AN ANALYSIS OF TIME ALLOCATION, DEPARTURE TIME AND

ROUTE CHOICE BEHAVIOR UNDER CONGESTION PRICING

by

Toshiyuki Yamamoto, Satoshi Fujii, Ryuichi Kitamura

Department of Civil Engineering Systems, Kyoto University

Yoshida-honmachi, Sakyo-ku, Kyoto 606-8501, Japan.

Tel: +81-75-753-5136, Fax: +81-75-753-5916

e-mail: yamamoto@term.kuciv.kyoto-u.ac.jp

fujii@term.kuciv.kyoto-u.ac.jp

rkitamura@term.kuciv.kyoto-u.ac.jp

and

Hiroshi Yoshida

Toda Corporation

1-7-1 Kyobashi, Chuo-ku, Tokyo 104-8388, Japan.

Tel: +81-3-3562-6111, Fax: +81-3-3564-6713

July 1999Revised, November 1999

Submitted for presentation at the79th Annual Meeting of the Transportation Research Board

Washington, D.C., January 2000

1

AN ANALYSIS OF TIME ALLOCATION, DEPARTURE TIME AND

ROUTE CHOICE BEHAVIOR UNDER CONGESTION PRICING

Toshiyuki Yamamoto, Satoshi Fujii, Ryuichi Kitamura and Hiroshi Yoshida

ABSTRACT

Driver behavior under congestion pricing is analyzed in this study to evaluate the effects of

alternative congestion pricing schemes. The analysis, which is based on stated-preference

survey results, focuses on time allocation, departure time choice and route choice when a

congestion pricing scheme is implemented on toll roads. A unique feature of the model

system of this study is that departure time choice and route choice are analyzed in

conjunction with the activities before and after the trip. A time allocation model is

developed in this study to describe departure time choice, and a route and departure time

choice model is developed as a multinomial logit model with alternatives representing the

choice between freeways and surface streets and, for departure time, choice from among

before, during, or after the period when congestion pricing is in effect. The results of the

empirical analysis suggest that departing during the congestion pricing period tends to have

higher utilities, and that a worker and a non-worker have quite different utility functions. The

comparative analysis of different congestion pricing schemes is carried out based on the

estimated parameters, and the results suggest that the probability of choosing each alternative

is stable even if the length of the congestion pricing period changes, but that a higher

congestion price causes more drivers to change the departure time to before the congestion

pricing period.

Keywords: congestion pricing, departure time choice, activity time allocation, stated

preference data.

2

INTRODUCTION

Traffic congestion has been a prevalent problem in most urban areas of Japan, causing not

only drivers’ displeasure but also negative impacts on the economy through increases in

travel cost. Expanding transportation infrastructure, which was considered as the principal

solution to the congestion problem in earlier days, is often no longer feasible because of

limitations in funds, available land, or political support. Travel demand management

(TDM) schemes have drawn substantial attention recently as alternatives to facility

construction. TDM schemes aim at making travel demand match traffic capacity by altering

travelers’ behavior. Assessing the full impacts of such transportation policy options calls

for their rigorous evaluation which incorporates into its scope a wide variety of travelers’

responses to changes in the travel environment (Kitamura et al., 1996; Pas, 1996). For

example, congestion pricing, which may be considered as one of the most promising TDM

schemes (Downs, 1992; Hau, 1992; Small, 1992; Smith, 1979), may cause travelers to

modify their routes, means of travel, departure times or even activity engagement. These

multitudes of possible responses must be well understood and properly represented in the

evaluation of alternative TDM schemes.

In Japan, most toll roads are built and operated by semi-public organizations. Toll revenues

are serious concerns of these organizations which are typically pressed by the mandate of

repaying the initial capital investment. Congestion pricing thus calls for a critical market

analysis because of its fiscal implications. If congestion pricing is implemented in such a

way that the toll will increase in all periods, then the total number of toll road users will

certainly decrease. Whether this will lead to a reduction in the toll revenue, however, is not

immediately apparent because the increase in the toll may compensate for the reduction in

users. How congestion pricing schemes may impact the toll revenue will be more complex

when congestion pricing is applied to spread the peak demand by increasing the toll during

peak periods but reducing it during off-peak periods. Toll road operators, which must

achieve the dual objectives of reducing traffic congestion and maintaining a necessary level of

toll revenues, must have a thorough understanding of how road users react to congestion

pricing schemes before it can implement them successfully.

