Integrating Origin-Destination Survey and Stochastic User Equilibrium: A Case Study for Route Relocation

doi:10.4236/jtts.2012.24032

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Journal of Transportation Technologies, 2012, 2, 297-304

http://dx.doi.org/10.4236/jtts.2012.24032 Published Online October 2012 (http://www.SciRP.org/journal/jtts)

Integrating Origin-Destination Survey and Stochastic User

Equilibrium: A Case Study for Route Relocation

Deo Chimba*, Daniel Emaasit, Boniphace Kutela

Department of Civil Engineering, Tennessee State University, Nashville, USA

Email: *[email protected]

Received June 22, 2012; revised July 20, 2012; accepted August 2, 2012

ABSTRACT

The paper analyses integrating Origin-Destination (O-D) survey results with Stochastic User Equilibrium (SUE) in traffic

assignment. The two methods are widely used in transportation planning but their applications have not yet fully inte-

grated. While O-D gives a generalized trip patterns, purpose and characteristics, SUE provides optimal trip distributions

using the characteristics found in O-D survey. The paper utilized O-D and SUE in route relocation study for the town of

Coamo in Puerto Rico. The O-D survey was used initially in studying possible trip distribution and assignment for the

new route. Initial distribution and assignment of traffic to the existing roadway networks and the proposed route were

allocated utilizing the O-D survey findings. The SUE was then used to optimize the assignments considering roadway

characteristics such as number of lanes, capacity limits, free flow speed, signal spacing density, travel time and gasoline

cost. The travel time was optimized through the Bureau of Public Roads (BPR) equation found in 2000 HCM. The op-

timal trips found from the SUE were then used to propose the final alignment of the new route. Traffic assignment from

the SUE was slightly different from those initially assigned using O-D, indicating there was optimization. The assign-

ment on new route was increased by 13.8% from the one assigned using O-D while assignment on the existing link was

reduced by 22%.

Keywords: Route Relocation; Origin-Destination; Stochastic User Equilibrium

1. Introduction and Background

Knowledge of the travel patterns for a defined jurisdic-

tion or roadway network is an important aspect in trans-

portation planning [1]. The patterns may include vehicle

classifications, trip purposes, travel time, age differentia-

tions, life styles and vehicle occupancy among others.

The information can be used for different purposes in-

cluding traffic impact studies, corridor and area planning,

zoning, master plans, traffic projection and traffic as-

signments. There are different methodologies used in

studying traffic patterns, one of them being Origin and

Destination (O-D) survey. While some studies use O-D as

a stand-alone approach in traffic pattern studies, some

have combined the information from O-D report with

other supporting traffic data to facilitate the findings and

conclusions. For instance, O-D can be used in demand

estimation using turning movement counts [2]. There are

some studies whose objectives can be fulfilled with the

O-D survey information only, but most of them will need

supporting data or analysis in order to draw practical

conclusions. Taking example of the O-D survey giving

the percentage of trips from city A to city B, in rare cases

the same survey will give the route assignment used by

the interviewed travelers. In this case, while the percent-

age of trips from city A to city B will be obtained for

planning purposes, supporting information related to the

route assignments will be needed. In other words, the

results from O-D study will need supporting analysis to

make final recommendations. The O-D study gives the

details of what type of trips in terms of purpose at origin

and destination are made by the travelers. Through O-D,

one can determine which among home-based, education,

shopping, recreational or any other trip purpose are

dominant in the area. In case of route relocation study,

diversions, road expansion and other similar kind of pro-

jects, O-D survey becomes not a stand-alone but a sup-

porting document [3].

1.1. Study Objectives

This study therefore combines the O-D survey with the

traffic assignment analysis using stochastic user equili-

brium in route relocation study. The objective is to evalu-

ate which approaches (between utilizing O-D survey only,

SUE only or integrated O-D and SUE) yield the optimal

and desired results. The desired results in this case are

*Corresponding author.

D. CHIMBA ET AL.

298

defined in terms of attributes such as traffic volumes

which eventually lead to choosing number of lanes and

intersection configurations. The project required the for-

mulation and evaluation of a number of alternatives and

combination of alternatives for the selection of a new

improved roadway connection between the PR-52 inter-

change and the central area of the town of Coamo in

Puerto Rico, Figure 1. PR-52 is the 4-lane limited access

highway running E-W just south of the town connecting

to the other major cities to the west, south and east. The

existing roadway system PR-153 and PR-545 are the

main roadways connecting central Coamo and PR-52.

