rs i rs

m k mk

f q=∑ , , ,, ,

, ,

im m rs i rsa a k m k

r s kx fδ= ∑ ,

m ima a

ix x= ∑ , , ,

, 00, 0, 0, 0, 0, 0, 0m im i rs i rs im i ia a m k m r r rx x f q O O O≥ ≥ ≥ ≥ ≥ ≥ ≥ (4)

where *,

rsm kt : Equilibrium travel time of path k between OD pair rs by mode m.

,rsm kp : Fare (charge) of path k between OD pair rs by mode m.

zi : Amount spent on other than travel. yi : Income/budget of representative traveller.

iτ : Value of travel time of user class i. imax : Link flow on link a, mode m, by user class i. max : Link flow on link a, mode m. ( )m

at ⋅ : Link performance function of link a, mode m. map : Fare (charge) of link a, mode m.

,,

m rsa kδ : 1 if path k between OD pair rs by mode m includes link a, and 0 other-

wise. ,,

i rsm kf : Travel flow of path k between OD pair rs by mode m, by user class i. ,i rs

mq : OD travel flow between OD pair rs by mode m, by user class i. imrO : Number of trips originating from zone r by mode m, by user class i. irO : Number of trips originating from zone r by user class i.

Nri : Population index of zone r by user class i.

0irO : Number of people who make no trip on the study hour by user class i.

1mθ , 2

imθ , 3iθ , 4

iθ : Scale parameters to be estimated. imsC , ir

mC , riC : Dis-utility specific constants for each choice stage to be esti-

mated.

Now the representative traveller’s behaviour is formulated as following utility maximization problem.

max.i iV U= (5) s.t. (3),(4)

where Vi is indirect utility function of user class i. Solving this optimization problem, we have following Nested Logit model.

*1 , ,, ,

, *1 , ,

exp[ ( )]exp[ ( )]

im i rs rsk m k mi rs i rs

m k mim i rs rsk m k m

k

θ t pf q

θ t pτ

τ− +

=− +∑

, (6a)

, 2

2

exp[ ( )]exp[ ( )]

im im imi rs ims rsm rim im im

s rss

θ C Sq Oθ C S

− +=

− +∑, *

1 , ,1

1 ln exp[ ( )]im im i rs rsrs k m k mim

kS θ t p

θτ= − − +∑ (6b)

3

3

exp[ ( )]exp[ ( )]

i ir irim im mr ri ir ir

m mm

θ C SO Oθ C S

− +=

− +∑, 2

2

1 ln exp[ ( )]ir im im imm s rsim

sS θ C S

θ= − − +∑ (6c)

4

4

exp[ ( )]1 exp[ ( )]

i i ii ir rr ri i i

r r

θ C SO Nθ C S

− +=

+ − +, 3

3

1 ln exp[ ( )]i i ir irr m mi

mS θ C S

θ= − − +∑ (6d)

where log-sum variables imrsS , ir

mS , irS are inclusive cost (or equivalently expec-

tation of perceived minimum cost) for each choice stages. We can see that (6a) is route choice model, (6b) is destination choice model, (6c) is mode choice model, and (6d) is trip making model. It is well-known that logit model is equivalent to entropy model, so it may be understood intuitively that “nested” entropy formula (2) leads to Nested Logit model (6). Substituting (6) into direct utility function(1), we have the following conditional indirect utility function Vi, which has quasi-liner functional form.

44

1 ln{1 exp[ ( )]}i i i ii i r r ri

rV y N C S

θθ = + + − + ∑ (7)

Now, we define the expectation of perceived maximum utility irS for origin zone

r, user class i,

44

1 ln{1 exp[ ( )]}i i i ir r riS θ C S

θ= + − + (8)

Then we have following, i i

i i r rr

V y N S= + ∑ (9)

By comparing this utility value between with and without an investment, we can measure the User Benefit of the investment UB.

, ,

,( )i i with i without

r r ri r

UB N S S= −∑ (10)

where “with”, “without” is the superscript which denote with and without the investment. This value is consumer surplus, or equivalently EV (equivalent variations), CV (compensation variations) in this case, see Varian (1992) for

Microeconomic foundation of this issue. The above theoretical benefit meas-ure can be approximated by following rule-of-half formula.