In this study, driver behavior under congestion pricing is analyzed to evaluate the effects of

3

alternative congestion pricing schemes, based on stated-preference survey results. A

congestion pricing scheme implemented on a toll road leaves a traveler with a number of

choices. He may choose not to use the toll road but travel on surface streets, or he may

choose to travel on the toll road outside the periods when congestion pricing is in effect, thus

avoiding to pay the congestion charge. The traveler may also decide to switch to public

transit, choose a different destination, or he may choose not to make a trip altogether. Of

these many possible responses that may be exhibited by travelers, the analysis of this study

focuses on departure time choice and route choice. Based on stated-preference data, a

model system of departure time and route choice is developed while representing the effects

of the activities before and after the trip on the choice.

Stated-preference approaches, in which survey respondents’ statements on how they would

respond to hypothetical situations are used, have the advantage that they generate

observations of choice behaviors with choice sets which include alternatives that are non-

existent. Although stated preferences are less reliable than revealed preferences (Pearmain

et al., 1991), stated preference methods offer many other advantages, e.g., explanatory

variables can be well controlled to have a set of orthogonal variables. In fact many studies

in the transportation planning field are based on stated-preference data.1 Congestion

pricing has not been implemented on any roadways in Japan, and the stated-preference data

obtained from the survey conducted as part of this study are expected to provide a valuable

basis on which the effects of congestion pricing can be examined.

From the viewpoint that departure time choice is a result of time allocation to activities, a

time allocation model is developed in this study to describe departure time choice. The time

allocation model is based on the utilitarian resource allocation theory, that an individual

allocates available time to each activity such that the total utility derived from all activities

will be maximized. Using this model, departure time is represented along a continuous time

scale. A route and departure time choice model is developed as a multinomial logit model

with alternatives representing the choice between freeway (where congestion pricing is

applied) and surface streets (which are not priced) and, for departure time, choice from

among before, during, or after the period when congestion pricing is in effect. Travel time

1 Examples in the transportation planning field can be found in Bernardino et al. (1993); Bunch et al.(1993); Polak and Jones (1993); Hensher (1994); and Abdel-Aty et al. (1995).

4

varies among alternatives, resulting in different amounts of time available for activities across

alternatives. Constraints that govern time availability for activities would also vary

depending on whether the traveler departs before, during, or after the period when

congestion pricing is in effect. The departure time is determined for each alternative by the

time allocation model with the amount of available time and the constraints specific to each

alternative.

In the next section, the survey conducted in this study is described. The fractional factorial

designs are adopted in designing stated preference questions in the survey. After the time

allocation model of departure time choice is specified based on the utilitarian resource

allocation theory, a route and departure time choice model is developed as a multinomial

logit model in the third section. The results of the empirical analysis is presented in the

forth section, which is followed by a conclusion.

SURVEY

The data set used in this study were collected as part of a four-wave panel study conducted in

Osaka-Kobe metropolitan area in 1993 through 1996 (Fujii and Kitamura, 1996). The

panel study was initiated with the objective of evaluating the effects of a new freeway which

was to open. After the Kobe-Awaji Earthquake of January 1995, the objective of assessing

the effects of the breakdown and reconstruction of the freeway system was added to the

scope of the study.

To recruit panel participants, short and simple questionnaires were distributed at the outset of

the panel study to an address-based, geographically-stratified sample of households by mail

and handed to the drivers passing several survey points located along the freeways. The

initial sample of the panel survey comprised household members of at least 16 years old (up

to four members per household) who returned the short questionnaires. The stated-

preference questions on congestion pricing were included in the questionnaires of the fourth-

wave survey conducted in 1996. The questionnaires were distributed to 3,170 households,

and the response rate was 12.9%. The low response rate is partially due to residential

relocations caused by the earthquake, and also because the questionnaires were sent to all

households which were on the panel at least once, including those that had dropped out.