PR-545 connects PR-52 to PR-14, which runs to the down-

town area. Currently PR-153 is operating beyond the ca-

pacity while PR-545 is substandard. The proposed new

alternative route (Route A in Figure 1) is expected to

capture some traffic currently using PR-153 and used as

a substitute for the trips using PR-545.

1.2. The Use of O-D Survey and SUE in

Transportation Planning

The use of O-D survey in transportation planning has

been applied widely under various scenarios [4-9]. One

of the previous studies which align with the objectives of

this paper is the one conducted by Yang and Zhou [10]

who highlighted that the quality of an estimated O-D

matrix depends much on the reliability of the input data,

and the number and locations of traffic counting points in

the road network. They then addressed the problem of how

to determine the optimal number and locations of traffic

counting points in a road network for a given prior O-D

distribution pattern. Origin and destination surveys can

also be used for public transportation studies. Hu et al.

[11] proposed the origin-destination of public transporta-

tion to help optimize layout of bus stops, reduce the in-

fluences of origin-destination of public transportation

and improve the traffic efficiency of bus stations. They

based their study on the nagel-schreckenberg traffic flow

models and used the two-lane aggressive lane-changing rule

to examine the influence of the origin-destination of the

public transportation on the urban bidirectional four-lane

mixed traffic flow. As for the O-D studies, user equili-

briums has also been applied in different transportation

planning studies [12-14]. For instance, Hazelton [15]

indicated that the behavioral foundation of Stochastic User

Equilibrium is that each traveler attempts to minimize

Figure 1. Town of Coamo existing road network.

D. CHIMBA ET AL. 299

his or her perceived travel costs, where these costs are

study analyzed

As, Town of Coamo was the epicenter

composed of a deterministic measured cost and a random

term which can be interpreted as perceptual error. In his

study, he presented Stochastic User Equilibrium as a

probability distribution defined by the conditional route

selection of each individual given the choices of all other

travelers. He also investigated the limiting behavior as

the travel demand becomes large. Some of the methodo-

logies and procedures used in these previous studies

which utilized O-D and SUE are replicated in this paper.

1.3. Study Data and Methodology

To achieve the project objectives, the

existing traffic condition for the PR-52, PR-153, PR-545

and PR-14. The 7-days, 24-hours count along these road-

ways were used to develop existing traffic characteristics.

Historical traffic data, population growth, economic trends,

employment growths and number of registered vehicles

for the past years was used to develop the growth rates

for traffic projection to the year 2027. The origin-desti-

nation survey was then conducted to determine major

areas where the traffic enter and leave the Coamo town.

The O-D provided the percentage of trips to and from the

town of Coamo from different cities and zones, break-

down of trips by purpose, vehicle occupancy and classi-

fications. Apart from revealing which highways were

currently the major collectors and distributors to and from

Coamo, the O-D study survey was also used to determine

the possible future traffic pattern changes. The projected

ADT (annual daily traffic) was portioned along PR-545

and PR-153 and the proposed new roadway based on the

O-D survey results. As shown in Figure 1, Route A was

proposed as an alternative for the traffic currently using

PR-545 and those, which will be diverted from PR-153.

Stochastic User Equilibrium trip assignment was used to

distribute and balance the trips to and from Coamo along

PR-153 and the proposed Route-A. Stochastic User Equi-

librium (SUE) was used due to its underlying principle,

which considers a population of drivers with homogene-

ous characteristics and perceive the same set of network

costs except for the variation allowed by the stochastic

choice model considered. With the fixed origin-desti-

nation within the known roadway networks, stochastic

equilibrium assumes that the drivers will react to changes

in network conditions as a result of change in route cha-

racteristics stochastically.