, , , , , ,

, ,

1 ( )( )2

i rs with i rs without im without im withm m rs rs

i rs mUB q q S S= + −∑ (11)

We investigate the accuracy of this approximation empirically later. One of the advantage to use the rule-of-half formula is we can derive benefits of each mode separately. 3.2 Congestion and Network Equilibrium The congestion in road and railway network is expressed by link cost function on each links (Figure 1 lower side). The link cost function varies according to the link flow m

ax and path flow ,,

i rsm kf which is the result of travellers’ behaviour.

On the other hand, the travel time *,

rsk mt in behavioural model varies according

to the link cost function. So we have to consider the equilibrium point of above demand-performance interaction, and this equilibrium is namely stochastic user equilibrium because we use probabilistic behaviour model. If we assume the link cost function to be strictly increasing in link flow (such as the curve shown in Figure 1) and a function of its own flow only (Oppenheim, 1995), this stochastic equilibrium point can be obtained by solving the following equivalent convex minimization problem.

0, , ,

min . ( ) ( )max m im m i i

a a a im a i m a i

Z t d x p uω ω τ τ= + + −∑ ∑ ∑∫

s.t. (4) This model is one of the multi-class user equilibrium models (Lam and Huang, 1992; Yang, 1998). Partial linearization algorithm (Oppenheim, 1995) solves this problem efficiently. Although this problem has path flow entropy term, this model can be applied to large networks using the entropy decomposition method shown by Akamatsu (1997). It should be emphasized that by solving this mathematical minimization problem, we can obtain unique equilibrium so-lution of demand and performance interaction even in the large scaled analy-sis. 4. Application to Tokyo Area 4.1 Input Data We apply this combined model to the Tokyo Metropolitan Area (TMA), Japan. There are so many railway lines and complicated road networks in TMA. We use the same zoning system and network as Maruyama, et al. (2001) (Figure 2, Table 1). As you can see in Figure 2 (a), the road network has 2-level hier-archy. The network within 40km of central Tokyo is relatively dense, and the other is coarse. This network system saves the computational cost of equilib-rium analysis. We use GIS for construction and management of these spatial data. The increasing capabilities of computational platforms enable us to exe-cute this large-scaled travel demand analysis.

000000000 202020202020202020 (km)(km)(km)(km)(km)(km)(km)(km)(km)404040404040404040

(a) Road Network

000000000 202020202020202020 (km)(km)(km)(km)(km)(km)(km)(km)(km)404040404040404040

(b) Railway Network

Figure 2 Road Network and Railway Network in Tokyo Area

Legend

Other main roadOther main roadOther main roadOther main roadOther main roadOther main roadOther main roadOther main roadOther main roadMotorwayMotorwayMotorwayMotorwayMotorwayMotorwayMotorwayMotorwayMotorway

Newly planned roadNewly planned roadNewly planned roadNewly planned roadNewly planned roadNewly planned roadNewly planned roadNewly planned roadNewly planned road(Tokyo Outer Ring Road)(Tokyo Outer Ring Road)(Tokyo Outer Ring Road)(Tokyo Outer Ring Road)(Tokyo Outer Ring Road)(Tokyo Outer Ring Road)(Tokyo Outer Ring Road)(Tokyo Outer Ring Road)(Tokyo Outer Ring Road)

Legend

JR lines(Japan Railway Company)Other railways

Table 1 The Size of Network Components Network Nodes Links Dummy links Centroids

Road 10,692 22,911 1,324 149 Railway 1,654 4,902 3,666 144

We use OD matrices from TMA Person Trip (PT) survey in 1998, and Road Traffic Census OD survey in 1994 for the parameter estimation of the com-bined model. In order to accommodate congestion effects of road and railway networks, we build an hourly model. Our analysis is based on PT Medium-size zone, which divides TMA into 144 zones. Average area of Medium-size zones is about 100 km2. We do not deal with intra-zonal OD trips from the analysis. Under these conditions, 89.5 % of all trips are taken by automobile or railway. Therefore we neglect bus users and walkers in this analysis. We classify the trip purpose into 6 categories; home-work, home-school, business, private, to home, and freight. Freight data is from Road Traffic Census survey, and other data is from PT survey. 4.2 Model Settings Our trip making model (6d) have inclusive cost term, which means accessibil-ity index of origin zone, so we can forecast the increase of trip frequency by improved accessibility with road improvement. However, it seems natural to consider that increase of trip frequency will happen for business and private trips only. So we estimate trip making model only for business and private trips. Population index Nr

