ESTIMATION OF USER BENEFITS OF ROAD INVESTMENT CONSIDERING INDUCED TRAFFIC WITH COMBINED NETWORK EQUILIBRIUM
MODEL IN TOKYO AREA
Version,
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 alleviate 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 induced 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 investments. 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 services 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 problem 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 traveller’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 (Geographic 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.
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We estimated user benefits of Tokyo Outer Ring Road (Tokyo Gaikan Expressway), which is actually planned in Tokyo Area with this model. Some
people change their travel mode from railway to automobile because of increased 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 changing destination and increased trip frequency. Benefits estimated by our combined model considering induced traffic are compared with those by fixed demand 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 studies 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 recent 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 expansion. Abelson and Hensher (2001) describe how to evaluate and model induced traffic in the presence of new road infrastructure. They define the various 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 statistical significance and to derive elasticity values. They say this is common practice in the economic literature, but has been criticized by transportation planners, 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 alternatives (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 elastic equilibrium model is useful simplified appraisal method, but elasticity parameter used in the model is compound elasticities, that is, essentially subsuming all behavioural mechanisms other than route choice behaviour. It is
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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 forecast the strict equilibrium point of demand and performance. Another contribution of our model is the careful treatment of consistency among demand forecasting, benefit estimation and microeconomic theory. The details of our
model are shown in next session.
Travellers’ Behaviour
Trip making
(Generation)
Mode choice
(Modal split)
Railway
Destination choice
(Distribution) Destination 1
Route choice
(Assignment)
no trip
Make a trip
Car
Destination 2
route 1
route 2
(mode m)
Destination s
route k
Equilibrium
Bi-Modal Network Congestion
Congestion
disutility
Travel
Time
Railway Flow
Figure 1 Model Structure
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Road Flow
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 estimation under microeconomic theory with this approach. In addition, we use multiclass 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.
U i = − ∑ τ i f mi ,,rsk tmrs,*k + ui + zi
(1)
r , s ,m,k
ui = −
1 i , rs
1
f ln( f mi ,,rsk qmi , rs ) − ∑ im qmi , rs ln(qmi , rs Orim )
im m , k
r , s , m , k θ1
r , s , m θ2
∑
1 i,m
1
Or ln(Orim Ori ) − ∑ i Ori ln(Ori N ri ) + Ori 0 ln(Ori 0 N ri ) 
i
r , m θ3
r θ4
−∑
(2)
− ∑ qmi , rsCsim − ∑ OrimCmir − ∑ Ori Cri
r ,s,m
r ,m
r
Budget constraint of representative traveller is following,
∑ pmrs,k f mi,,rsk + zi = yi ,
(3)
r , s ,m,k
and flow conservation constraints,
Ori + Ori 0 = N ri , ∑ Orim = Ori , ∑ qmi , rs = Orim ,
m
s
x = ∑ x , x ≥ 0, x ≥ 0, f
m
a
im
a
m
a
im
a
i , rs
m,k
≥ 0, q
∑f
i , rs
m
i , rs
m,k
= qmi , rs , xaim =
k
∑δ
m , rs
a ,k
f mi ,,rsk ,
r , s ,k
im
r
i
r
≥ 0, O ≥ 0, O ≥ 0, Ori 0 ≥ 0
(4)
i
where
tmrs,*k
: Equilibrium travel time of path k between OD pair rs by mode m.
pmrs, k : 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.
i
τ
: Value of travel time of user class i.
xaim
: Link flow on link a, mode m, by user class i.
m
xa
: Link flow on link a, mode m.
m
ta (⋅) : Link performance function of link a, mode m.
pam
: Fare (charge) of link a, mode m.
δ am,k,rs : 1 if path k between OD pair rs by mode m includes link a, and 0 otherwise.
i , rs
f m ,k : Travel flow of path k between OD pair rs by mode m, by user class i.
qmi , rs : OD travel flow between OD pair rs by mode m, by user class i.
Orim
: Number of trips originating from zone r by mode m, by user class i.
i
Or
: Number of trips originating from zone r by user class i.
i
Nr
: Population index of zone r by user class i.
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Ori 0
: Number of people who make no trip on the study hour by user class i.
m
im
θ1 , θ 2 , θ 3i , θ 4i : Scale parameters to be estimated.
Csim , Cmir , Cir : Dis-utility specific constants for each choice stage to be estimated.
Now the representative traveller’s behaviour is formulated as following utility
maximization problem.