2. Formulation of Origin-Destination Matrix

and Findings

introduced earlier

of this study; hence, all trips surveyed were coded with

respect to routes to and from this town. Let i denote town

of Coamo, j denote the external cities, and n number of

cities or separate routes to those cities, then

ii Internal Trips within CoamoT



Trips from Coamo to other cities



Trips from other cities to Coam



The proportion trip among all surveyed vhicles is

given by;

Proportion of internal trips to total survey, Pii

;

11 111 

1





 

ij ji ii

ij jii

P (1)

ii nn

Proportion of outbound external trips to total survey, Pij;

11 111 

1





 

ij jiii

ij nn

ij jii

P (2)

Proportion of inbound external trips to total survey, Pji;

11 111 

1





 

ij ji ii

TTT

ji nn

ij jii

P (3)

Both trip proportionand sii

P, ij

e ex

are ut

termination of the trip thisting and proposed

routs.

fond b

ual Daily Traffic) was

ilized in de-

s along

The study was therere iitiatey preparing an O-D

questionnaire for designated locations along PR-52, PR-

153 and PR-14. Different considerations were taken into

account for effective O-D results including avoidance of

uncertainties. One of the uncertainties avoided was to

choose the interview locations which could have brought

conflicting responses. According to some previous stu-

dies, the O-D location should consider traffic flow co-

verage and minimize the expected uncertainties [16,17].

Interviews were conducted on March 15, 2007 on PR 52

at the entrance and exit ramps with PR 153 and on PR 14

at the intersection with PR 153. The findings from O-D

survey were summarized as

 PR 153 was the main highway from PR 52, used by

motorist to and from Coamo,

 The intersection of PR 14/PR 153 was the major in-

tersection used by motorist to/from Coamo,

 The PR 14 link from PR153 to downtown was the

main receiver and deliverer of traffic from/to PR 153,

 Home, work and personal based trips were the major

trip purposes to and from Coamo.

Figure 2 shows some of the results found from the

O-D survey. For all of the trips to and from the town,

22% originate or ended west of Coamo, 13% south of

oamo and 13% east of Coamo.

3. Proposed Alternative Route

The 2027 projected ADT (Ann

D. CHIMBA ET AL.

300

33,800 vpd on PR-153 and 6200 vpd on PR-545. These

4. Theory of User Equilibrium (UE)

Us p’s first

ADT were taken as external trips. From the Origin Desti-

nation (O-D) matrix developed, it was found that of all

external traffic to Coamo from PR-153, 46% originated

from the west, 28% from the south and 26% from the

east. This distribution led to traffic assignment with re-

spect to proposed route with 4-lane section and PR-153,

which remained as a 2-lane section.

Table 1 elaborates the trip assignment developed

based on origin destination survey analysis. Furthermore,

from the survey it was observed that, out of 26% of the

traffic going to Coamo from the east using PR 153, 11%

will be diverted to proposed Route A while 15% will

continue using PR-153 to Coamo. For the 28% of the

traffic originating from the South to Coamo, 21% will

continue using PR-153 while 7% will be diverted to

Route A. Traffic from the west which make up 46% of

external trips, 37% was found that utilize Route A and

9% PR-153. All traffic currently using PR-545 to down-

town Coamo were assumed to be diverted to Route A.

After all of the analysis using the O-D survey, PR 153

was found that will remain with 15,400 vehicles per day

vpd which according to HCM is Level of Service (LOS) D,

that was a reduction of 18,400 vpd (54%) from originally

33,800 vpd projected. The proposed Route A was ex-

pected to receive 18,400 vpd diverted from PR-153 and

6200 currently using PR-545, a total of 24,600 vpd (LOS

B) by the year 2027. These O-D survey results were im-

plemented in the Stochastic User Equilibrium analysis to

find the final traffic balance based on the characteristics

of existing PR-153 and the proposed Route A.

Stochastic User Equilibrium (SUE)

er Equilibrium can be derived from Wardro

principle which states that, under equilibrium conditions

traffic arranges itself in congested networks in such a

way that no individual trip maker can reduce his travel

cost by switching routes or all used routes between an

origin and destination pair have equal and minimum

costs while all unused routes have greater or equal costs

[14,18]. A SUE condition is derived from the user equi-

librium (UE) assumption which can be written as a given

O-D pair as:





fcu



 for all

PERCENTAGE TRIPS BY PURPOSE

52%

22%

13% 13%

10%

15%

20%

25%

30%

35%

40%

45%

50%

55%

60%

COAMO-INTERNAL TO/FROM-WESTTO/FROM-SOUTHTO/FROM-EAST

% TRIPS

HOME BASED TR IPS

WORK BASED TRIPS

ALL OTHE R PURPOSES

TOTAL

Figure 2. Percentage trips by location and purpose.

Table 1. Trip urvey results.