i is employee for business trip and the daytime popu-lation for private trip. We give exogenously the number of trips originating from zone r, Or

i for home-work, home-school, to-home, and freight purpose. Note that in Fig. 1 we assume that destination choice is conditional on mode choice. This means that we do not use the traditional nested hierarchy but re-verse nested hierarchy. This is because we estimated nested logit model with traditional hierarchy in former studies (Maruyama, et al; 2002), but we have parameters that is inconsistent with the random utility maximization theory. See also Abrahamsson and Lundqvist (1999) for another empirical analysis of this issue. 5. Parameter Estimation and Model Validation 5.1 Given Parameters and Settings We assume that value of travel time iτ =50 (Yen/min; 180 JPN Yen = 1 UK £, June 2002). Road network congestion is expressed by conventional link per-formance function in links, and we use the function estimated by Matsui and Yamada (1998). They estimated parameters of BPR function using observed data in Japan. Railway network congestion is expressed by disutility function in railway links. The disutility function explains travellers’ discomfort in crowded train, and the disutility grows up as the railway congestion gets heav-ier. We use the railway disutility functions estimated by Shida, et al. (1989).

The function is needed to express highly crowded train in peak period in this area. 5.2 Parameter Estimation Method and Overall Results Oppenheim (1995), Hicks and Abdel-aal (1998), Boyce and Zhang (1998) and Abrahamsson and Lundqvist (1999) showed some methods of parameter es-timation for combined model. In this paper, we use more simply sequential es-timation method. We estimate parameters sequentially from lower part of model structure. The estimated results are partly shown in Tables 2 and 3, and each parameter has correct sign and is statistically significant. We can check that the esti-mated scale parameter meet the condition

θ1 > θ2 > θ3 > θ4 for each purposes, so this model is consistent with random utility maximization theory. We will look into the estimation methods and results for each choice stage below. 5.3 Route Choice Model We assume route choice parameter in car 1

carθ =0.5 (1/min), and in railway 1railθ =0.05 (1/min). This value is determined by calibration procedure in each

mode. For example, in road network, we make fixed demand assignment with observed car OD and initial value 1

carθ and check the goodness-of-fit of link flow. Then we change the value 1

carθ slightly and make fixed demand assign-ment again. The value 1

carθ =0.5 produces the highest goodness-of-fit, so we take this value. We confirmed that some change of these parameters will lead to little change in the final combined equilibrium assignment results by sensi-tivity analysis. We assume unique parameter for each mode. The segmenta-tion of route choice model by trip purpose seems interesting, but it is difficult to estimate such model using current available data. 5.4 Destination Choice Model Theoretically, the utility function Vs

im in destination choice phase(6b) is desired to have the following form.

*2 2 *( ) ln ln jsim im im im im im

s s rs s rs jj s

AV C S A S

Aθ θ δ= − + = − + ∑ (7)

where As* is the standard scale variable (such as area of zone s), Ajs is other

scale variable (such as population of zone s), imrsS is inclusive cost, and δ,θ is

parameters to be estimated. The variable *ln sA is a measure of the size of a destination alternative and its coefficient is constrained to take the value of 1.0. This constraint is necessary if the model is independent of the zone system used for estimation (Ben-akiva, et al., 1978).

Our estimated results show that the goodness-of-fit of the destination choice model by railway is good, but that of the car model is not so good. We may need further trial on this issue. 5.5 Mode Choice Model We use location specific dummy variables in mode choice model. Yamanote dummy is 1 if the origin zone is within the railway Yamanote line (inner core area), 23ward dummy is 1 if the origin zone is within the Tokyo 23 ward (Cen-tral Tokyo area). These dummy variables and constant are railway specific variables, so if these parameters are high, the railway will be preferred. The constant values vary significantly across trip purposes, so we can confirm the effectiveness of segmentation of trip purposes.