Vi = max . U i
(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.
exp[−θ1im (τ i tkrs, m* + pkrs, m )] i , rs
i , rs
f m,k =
qm ,
(6a)
∑ exp[−θ1im (τ itkrs, m* + pkrs,m )]
k
qmi , rs =
exp[−θ2im (Csim + S rsim )] im im
1
Or , S rs = − im ln ∑ exp[−θ1im (τ i tkrs, m* + pkrs, m )] (6b)
im
im
im
θ1
k
∑ exp[−θ2 (Cs + Srs )]
s
Orim =
exp[−θ3i (Cmir + S mir )] i
1
Or , S mir = − im ln ∑ exp[−θ2im (Csim + Srsim )]
i
ir
ir
θ2
s
∑ exp[−θ3 (Cm + Sm )]
(6c)
m
exp[−θ4i (Cri + Sri )]
1
N ri , S ri = − i ln ∑ exp[−θ3i (Cmir + S mir )]
(6d)
i
i
i
θ3
1 + exp[−θ4 (Cr + Sr )]
m
where log-sum variables S rsim , S mir , Sri are inclusive cost (or equivalently expectation of perceived minimum cost) for each choice stages. We can see that (6
a) 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.
1
Vi = yi + ∑ i  N ri ln{1 + exp[−θ 4i (Cri + Sri )]}
(7)
r θ4
Now, we define the expectation of perceived maximum utility S i for origin zone
Ori =
r
r, user class i,
1
Sri = i ln{1 + exp[−θ4i (Cri + Sri )]}
θ4
Then we have following,
Vi = yi + ∑ N ri Sri
(8)
(9)
r
By comparing this utility value between with and without an investment, we
can measure the User Benefit of the investment UB.
UB = ∑ N ri ( Sri , with − Sri , without )
(10)
i ,r
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
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Microeconomic foundation of this issue. The above theoretical benefit measure can be approximated by following rule-of-half formula.
1
UB = ∑ (qmi , rs , with + qmi , rs , without )( Srsim , without − Srsim, with )
(11)
2 i , rs , m
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 xam and path flow f mi ,,rsk which is the result of travellers’ behaviour.
On the other hand, the travel time tkrs,m* 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.
xam
min .Z = ∑ ∫ tam (ω )dω + ∑ xaim pam τ i + ∑ (−ui τ i )
m,a
0
i ,m ,a
i
(4)
s.t.
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 solution of demand and performance interaction even in the large scaled analysis.
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 hierarchy. The network within 40km of central Tokyo is relatively dense, and the
other is coarse. This network system saves the computational cost of equilibrium analysis. We use GIS for construction and management of these spatial
data. The increasing capabilities of computational platforms enable us to execute this large-scaled travel demand analysis.
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
Legend
0
20
Motorway
Other main road
Newly planned road
(Tokyo Outer Ring Road)
40 (km)
(a) Road Network

Legend
0
20
40 (km)
JR lines
(Japan Railway Company)
Other railways
(b) Railway Network
Figure 2 Road Network and Railway Network in Tokyo Area
© Association for European Transport 2002
Network
Road
Railway
Table 1 The Size of Network Components
Nodes
Links
Dummy links
10,692
22,911
1,324
1,654
4,902
3,666
Centroids
149
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 combined 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 accessibility 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 Nri is employee for business trip and the daytime population for private trip. We give exogenously the number of trips originating from
zone r, Ori 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 reverse 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 τ i =50 (Yen/min; 180 JPN Yen = 1 UK £,
June 2002). Road network congestion is expressed by conventional link performance 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 heavier. We use the railway disutility functions estimated by Shida, et al. (1989).
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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 estimation for combined model. In this paper, we use more simply sequential estimation 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 estimated 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 θ1car =0.5 (1/min), and in railway
θ1rail =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 θ1car and check the goodness-of-fit of link
flow. Then we change the value θ1car slightly and make fixed demand assignment again. The value θ1car =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 sensitivity analysis. We assume unique parameter for each mode. The segmentation 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 Vsim in destination choice phase(6b) is desired
to have the following form.
Ajs
Vsim = −θ 2im (Csim + S rsim ) = ln As* − θ 2im S rsim + ∑ δ j ln *
(7)
As
j
where As* is the standard scale variable (such as area of zone s), Ajs is other
scale variable (such as population of zone s), S rsim is inclusive cost, and δ,θ is
parameters to be estimated. The variable ln As* 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).