5

The resulting fourth-wave sample, which comprised 657 individuals, is used in this study.

The forth-wave data contain, in addition to personal attributes including daily work schedules,

attributes of the most recent trip on a freeway and the stated preferences under hypothetical

situations in which alternative congestion pricing schemes are implemented on freeways.

The attributes of the most recent freeway trip in the data include: departure time, travel time,

freeway toll, and anticipated travel time if the trip were to be made on surface streets, and

attributes of the activities before and after the trip. The attributes of the activities include

the type, starting time, and ending time of each activity. Hypothetical situations were

generated based on the most recent freeway trip actually made to avoid setting unrealistic

situations for each respondent. Hypothetical congestion pricing was presented to the

respondent with a certain price and pricing hours on freeways, with the travel time on

freeways reduced during the pricing hours and the anticipated travel time by surface streets

increased. The travel times on freeways and surface streets before and after the congestion

pricing period were set equal to those indicated in the survey for the most recent freeway trip.

The experimental design involving four attributes with four levels each, as shown in Table 1,

was used to describe the hypothetical situations.

By using a fractional factorial design, 16 situations were selected from the total of 256 (= 44)

situations and were grouped into 4 blocks, to be completed by 4 sets of respondents, each

responding to a set of 4 situations (Pearmain et al., 1991). This made it possible to reduce

the number of questions presented to each respondent, reducing the burden on the

respondents and presumably improving the reliability of the responses obtained.

Table 1 Experimental design

Attributes Levels

Pricing periods* all day 1 hour 2 hours 3 hours

Congestion price (yen) 100 300 500 700

Decrease in travel time of freeway (minutes) 5 10 15 20

Increase in travel time of surface streets (minutes) 0 5 10 20* Pricing period is set to be centered around the time when the respondent departed atthe most recent trip.

6

The respondent was asked to indicate what he would do under each hypothetical situation by

selecting one of the alternatives shown in Table 2 and stating an anticipated departure time.

In the case where congestion pricing is enforced all day, the second, third, fifth, and sixth

alternatives (departing before or after the congestion pricing period) in Table 2 were omitted.

Those respondents who made a freeway trip and engaged in mandatory activities both before

and after the trip are excluded from the model estimation sample because those respondents

would have no choice but to travel on freeways if congestion pricing were implemented.

From the full sample, 409 cases for which pertinent explanatory variables are available were

obtained and used in the model estimation. The distribution of chosen alternatives is

presented in Table 2. Although attribute levels vary substantially across the situations,

slightly over two-thirds of the respondents indicated not to change the route nor the

departure time, and to continue to use the freeway. The predominant alternative chosen to

avoid paying the congestion price is to use the surface streets during the congestion pricing

period, but not to change the departure time. This is in part because congestion pricing is

effective all day in about a quarter of the total cases, making it ineffective to change

departure times. Among those who chose to change departure times, a majority chose to

depart before the pricing period than after it, both on freeways and surface streets.

Evidently leaving earlier is preferred to leaving later. In particular, traveling on surface

streets after the pricing period was seldom chosen.

Table 2 Response frequency by alternative

Alternatives Frequency Percentage

1. Travel on freeway during the congestion pricing period 275 67.2%

2. Travel on freeway before the congestion period 28 6.8%

3. Travel on freeway after the congestion pricing period 6 1.5%

4. Travel on surface streets during the congestion pricing period 77 18.8%

5. Travel on surface streets before the congestion pricing period 22 5.4%

6. Travel on surface streets after the congestion pricing period 1 0.2%

Total 409 100.0%

7

DEPARTURE TIME AND ROUTE CHOICE MODEL

The departure time and the duration of a trip are associated with the durations and the timing

of the activities before and after the trip. Suppose, therefore, an individual chooses the

departure time and the route to maximize the utility associated with the trip itself and the

activities before and after the trip. Let the total utility be the sum of the utility associated

with the trip and that associated with activities (Donnea, 1972),

Ui = UTi + UAi , (1)

where Ui is the total utility, UTi is the utility of the trip, and UAi is the utility of the activities,

obtained when alternative i in Table 2 is chosen. The utility of the trip is assumed as,

UTi = γXi + εi, (2)

where γ is a vector of coefficients, Xi is a vector of explanatory variables, and εi is a random

error term of the utility of the trip, for alternative i in Table 2.