Table 2 Estimation Results of Mode, Destination and Route Choice Models for Home-Work and Home-School Trip

trip purpose home-work home-school estimates (t-statistic) estimates (t-statistic)

inclusive cost 3θ− -0.017 (-808.9) -0.012 (-164.)

constant -4.44 (-687.9) -2.65 (-81.2) mode ρ2 0.16 0.69 ln(zone area) 1.00 (-) 1.00 (-)

inclusive cost 2carθ− -0.041 (-156.8) -0.047 (-74.2)

ln(density of working people) -0.06 (-5.5) ln(density of employee) 0.56 (150.1)

destination car

ln(density of student) 0.30 (21.9) # of samples N 6,328 876 correlation coefficient R 0.80 0.62 regression coefficient a 0.54 0.35

route car generalized cost

1carθ− -0.50 (-) -0.50 (-)

ln(zone area) 1.00 (-) 1.00 (-) inclusive cost

2railθ− -0.022 (-131.5) -0.019 (-97.9)

ln(density of working people) -0.31 (-33.8) ln(density of student in school) 1.002 (256.8)

ln(density of employee in secondary industry) 0.17 (6.4)

ln(density of employee in tertiary industry) 1.03 (44.1)

destination railway

# of samples N 8,028 5,770 correlation coefficient R 0.87 0.81 regression coefficient a 1.04 0.73

route railway generalized cost 1

railθ− -0.05 (-) -0.05 (-)

Note) if t-statistic is (-) then the estimates is given by calibration or assumed to be fixed in estimation procedure.

5.6 Trip Making Model In trip making model, we use the inclusive cost, which means accessibility in-dex of origin zone, time period dummy variable and population index. The population index express the phenomena, for example in business trip, people

Table 3 Estimation Results of Trip Making, Mode, Destination and Route Choice Models for Business and Private Trip

trip purpose business private estimates (t-statistic) estimates (t-statistic) time period 09-18 10-16

inclusive cost 4θ− -0.006 (-218.1) -0.003 (-192.) ratio of employee in tertiary

industry to whole employee 1.122 (128.1)

ratio of non-workers*) 1.458 (240. ) 9 0.995 (252.5) 10 1.231 (321.9) 0.186 (77.4) dummy variable for each

time periods 11 1.215 (317.5) 0.009 (3.8) 12 0.793 (196.7) -0.193 (-73.8) 13 1.329 (351.3) -0.005 (-2. ) 14 1.211 (316.4) -0.132 (-51.1) 15 1.217 (318. ) -0.122 (-47.4) 16 1.055 (270.4) 17 0.826 (203.4)

constant -7.515 (-1149.) -6.247 (-752.) correlation coefficient R 0.978 0.827

trip making

regression coefficient a 0.95 0.81 inclusive cost 3θ−

-0.016 (-248.5) -0.018 (-409.) Yamanote dummy 1.210 (306.5) 0.810 (205.7)

23ward dummy 0.347 (93.6) constant -11.26 (-297.7) -6.09 (-436.)

mode

ρ2 0.28 0.14 ln(zone area) 1.00 (-) 1.00 (-)

inclusive cost 2carθ− -0.033 (-143.5) -0.036 (-127.)

ln(density of employee in secondary industry) 0.15 (4.5)

destina-tion car

ln(density of employee in tertiary industry) 0.38 (13.0) 0.36 (76.8)

# of samples N 7,389 5,042 correlation coefficient R 0.81 0.69 regression coefficient a 0.50 0.34

route car generalized cost

1carθ− -0.50 (-) -0.50 (-)

ln(zone area) 1.00 (-) 1.00 (-) inclusive cost

2railθ− -0.018 (-78.6) -0.021 (-108.)

ln(density of employee in tertiary industry) 1.10 (212.2) 0.86 (214.6)

destina-tion

railway # of samples N 3,131 5,976

correlation coefficient R 0.97 0.78 regression coefficient a 0.88 0.66

route railway generalized cost 1

railθ− l -0.05 (-) -0.05 (-)

Note) ratio of non-workers = “population of people who do not work and are not students” / “the daytime population”, “the daytime population” = “population of non-workers + employee”.

tend to make a trip more frequently in the zone which have many employee in tertiary industry. 5.7 Model Validation We validate this model for several goodness-of-fit measures, such as car link flow, railway link flow, car OD travel time, and equilibrium OD flow in each mode (Table 4) in equilibrium state. We also show the value by conventional fixed demand model. In fixed demand model we make fixed assignment with observed current OD matrix. We can see that the goodness-of-fit of our com-bined demand model is as good as that of traditional fixed demand model. We can conclude from these figures that our models are applicable for policy evaluations.