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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 (Central 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
mode
inclusive cost
constant
home-work
home-school
estimates (t-statistic) estimates (t-statistic)
−θ 3
ρ2
ln(zone area)
destination
car
route
car
inclusive cost
−θ
car
2
ln(density of working people)
ln(density of employee)
ln(density of student)
N
# of samples
R
correlation coefficient
a
regression coefficient
generalized cost
−θ1car
ln(zone area)
inclusive cost
destination
railway
−θ
rail
2
ln(density of working people)
ln(density of student in school)
ln(density of employee in secondary
industry)
ln(density of employee in tertiary
industry)
N
# of samples
R
correlation coefficient
a
regression coefficient
-0.017
-4.44
0.16
1.00
(-808.9)
(-687.9)
-0.041
-0.06
0.56
(-156.8)
(-5.5)
(150.1)
(-)
6,328
0.80
0.54
-0.012
-2.65
0.69
1.00
(-164.)
(-81.2)
-0.047
(-74.2)
0.30
876
0.62
0.35
(21.9)
(-)
-0.50
(-)
-0.50
(-)
1.00
(-)
1.00
(-)
-0.022
-0.31
(-131.5)
(-33.8)
-0.019
(-97.9)
1.002
(256.8)
0.17
(6.4)
1.03
8,028
0.87
1.04
(44.1)
5,770
0.81
0.73
route
generalized cost
-0.05
(-)
-0.05
(-)
−θ1rail
railway
Note) if t-statistic is (-) then the estimates is given by calibration or assumed to be fixed in
estimation procedure.
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Table 3 Estimation Results of Trip Making, Mode, Destination
and Route Choice Models for Business and Private Trip
trip purpose
business
estimates (t-statistic)
09-18
time period
trip
making
mode
inclusive cost
−θ 4
ratio of employee in tertiary
industry to whole employee
ratio of non-workers*)
9
dummy variable for each
10
time periods
11
12
13
14
15
16
17
constant
R
correlation coefficient
a
regression coefficient
inclusive cost
Yamanote dummy
23ward dummy
constant
−θ 3
ρ2
ln(zone area)
destination
car
route
car
inclusive cost
−θ
car
2
ln(density of employee
in secondary industry)
ln(density of employee
in tertiary industry)
N
# of samples
R
correlation coefficient
a
regression coefficient
generalized cost
−θ1car
ln(zone area)
destination
railway
inclusive cost
−θ
rail
2
ln(density of employee
in tertiary industry)
N
# of samples
R
correlation coefficient
a
regression coefficient
-0.006
1.122
(-218.1)
(128.1)
0.995
1.231
1.215
0.793
1.329
1.211
1.217
1.055
0.826
-7.515
0.978
0.95
(252.5)
(321.9)
(317.5)
(196.7)
(351.3)
(316.4)
(318. )
(270.4)
(203.4)
(-1149.)
-0.016
1.210
(-248.5)
(306.5)
-11.26
0.28
1.00
(-297.7)
private
estimates (t-statistic)
10-16
-0.003
(-192.)
1.458
(240. )
0.186
0.009
-0.193
-0.005
-0.132
-0.122
(77.4)
(3.8)
(-73.8)
(-2. )
(-51.1)
(-47.4)
-6.247
0.827
0.81
(-752.)
(-409.)
(205.7)
(93.6)
(-436.)
(-)
-0.018
0.810
0.347
-6.09
0.14
1.00
-0.033
(-143.5)
-0.036
(-127.)
0.15
(4.5)
0.38
7,389
0.81
0.50
(13.0)
0.36
5,042
0.69
0.34
(76.8)
-0.50
(-)
-0.50
(-)
1.00
(-)
1.00
(-)
-0.018
(-78.6)
-0.021
(-108.)
1.10
3,131
0.97
0.88
(212.2)
0.86
5,976
0.78
0.66
(214.6)
(-)
route
l
generalized cost
-0.05
(-)
-0.05
(-)
−θ1rail
railway
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”.
5.6
Trip Making Model
In trip making model, we use the inclusive cost, which means accessibility index of origin zone, time period dummy variable and population index. The
population index express the phenomena, for example in business trip, people
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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 combined 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
car link flow
railway link flow
car OD travel
time
car OD matrix
railway OD matrix
model
fixed demand
combined demand
fixed demand
combined demand
fixed demand
combined demand
combined demand
combined demand
correlation
coefficient R
0.72
0.75
0.95
0.94
0.51
0.65
0.86
0.88
regression
coefficient a
0.73
0.90
0.82
1.16
0.91
0.84
0.56
0.84
RMSE
11,740 (vehicle)
14,313 (vehicle)
122,615(person)
139,263(person)
31.56 (minute)
20.50 (minute)
1,498 (vehicle trip)
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 Expressway, 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 saving 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 behavioural change of travellers. Some people change their travel mode from railway 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© Association for European Transport 2002
Table 5 Comparison of User Benefit by Fixed Demand / Combined
Demand Models (Unit: 103 Yen per a hour)
Fixed DeDifference
Combined Demand Model
mand Model
between
Fixed /
Rule-of-Half(ROH) Formula
Benefit of
Difference
Combined
Congestion Benefit of Benefit of
Log-Sum
between
Demand
time Relief in car Congestion Congestion
Formula
ROH and
Total
Model
period
Log-Sum
Relief in car Relief in
railway
(A)
(D)
[(B+C)-D] /D
(A-D)/D
(B)
(C)
(B+C)
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%
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 below.