The utility of the activities, UAi, is assumed to be the sum of the utilities of all activities,

∑=k

kii UAUA , (3)

where UAki is the utility of engaging in the kth activity of the day. The activities can be

grouped into two categories: mandatory and discretionary. Mandatory activities are those

which the individual has committed to perform, and their timing, durations and locations are

assumed in this study to have been predetermined and fixed. It is further assumed in this

study that mandatory activities are performed in the same way and their utilities are invariant

regardless of the choice of departure time or route. The utility value of a mandatory activity

is therefore assumed to be constant and is set to 0 in the model.

The individual decides whether to engage in a discretionary activity, and determines the

amount of time spent on it and its location. Discretionary activities are engaged in

uncommitted (or “open”) periods between mandatory activities. The model of this study is

8

thus concerned with discretionary activities engaged in the period between the time when the

last mandatory activity ends, ts, and the time when the next mandatory activity starts, te.

The utility of each discretionary activity is assumed to have a logarithmic function of the time

spent on it (Kitamura, 1984),

UAki = αAkilntk = exp(βXAki + εAki)lntki, (4)

where β is a vector of coefficients, XAki is a vector of explanatory variables, εAki is a random

variable, and tki is the time spent on the kth activity. This specification satisfies the condition

that the utility increases and the marginal utility diminishes as the amount of the time

allocated to it increases. Note that some discretionary activities might have its own optimal

duration beyond which its utility may start declining. In such cases the logarithmic function

of time spent on the activity would not be suitable as a component of the utility function. It

is, however, theoretically impossible to observe cases where more time is allocated to an

activity over its optimal amount as long as, as is assumed in this study, the activity is

discretionary and its duration is unconstrained. It would therefore be impossible to

determine what functional specification would be more appropriate than the logarithmic

function used in this study.

The optimum durations of the activities are determined per utilitarian resource allocation

theory by solving the optimization problem given as

Tisek

Aki

K

kkiAki

tttt

t

−−=∑∑

=

s.t.

lnmax1

α, (5)

where K is the total number of discretionary activities engaged in the open period of concern,

and tTi is the travel time. If the departure time is not constrained, the optimum duration ofthe activity, *

Akit , is given at the time when all marginal utilities of the activities are the same,

9

( )TiseK

kAki

AkiAki tttt −−=

∑=1

*

α

α. (6)

Each alternative, however, has a constrained departure time period in relation to the

congestion pricing period. For example, if the respondent chooses to depart before the

pricing period, the total time for the activities before the trip should be decreased and the last

activity before the trip should end before the pricing period starts. On the other hand, if the

respondent chooses to depart during the pricing period, the last activity before the trip must

end during the pricing period. For alternatives 1 and 4 of Table 2, in which a trip is made

during the congestion pricing hours, the constraint is introduced into the maximization

problem as,

se

K

kAkiss tpttp −≤≤− ∑

=

'

1

s.t. , (7)

where ps and pe are the earliest and the latest departure time to make a trip during the

congestion pricing period, respectively, and K’ is the number of the discretionary activities

engaged before the trip from among the total K discretionary activities in the open period.

The optimum duration of each activity, then, is given as,

( ) se

K

kAkissTiseK

kAki

AkiAki tpttptttt −<<−−−= ∑

∑ =

=

'

1

*

1

* ifα

α , (8)

( )

( )ss

K

kAki

TiseK

KkAki

Aki

ssK

kAki

Aki

Aki tptK'ktpt

K'ktp

t −=

>−−

≤−

= ∑

∑

∑=

+=

='

1

*

1'

'

1* iffor

for

α

α

α

α

, and (9)

10

( )

( )se

K

kAki

TieeK

KkAki

Aki

seK

kAki

Aki

Aki tptK'ktpt

K'ktp

t −=

>−−

≤−

= ∑

∑

∑=

+=

='

1

*

1'

'

1* iffor

for

α

α

α

α

. (10)

For Alternative 2 and 5 of Table 2, in which a trip is made before the congestion pricing

hours, the following constraint is introduced to the maximization problem:

ss

K

kAki tpt −<∑

=

'

1

.s.t . (11)

For Alternatives 3 and 6, the following constraint is introduced:

∑=

<−'

1

.s.tK

kAkise ttp . (12)

The optimum duration of each activity is given in the same manner for Alternatives 1 and 4.