Table 4 Goodness-of-fit measure of model

index model correlation

coefficient Rregression

coefficient a RMSE fixed demand 0.72 0.73 11,740 (vehicle)car link flow combined demand 0.75 0.90 14,313 (vehicle)fixed demand 0.95 0.82 122,615(person)railway link flow combined demand 0.94 1.16 139,263(person)fixed demand 0.51 0.91 31.56 (minute) car OD travel

time combined demand 0.65 0.84 20.50 (minute) car OD matrix combined demand 0.86 0.56 1,498 (vehicle trip)

railway OD matrix combined demand 0.88 0.84 1,326 (person trip)Note) R, a, RMSE(root mean squared error) are the statistic between observed and estimated value. Source of observed data: car link flow (daytime 12hour flow); Road Traffic Census Survey in 1997. railway link flow (24hour flow); Transportation Census in Metropolitan Area in 1995 car OD travel time (hourly average value); Road Traffic Census OD Survey in 1994. OD matrix; Person Trip survey in 1998.

6. Example of Estimation of Road Investment Benefit We estimate user benefit of Tokyo Outer Ring Road (Tokyo Gaikan Express-way, see Figure 2(a)), which is actually planned in Tokyo Area with this model. We estimate benefits of this new road by comparing model situation with and without the investment. Benefit of road investment measured in our model is come from congestion relief. The congestion relief leads to the travel time sav-ing in driving a car and ease discomfort in crowded train. Population and other socio-economic factors are assumed to be same as current situation. Increased level of service with the new road brings several kinds of behav-ioural change of travellers. Some people change their travel mode from rail-way to automobile. Our model forecast the number of such trip is 30,492 (trips/day). This modal sift worsen the congestion in road network, but it partly relieve the congestion in railway network especially in the peak periods. The increased accessibility brings another induced traffic that consists of longer distance trips by changing destination and increased trip frequency. Our model forecast that the increased number of trip is 4,349 (trips/day). The tradi-

traditional fixed demand model neglects such change of behaviours. It may seem the number of such trips is relatively small, but such a little change of demand may lead to a big change of benefit estimation especially the current congestion is heavy. See Williams et al. (1990, 1991 a,b,c) for the example of theoretical consideration of this issue. We consider this issue empirically be-low. In order to investigate the impact of induced traffic on benefit estimation, we compare the results of combined model with those of fixed demand model in each time periods. We now show estimation result of user benefits of the road investment in Table 5. In combined models we express the railway congestion, so benefits of congestion relief in railway are added in road investment. It should be noted road investment not only raises road users’ utility but also railway users’ utility in combined models in Tokyo area where railway conges-tion is serious. We confirm that the benefits measured by Rule-of-Half formula (11) are very close to that measured by log-sum formula(10). On the whole, the benefits estimated by fixed demand model are higher than those esti-

Table 5 Comparison of User Benefit by Fixed Demand / Combined Demand Models (Unit: 103 Yen per a hour)

Fixed De-mand Model Combined Demand Model

Rule-of-Half(ROH) Formula

time period

Benefit of Congestion Relief in car

(A)

Benefit of Congestion Relief in car

(B)

Benefit of Congestion

Relief in railway

(C)

Total

(B+C)

Log-Sum Formula

(D)

Difference between ROH and Log-Sum

[(B+C)-D] /D

Difference between Fixed /

CombinedDemand Model

(A-D)/D

0 1,812 1,860 6 1,866 1,861 0.24% -3%1 1,238 1,293 0.5 1,293 1,290 0.24% -4%2 1,194 1,271 0 1,271 1,267 0.29% -6%3 1,449 1,518 0 1,518 1,512 0.46% -4%4 2,603 2,541 0.2 2,541 2,530 0.45% 3%5 11,018 6,991 51 7,042 7,014 0.40% 57%6 42,889 13,230 1,425 14,655 14,505 1.04% 196%7 82,306 20,984 5,049 26,033 25,657 1.47% 221%8 71,723 21,045 2,376 23,420 23,125 1.28% 210%9 67,605 23,196 432 23,629 23,353 1.18% 189%