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 congestion 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© Association for European Transport 2002
mated by combined model. Furthermore this overestimation is larger in peak
periods. These are the empirical verification of the following well-known findings. “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 periods. 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 traditional 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 investment, 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 performance 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 Expressway), which is actually planned in Tokyo area with this model. Some
people change their travel mode from railway to automobile because of increased 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 changing destination and increased trip frequency. Benefits estimated by our combined 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
© Association for European Transport 2002
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’ behaviour and congestion phenomena but also equilibrium state between demand and performance interaction.
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© Association for European Transport 2002
Estimation of user benefits of road
investment considering induced
traffic with combined network
equilibrium model in Tokyo area
Takuya MARUYAMA,
Noboru HARATA and Katsutoshi OHTA,
Univ. of Tokyo, Japan
Outline
Introduction
n Induced traffic and modelling approach
n Model formulation
n Application to Tokyo area
n Parameter estimation and model validation
n Estimation of road investment benefit
n Conclusion
n
Background
Heavy traffic congestion in Tokyo area,
Japan
n Plan of new road to reduce congestion
n “Does new road investment really
alleviate the traffic congestion?”
n Debate on Induced traffic
n Needs for considering induced traffic in
evaluation of road investment
n
Study Objective
Discussion on modelling induced traffic
n Development of combined network
equilibrium model in Tokyo area
n Evaluation of user benefit of road
investment considering induced traffic
n Comparison with conventional model
n
Induced traffic
n
Some people says,
“Transport investment for reduction of
traffic congestion may induce new travel
demand, so it do not lead to the reduction
of traffic congestion”
n
Is it possible?? How much is it?
After reduction of congestion by
road investment
n “Now
let’s commute by car instead
of by railway”
n “We can go shopping in further
shopping center”
n “Let’s go driving more”
n
Behavioral change
Classification of induced traffic
Route change
n Modal split
n Longer trip by change of destination
n Increasing trip frequency
n
Our research’s target
n Change of vehicle occupancy
n Development traffic by land use change
Induced Traffic
n
Change of users’
¨ Increase
behaviour
of demand for car-trip
n Congestion occurs again
¨ Worsen
than the investment??
¨ If the congestion get worsen, users will
change their behaviour again.
n
We have to compute equilibrium
state
Model Requirements
n
Users’ Behavior (Demand Side)
¨ Route,
mode, destination, trip-making, and
departure time choice …
n
Network Congestion (Supply Side)
¨ In
road network (and railway network)
n Interaction between Behavior and
Congestion (Equilibrium Point)
¨ Feedback
effect
Our Combined Model
n
4-level Nested Logit based combined
stochastic network equilibrium model
¨ Users’
behavior: Nested Logit
¨ Car and railway network congestion: multimodal Network equilibrium
¨ Consistency among demand forecasting,
benefit estimation and microeconomic theory
Model Structure
User’s Behavior
Generation
Make a trip
Modal split
Railway
Distribution
Destin
ation 1
Bi-modal Network
Congestion
Travel
Time
no trip
Link cost
function
Road
Flow
Car (mode m)
Equilibrium
Destin Destin
ation 2 ation s
Assignment
route 1 route 2 route k
Nested Logit model
Congestion
Disutility
Railway
Flow
Equivalent Optimization Problem
xam
min.Z ( x(f ), q, O) = ∑ ∫ tam (ω ) dω +
nWe
1 rs
rs
rs
f
ln(
f
q
)
∑
m
,
k
m
,
k
m
m
r ,s , m , k ?1
can obtain the strict
1
1
+
q
ln(
q
O
)
+
O ln(O O )
∑?
∑solution
equilibrium
by
?
1
efficient
even
in
+ ∑ O ln(O N algorithm
) + O ln(O N ) 
?