It can be seen that the optimum durations of the activities are determined along a continuous

time dimension based on the utilitarian resource allocation theory. Consequently the

departure time choice behavior is described on the continuous time dimension in this model.

A sequential procedure is adopted in this study to estimate the model parameters. Firstly,

rewriting Eq. 6 as follows, the vector of the parameters, β, is estimated by least-squares

regression assuming (εAki - ε Ak’i) is a normal random variate with a mean of 0 and a variance

of σ2:

( ) ( ) iAkAkiiAkAkiiAkAki XXtt ''*

'*ln εεβ −+−= . (13)

Next, after calculating the expected value of αAki using the estimated parameter vector, β̂ ,

and setting the random variable, εAki, to 0, the optimum durations of all discretionaryactivities for each alternative, *

Akit , are obtained by solving the optimization problem

11

described above. In solving the optimization problem, the optimum durations of the

discretionary activities included in each of the alternatives in the choice set of Table 2 are

obtained by maximizing the utility of the activities, UAi, given that the alternative is chosen.

Finally, the discrete choice behavior with the six alternatives in Table 2 is formulated as a

multinomial logit model assuming the random variables, the ε i’s, are i.i.d. with a Gumbel

distribution, and the parameter vector, γ , is estimated by the method of maximum likelihood.

The probability of choosing an alternative i, Pr( i), is given as,

( )( ) ( )

( ) ( )∑ ∑

∑

= =

=

+

+

=6

1 1

*

1

*

lnˆexpexp

lnˆexpexp

Pr

i

K

kkiAkii

K

kkiAkii

tXX

tXXi

βµγ

βµγ, (14)

where µ is a scale parameter.

A nested logit model which assumes correlated error terms, can be considered as an

alternative model formulation for route and departure time choice behavior. In this study,

however, a multinomial logit model is applied mainly because the frequency of choice varies

substantially among alternatives, with some alternatives chosen only in very few cases,

making the estimation on nested logit models difficult.

Multidimensional integration would be required to account for the randomness in the Uai ’s in

the multinomial logit model. To avoid this highly time consuming, if feasible at all,

integration, the expected value of αAki is used in this study as an instrumental variable (Ben-

Akiva and Lerman, 1985).

ESTIMATION RESULTS

The parameters are estimated using the data set described in the second section. At first,

the data on the time allocation to discretionary activities before and after the most recent

freeway trip are used to estimate the parameter vector, β, by ordinary least-squares

regression. Because detailed information was obtained in the survey only for the activities

12

immediately before and after the trip, the 131 cases in which discretionary activities are

engaged both before and after the trip are used to estimate the parameters (potential

selectivity bias resulting from this is not examined in this study). The explanatory variables

used are summarized in Table 3, and the estimation results are presented in Table 4. The

constant is not included in the regression model because the explanatory variables are defined

in terms of the differences between the activities before and after the trip and theoretically the

model should not contain a constant term. Although the goodness of fit statistics, R 2 and2R , are not particularly high, the model as a whole is highly significant and the effects of the

explanatory variables on time allocation behavior as implied by the coefficient estimates are

quite plausible.

Table 3 Explanatory variables used in the regression model

Variable DefinitionActivity typeIn-home1 Binary variable: 1 if the activity is the first or the last in-home activity of

the day; 0 otherwiseIn-home2 Binary variable: 1 if the activity is an in-home activity, except for the first

and the last in-home activity of the day ; 0 otherwiseHobby Binary variable: 1 if the type of the activity is hobby or sports; 0

otherwiseSocial Binary variable: 1 if the type of the activity is social-recreational ; 0

otherwiseShopping Binary variable: 1 if the type of the activity is shopping; 0 otherwisePersonal attributeMultiHome Binary variable: 1 if the type of dwelling is a multiple family home; 0

otherwiseSingleHome Binary variable: 1 if the type of dwelling is a single family home; 0

otherwiseWorker Binary variable: 1 if the individual is a worker; 0 otherwiseHousewife Binary variable: 1 if the individual is a housewife; 0 otherwiseOther Binary variable: 1 if the individual is neither a worker nor a housewife; 0

otherwiseHighIncome Binary variable: 1 if annual income is 7,000,000 yen or higher; 0

otherwiseCar Binary variable: 1 if the household owns at least one vehicle; 0 otherwise