10 62,022 22,805 102 22,907 22,664 1.07% 174%11 60,172 22,559 55 22,615 22,417 0.88% 168%12 40,832 17,989 16 18,005 17,897 0.60% 128%13 60,753 22,079 76 22,156 21,945 0.96% 177%14 68,914 24,475 67 24,543 24,362 0.74% 183%15 78,418 26,481 382 26,863 26,666 0.74% 194%16 83,258 26,219 700 26,919 26,735 0.69% 211%17 109,422 28,729 2,915 31,644 31,404 0.76% 248%18 84,887 25,406 3,106 28,512 28,365 0.52% 199%19 55,352 20,321 983 21,304 21,233 0.34% 161%20 40,213 17,039 602 17,641 17,597 0.25% 129%21 29,303 14,322 380 14,702 14,673 0.20% 100%22 15,710 10,086 153 10,239 10,221 0.17% 54%23 7,240 5,807 43 5,850 5,838 0.20% 24%

total 1,080,333 378,245 18,922 397,167 394,130 0.77% 174%

mated by combined model. Furthermore this overestimation is larger in peak periods. These are the empirical verification of the following well-known find-ings. “Errors introduced by neglecting induced traffic are likely to greater where congestion, and thus suppression of travel, is greater” (e.g. Coombe, 1996). On the other hand, there is a certain time periods when the benefits are slightly underestimated by fixed demand model especially in off-peak pe-riods. These phenomena are verified by theoretical consideration. If the initial congestion level is low, the benefits of new induced traffic are simply added to those of existing traffic so the fixed demand model will underestimate the benefits. The results shown here is one of test calculation, but we can conclude tradi-tional fixed demand model gives overestimated results of road investment in this crowed area. Furthermore we can verify that our combined model has the policy sensitivity that is consistent with the former studies. 7. Conclusion In this paper, we develop a consistent model for the evaluation of road in-vestment, that is 4-level nested logit based stochastic user equilibrium model under bimodal network congestion. This model represent travellers’ behaviour following random utility maximization accommodating congestion effects in both car and railway network and equilibrium state of these demand and per-formance interactions. Furthermore our model is a multi-class user equilibrium model which has segmentation of travellers’ trip purposes. With this model we can represent change of travellers’ behaviours such as route choice, mode choice, destination choice, and increase of trip frequency. This model produces logically consistent demand forecasting and benefit estimation under microeconomic theory. We show an application and parameter estimation of this model for Tokyo metropolitan area. We estimated user benefit of Tokyo Outer Ring Road (Tokyo Gaikan Ex-pressway), which is actually planned in Tokyo area with this model. Some people change their travel mode from railway to automobile because of in-creased accessibility of the road system according to our model. This modal sift worsen the congestion in road network, and it partly relieve the congestion in railway network especially in peak periods. The increased accessibility brings another induced traffic that consists of longer distance trips by chang-ing destination and increased trip frequency. Benefits estimated by our com-bined model considering induced traffic are compared with the results of fixed demand model. In our case, the benefits estimated by the conventional fixed demand model are shown to give overestimated results. So, the effect of road investment as an attempt to reduce congestion is reduced by trips induced by the new investment itself. The model shown here is a prototype model, and results shown here is one of test calculation. Parameters shown here are estimated against cross-sectional data using representative traveller approach, so the elasticities of the model may be different from real-life elasticities. Estimation with time series data or panel survey data will be needed in further study. Model improvement are also