+ ∑ qlarge
V + ∑ O Vscaled
+ ∑ O [V + V (t )]
the
area with
this
O + Oapproach
=N
∑q = O
∑O = O
m ,a
i, r , s , m
i , rs
m
im
2
i
r
i
r
i , rs im
m
s
i, r , s , m
i
r
im
r
i
r
i
r0
i
r0
i
r0
im ir
r
m
i ,r , m
i
r
i
i , rs
m
= qmrs
im
r
i
r
i
r
r
i
i
i ,r
im
r
i
r
∑f
k
i , rs
m
i
r
im
r
s
m
∑q
im
r
i
3
i , r ,m
i
4
i, r
i , rs
m
0
rs
m,k
= qmrs
xam =
m ,rs rs
δ
∑ a, k f m ,k
r , s ,k
xam ≥ 0, f mrs,k ≥ 0, q mi, rs ≥ 0, qmrs ≥ 0, Orim ≥ 0, Ori ≥ 0, Ori 0 ≥ 0
Benefit measure
n
Logically superior measure
¨ Log-sum
variable (~4 level-Nested)
¨ Consistent with consumer surplus of
representative traveller approach based upon
Microeconomic theory
n
Rule-of-Half formula
¨ Approximation
Input Data of Tokyo Area
n
O-D matrices
Tokyo Person Trip (PT) survey in 1998
¨ Road Traffic Census OD survey in 1994
¨
n
Zoning System
¨
n
144 zones
Large networks
Automobile
¨ Railways
¨
Congestion Disutility Function in
Railway
Users’ discomfort in crowded train
n Estimated by Shida, et al(1989) in Tokyo
area
n
Congestion
Disutility
Parameter Estimation
Sequential estimation of Nested Logit
model
n For each trip purposes
(home-work, school, business, private,
etc)
n Value of travel time and route choice
parameters are given
n
Estimation Results
Generation
Modal split
Make a trip
Railway
Distribution Destin
ation 1
no trip
Car (mode m)
Destin Destin
ation 2 ation s
Assignment
route 1 route 2 route k
n
Scale
parameters
>>>
θ4
θ3
Nested
Logit
model
θ2
θ1
Consistent with random utility
maximization theory !!
Application Results
By Partial Linearization method
n Small computational burden
n
n
Link flow /OD time goodness-of-fit
Evaluation of Road Improvement
n
Effect of Tokyo Outer
Ring Road (about 16km)
Estimation by 2 models
n
By fixed demand model
¨ Conventional
model
¨ No induced traffic (route change only)
n
By combined demand model
¨ Considering
induced traffic
¨ Mode change/ redistribution / new generation
¨ Multi-modal studies
Comparison of User Benefit for
each hour
8
1.5
6
1.0
4
0.5
2
0.0
-
4 a.m.
6
(×10 Yen/Hour)
in railway
60
in car
30
-
5 a.m.
combined
2.0
90
fixed
10
(×10 Yen/Hour)
combined
2.5
combined
12
fixed
3.0 (×10 Yen/Hour)
6
fixed
6
7 a.m.
Findings
Benefits of congestion relief in railway are
added in road investment
n Benefits estimated by fixed demand model
are higher than those estimated by
combined model
n Overestimation is larger in peak periods
n
n
These results are consistent with
theoretical consideration (Williams et al. 1991)
User Benefit Fixed Demand
Generalized
cost
Fixed
demand
curve
Network
performance
curve
Trip
User Benefit Variable Demand
Generalized
cost
Variable
demand
curve
Network
performance
curve
Bias
Trip
User Benefit Congested Case
Generalized
cost
Bias: Overestimation
Trip
User Benefit Uncongested case
Generalized
cost
Bias: Underestimation
Trip
Evaluation Bias
In congested area / congested time period
Fixed demand model overestimate user
benefit
n In uncongested area/ off-peak period
Difference between fixed demand model
and variable demand model is small
n
Conclusion (1)
n
A logically consistent model for the
evaluation of road investment is developed
¨ 4-level
nested logit based combined stochastic
user equilibrium model with bi-modal network
congestion
¨ Consistent with benefit estimation and
microeconomic theory
n
Application to Tokyo Area
¨ Parameter
estimation
Conclusion (2)
n
Estimation of user benefit of new road
¨ Considering
n
induced traffic
Empirical analysis of evaluation bias
caused by neglecting induced traffic
¨ Conventional
results
model gives overestimated
Further research needed
n
Parameter estimation method
¨ Simultaneous
estimation of nested logit model
¨ Estimation with time series data / several data
source
n
Modelling framework
¨ Incorporating
departure time choice
¨ Trip-chaining behaviour
¨ Dynamic analysis