13

Among the explanatory variables, In-home2*MultiHome has a negative coefficient estimate

and largest t-statistic. It indicates that in-home activities, except for the first or the last one

of the day, tend to have shorter durations if the individual lives in a multiple family housing

unit. But In-home2*SingleHome does not have a statistically significant coefficient

estimate; if the individual lives in a single family home, this tendency is not present. In-

home1*SingleHome, on the other hand, has a statistically significant negative coefficient

estimate, indicating the first and the last discretionary activities of the day tend to have

shorter durations if the individual lives in a single-family home. The results suggest that the

durations for in-home discretionary activities are strongly affected by dwelling type. This

may be partly because dwelling type plays a role as an indicator of residential location.

Other than in-home activities, Hobby*Other has a statistically significant positive coefficient

estimate. It indicates that a hobby or sports activity tends to have a longer duration if the

individual is neither a worker nor housewife. Hobby*Worker and Hobby*Housewife also

have positive coefficient estimates, but not significant, indicating a worker or a housewife

does not have the tendency with the same intensity as others do. The results imply that the

duration of a hobby or sports activity is affected by both out-of-home and in-home

Table 4 Regression model of time allocation todiscretionary activities before and after a trip

Variable Coef. t-stats

In-home1*SingleHome -0.997 -2.63

In-home2*Multihome -1.287 -3.57

In-home2*SingleHome -0.136 -0.30

Hobby*Worker 0.047 0.10

Hobby*Housewife 0.367 0.71

Hobby*Other 1.362 2.85

Social 1.807 2.71

Social*HighIncome -1.340 -2.24

Social*Car -1.177 -1.61

Social*SingleHome -0.801 -1.39

Shopping -0.307 -1.18

Sample size: 131, R2 = 0.34, 2R = 0.28,F = 5.70

14

mandatory activities. Social has a statistically significant positive coefficient estimate, but

Social*HighIncome, Social*Car, and Social*SingleHome have negative coefficient

estimates; the duration of a social activity varies by income, mobility, and dwelling type.

Shopping has a negative coefficient estimate, indicating shorter durations of shopping

activities, but the estimated t-statistic indicates the tendency is insignificant. Note that

interaction terms of activity type and personal attribute are included in the model for many

types of activities. Although variables with low significance tend to be excluded in model

development, interaction terms are included in this study even when their significance is low

because the model estimation is based on a relatively small sample. It would be desirable

that explanatory variables are selected with a larger sample in the future research.

Using the estimated parameters of Table 4, the optimum durations of all discretionary

activities are calculated for each response alternative for the 409 cases used in the estimation

of a multinomial logit model. The explanatory variables are summarized in Table 5, and the

estimation results are presented in Table 6. The likelihood ratio statistics indicate the model

is highly significant.

iUA *NonWorker has a marginally significant positive coefficient estimate, and it indicates

that an alternative with a higher utility of activities is preferred if the individual is not a

worker. On the other hand, iUA *Worker does not have a significant coefficient estimate,

indicating departure time and route choice behavior is not affected by the utility of activities

Table 5 Explanatory variables used in the multinomial logit modelVariable Definition

iUA Expected value of the utility of the activities

Price Congestion price (yen)

Time Travel time (minute)

Worker Binary variable: 1 if the individual is a worker; 0 otherwise

NonWorker Binary variable: 1 if the individual is not a worker; 0 otherwise

Age30 Binary variable: 1 if the age of the individual is 30s; 0 otherwise

Female Binary variable: 1 if the individual is female; 0 otherwise

HighIncome Binary variable: 1 if annual income is 7,000,000 yen or higher; 0otherwise

15

if the individual is a worker. The values of iUA are computed from the expected values of

αAki, which is estimated by the regression model, assuming the error terms, εAki, in the utilities

of discretionary activities are independent of the error terms of the multinomial logit model.