needed such as considering departure time choice, simultaneous estimation of Nested Logit models and equilibrium traffic flow. Anyway it will be important to use logically consistent framework which considers not only travellers’ be-haviour and congestion phenomena but also equilibrium state between de-mand and performance interaction. Bibliography Abelson, P. W. and Hensher, D. A. (2001) Induced travel and user benefits: clarifying definitions and measurement for urban road infrastructure, in Button, K.J. and Hensher, D.A. (eds.) Handbook of Transport Systems and Traffic Control, 125-141. Abrahamsson, T. and Lundqvist, L. (1999) Formulation and estimation of combined network equilibrium models with application to Stockholm, Trans-portation Science, 33 (1) 80-100. Akamatsu, T. (1997) Decomposition of path choice entropy in general trans-port networks, Transportation Science, 31 (4) 349-362. Boyce, D. E. and Zhang, Y. F. (1998) Parameter estimation for combined travel choice models, in Lundqvist, L. et al. (eds.), Network Infrastructure and the Urban Environment, Springer, 177- 193. Bowman, J. L. and Ben-Akiva, M. E. (2001) Activity-based disaggregate travel demand model system with activity schedules, Transportation Research Part A, 35 (1) 1-28. Coombe, D. (1996) Induced traffic: What do Transportation models tell us?, Transportation, 23 (1) 83–101. DeCorla-Souza, P. and Cohen, H. (1999) Estimating induced travel for evaluation of metropolitan highway expansion, Transportation, 26 (3) 249-262. Fujii, S. and Kitamura, R. (2000) Evaluation of trip-inducing effects of new freeways using a structural equations model system of commuters' time use and travel, Transportation Research Part B, 34 (5) 339-354. Hicks, J. E. and Abdel-aal, M. M. (1998) Maximum likelihood estimation for combined travel choice model parameters, Transportation Research Re-cord, 1645, 160-169. Lam, W. H. K. and Huang, H. J. (1992) A combined trip distribution and as-signment model for multiple user classes, Transportation Research Part B, 26 (4) 275-287. Maruyama, T., Muromachi, Y., Harata, N., and Ohta, K. (2001) The combined modal split/assignment model in the Tokyo metropolitan area, Journal of the Eastern Asia Society for Transportation Studies, 4 (2) 293-304.

Maruyama, T., Harata, N., and Ohta, K. (2002) An application of combined stochastic user equilibrium model to the Tokyo area: combined trip distribution, modal split and assignment model with explicitly distinct trip purposes, Traffic and Transportation Studies, Proceedings of ICTTS, to appear. Matsui, H. and Yamada, S. (1998) Estimation of the BPR functions by using road traffic census data, Traffic Engineering, 33 (6) 9-16 (in Japanese). Noland, R.B. and Lem, L.L. (2002) A review of the evidence for induced travel and changes in transportation and environmental policy in the US and the UK, Transportation Research part D, 7 (1) 1-26. Oppenheim, N. (1995) Urban travel demand modeling: from individual choices to general equilibrium, John Wiley & Sons, N. Y. Shida, K., Furukawa, A., Akamatsu, T. and Ieda, H. (1989) A study of trans-ferability of parameters of railway commuter’s dis-utility function, Proceedings of Infrastructure Planning, 12, 519-525 (in Japanese). Varian, H. R.(1992) Microeconomic analysis, Norton, N. Y. Williams, H. C. W. L., and Moore, L. A. R. (1990) The appraisal of highway investments under fixed and variable demand, Journal of Transport Economics and Policy, 24 (1) 61–81. Williams, H. C. W. L., and Lam, W. M. (1991a) Transport policy appraisal with equilibrium models I: Generated traffic and highway investment benefits, Transportation Research part B, 25 (5) 253-279. Williams, H. C. W. L., and Lai, H. S. (1991b) Transport policy appraisal with equilibrium models II: Model dependence of highway investments benefits, Transportation Research part B, 25 (5) 281-292. Williams, H. C. W. L., Lam, W. M., and Kim, K. S. (1991c) Transport policy appraisal with equilibrium models III: Investment benefits in multi-modal sys-tems, Transportation Research part B, 25 (5) 293-316. Williams, H. C. W. L., van Vliet, D., Parathira, C. and Kim, K. S. (2001a) Highway investment benefits under alternative pricing regimes, Journal of Transport Economics and Policy, 35 (2) 257-284. Williams, H.C.W.L., van Vliet, D., and Kim, K.S. (2001b) The contribution of suppressed and induced traffic in highway appraisal, part 1: reference states, Environment and Planning A, 33 (6) 1057-1082. Williams, H.C.W.L., van Vliet, D., and Kim, K.S. (2001c) The contribution of suppressed and induced traffic in highway appraisal, part 2: policy tests, Envi-ronment and Planning A, 33 (7) 1243-1264. Yang, H. (1998) Multiple equilibrium behaviors and advanced traveler informa-tion systems with endogenous market penetration, Transportation Research Part B, 32 (3) 205-218.