This may have caused the lower significance in coefficient estimates for iUA and

iUA *Worker. The low goodness of fit of the regression model may also have contributed

to the low significance of the coefficient estimates for iUA *NonWorker and iUA *Worker.

Time, Time*Worker, and Time*Age30 all have statistically highly significant negative

coefficient estimates; an alternative with a shorter travel time tends to be preferred and the

tendency is amplified if the individual is a worker, in his thirties, or a female. Price has a

most highly significant negative coefficient estimate, which indicates that a higher congestion

pricing causes more drivers change their departure times or routes to avoid paying the

congestion price. Note that the value of time should not be calculated as the coefficient of

Table 6 Multinomial logit model of departure time and

route choiceVariable Alternative Coef. t-stats

iUA *Worker all 0.0020 0.05

iUA *NonWorker all 0.0534 1.55

Time all -0.0065 -2.08

Time*Worker all -0.0151 -2.77

Time*Age30 all -0.0113 -2.12

Time*Female all -0.0064 -1.57

Price 1 -0.0022 -4.88

Price*HighIncome 1 0.0011 1.69

Constant 2 -2.47 -8.94

Constant 3 -4.14 -9.10

Worker 4 0.91 2.22

Constant 4 -1.16 -3.20

Constant 5 -1.76 -5.09

Constant 6 -4.88 -4.72

Sample size: 409, L(0) = -732.8, L(C) = -618.2,

L(β) = -349.5, ρ2 = 0.52, χ02 = 766.6 (df = 14),

χc2 = 537.2 (df = 9)

16

time divided by the coefficient of price, because the increase of travel time also affects the

utility of the activities. Worker has a statistically significant positive coefficient for

Alternative 4. It indicates that a worker tends to prefer not to change the departure time.

The estimated value of constant for each alternative indicates that Alternatives 3 and 6, in

which a trip is made after the congestion pricing period, have far lower utilities than other

alternatives. The results suggest that a worker and a non-worker have quite different utility

functions to determine the reaction against the road pricing each other.

Using all the estimated parameters, a comparative analysis of different congestion pricing

schemes is carried out with those 252 sample cases for which all 6 alternatives are available.

The differences in the mean probability of choosing each alternative with respect to the

congestion pricing period, congestion price, decrease in travel time on freeways, and increase

in travel time on surface streets, are analyzed here. The probability of choosing each

alternative is calculated for each sample case by setting the variables other than the variable

of concern at the same values as in the survey and the variable of concern at a certain value,

then a mean probability is evaluated for the 252 sample cases. The results are presented in

Table 7.2 The results indicate that the probability of choosing each alternative does not

change very much even if the length of the congestion pricing period changes from 1 hour to

2 hours, but that the increase in the congestion price from 100 yen to 300 yen lead to a

decrease in the probability of choosing Alternative 1, and an increase in the probability of

choosing Alternatives 2; a higher congestion price causes more drivers to change the

departure time to before the congestion pricing period. The reduction in travel time on

freeways causes more drivers choosing Alternative 1, but the increase in travel time on

surface streets doesn’t influence the probability so much.

2 In spite of the sample counts in Table 2 , the mean probability of Alternative 2, in which a trip is madeon freeways before the congestion pricing hours, is higher than that of Alternative 4, in which a trip ismade on surface streets during the congestion pricing period. This is because the sample cases used inthe comparative analysis are only those cases for which the options of changing the departure time isavailable.

17

SUMMARY AND CONCLUSION

In this study, a departure time and route choice model under congestion pricing is developed

using stated-preference data. A regression model of time allocation to discretionary

activities is developed based on the utilitarian resource allocation theory. As a result it is

possible to depict departure time on a continuous time dimension in the model. A

multinomial logit model of route and departure time choice behavior is then developed

considering the utilities of the activities before and after the trip.

Table 7 The mean probabilities of choosing each alternative(a) Congestion pricing period

Alternative 1 2 3 4 5 61 hour 0.861 0.086 0.017 0.025 0.010 0.0012 hours 0.864 0.084 0.016 0.025 0.010 0.001Difference +0.003 -0.002 -0.001 ±0.000 ±0.000 ±0.000

(b) Congestion priceAlternative 1 2 3 4 5 6

100 yen 0.921 0.044 0.009 0.019 0.006 0.001300 yen 0.888 0.064 0.012 0.026 0.009 0.001Difference -0.033 +0.020 +0.003 +0.007 +0.003 ±0.000 (c) Decrease in travel time of freeway

Alternative 1 2 3 4 5 65 minutes 0.805 0.110 0.022 0.048 0.014 0.00110 minutes 0.852 0.081 0.016 0.038 0.010 0.001Difference +0.047 -0.029 -0.006 -0.010 -0.004 ±0.000

(d) Increase in travel time of surface streetsAlternative 1 2 3 4 5 6

5 minutes 0.870 0.081 0.016 0.022 0.011 0.00110 minutes 0.875 0.082 0.016 0.015 0.011 0.001Difference +0.005 +0.001 ±0.000 -0.007 ±0.000 ±0.000

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The empirical analysis has used stated-preference data obtained in the Osaka-Kobe

metropolitan area. The results of parameter estimation of a regression model indicated that

an in-home activities, except for the first or the last one of the day, tend to have shorter

durations if the individual lives in a multiple family housing unit, but not if the individual lives

in a single family home. The results suggest that the durations for in-home discretionary

activities are strongly affected by the dwelling type. Although a hobby or sports activity

tends to have a longer duration, this tendency is almost canceled if the individual is a worker,

and is weakened if the individual is a housewife. The results imply that the duration of a

hobby or sports activity is affected by both out-of-home and in-home mandatory activities.

The duration of a social activity is dependent on the income level, mobility, and dwelling

type.

The estimation results of the multinomial logit model of route and departure time choice

indicate that an alternative with a higher utility of activities is preferred if the individual is not

a worker, but that departure time and route choice behavior is not affected by the utility of

activities if the individual is a worker. An alternative with a shorter travel time tends to be

preferred and the tendency is amplified if the individual is a worker, in his thirties, or a female.

A higher congestion pricing causes more drivers change their departure times or routes to

avoid paying the congestion price. The results suggest that a worker and a non-worker

have quite different utility functions with each other. The differences in utility functions

cause differences in their respective reactions to road pricing.

Using all the estimated parameters, a comparative analysis of different congestion pricing

schemes is carried out. The differences in the mean probabilities of choosing the respective

alternatives with respect to the congestion pricing period, congestion price, decrease in travel

time on freeways, and increase in travel time on surface streets, are analyzed. The results

indicate that the probability of choosing each alternative is stable even if the length of the

congestion pricing period changes from 1 hour to 2 hours, but that the increase in the

congestion price from 100 yen to 300 yen causes more drivers to change the departure time

to before the congestion pricing period. The reduction in travel time on freeways causes

more drivers choosing freeway departing during the road pricing period, but the increase in

travel time on surface streets doesn’t affect the choice behavior so much.

19

In this study, the number and the sequence of discretionary activities engaged in an open

period are assumed to be invariant. In reality, some activities may be canceled if the time

available decreases, and sometimes activities engaged may be chosen based on the amount of

time available. The number and types of activities engaged may be thus endogenous.

Relaxing this assumption remains as a future task. The model of drivers’ behavior was

developed in this study while treating travel time as exogenous. In other words,

interactions among travelers are not considered in the study. Capturing the dynamics of

road network flow that arises from individual travelers’ time allocation, departure time, and

route choice decisions, also remains as a future task. In addition, the premises underlying

the utility theory on which the proposed model is based have been intensely questioned (e.g.

Simon, 1990; Slovic, 1995). There are pressing needs for the development of tools for

travel demand analysis based on alternative behavioral theories (Gärling, 1998).

Nevertheless, we believe that this study constitutes a constructive step within a utilitarian

framework by introducing activities before and after a trip into the model of departure time

and route choice for the trip.

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