-Route

Assignment along PR-153 and new route using O-D s

To/From Coamo Through PR-153 Through New

% DT

AADT ADT

To/Fro East 26% m8900 5300 3600

To/From South 28% 9300 7000 2300

To/From West 46% 15,600 3100 12,500

Pr-545 6200

Total 100% 33,800 15,400 24,100

D. CHIMBA ET AL. 301

for all



0cu

i i

q

 and

where,

0

is the flow on Rout

e travel cost on

e minimum cost

an .

So s are obtained by solv-

ing arogram

The assumptions regarding UE is include the road user

having perfect knowledge of the routost, travel time

on a given link is a function of the flow on that link only

ticity.

of SUE can be summarized as

(4)

where,

 The first term represent expected minimum route cost

for all links,

second term represents expected total system

represents UE formulation,

e v,

dels in stochastic as-

se utilities which are

n Fig-

speed limits, link lengths and sdensity along each

gment utiureau of Puads (BPR) [19].

oute i

cis th

uis th

dqis the combined flow

lution to the above condition

n equivalent optimization p



Min zd

tv v

e c

d travel time functions being positive and increasing.

The SUE extends the UE concept by considering the fol-

lowing assumptions and implications:

 Traveler has perfect knowledge of the network and

travel cost,

 Traveler will choose the perceived least cost route,

 Different traveler perceives differently, thus intro-

ducing stochas

The SUE route choice can then be analyzed using logit

model, which treats all alternatives statistically inde-

pendent. The formulation

in Equation (4) [19]:

 

Min min zvq cv 







ii ii

vt vt v





 The

travel time,

 The third term

 z(v) = function for a given traffic volume v,

c(v) = route c apacity for given traffic volum

 v = traffic volume for route i,

 t = travel time for route i,

 dv = change in traffic volume.

SUE utilizes multinomial mo

signment. Multinomial models u

independent and identically distributed mainly with a

Gumbel distribution. They response homogeneity across

individuals and there is error variance-covariance homo-

geneity across individuals.

5. Application of SUE Coamo Route

Relocation Study

ADT volumes along PR-153 and Route A shown i

ure 3. The travel times were formulated using poste

ignal

selizing Bblic Ro

1tt











(5)















 (6)

Combining Equations (5) and (6) gives;

























(7)

where,

L = link length (mi),

S0 = link Free-Flow Speed (FFS),

V = link traffic volume in ADT,

nk ADT capacity,

eters are from Ex-

hi].

w for each link V1 and V2 were

baiscussed earlier. As

sh roximately 5 miles by

leroximately 5.5 miles. The first

to Pr-14 to

t = link average travel time (hr),

t0 = free flow link traversal time (hr),

C = li

a and b = The BPR function param

bit C30-1 and C30-2 of 2000 HCM [20

The initial traffic flo

sed on the O-D survey results d

own in Figure 3, Route A is app

ngth while PR-153 is app

ction of Route A from PR-52 is an uninterrupted flow

while the second section which connects

wntown is an arterial with two signalized intersection.

Therefore signal density for Route A was taken as 0.5 per

mile. PR-153 is an arterial with 4 signalized intersection

making signal density to be 0.73 per mile. Posted speed

limit for Route A is expected to be 55 mph while for

Pr-153 is 40 mph. Using exhibit C30-2 in 2000 HCM

[18], “a” and “b” values for each link were estimated as;

a = 0.31 and b = 3.64 for Route A and a = 0.38 and b =

5.0 for PR-153

PR-153

15, 400 vpd , 2-Lanes

ROUTE A

24,600 vpd, 4-Lanes

LOS D Capacity = 34,200

5.0 Miles Long

55 MPH Speed Li

TO/FROM COAMO

LOS D Capacity = 15,500 vpd

5.5 Mil es Long

40 MPH Speed Limit

4 Signals

mit

2 signals

TO/FROM OTHER CITIES

Figure 3. PR-153 and proposed Route A characteristics.

D. CHIMBA ET AL.

302

By inserting these values in Equation (7) above yields

the following formulations which are also illustrated in

Figure 4:

Route A;

3.64

10.09110.3134200

t















with Initial V1 =24,600 vpd

PR-153;

5.0

20.138 10.3815500

t















with Initial V2 =15,400 vpd.

n in Equations (8) and (9).

tility function which is formulated as;

.1. SUE Logit Utility Function

The generalized cost functions used for each route are set

based on theory developed by Kato et al. [20] using logit

utility functio

The logit u

11123

**Cost* *

GC tt

 



 





(8)

21223

**Cost* *

t t

 



 



 (9)

where

ute 1,

ute 2,

GC1 = general Cost for Ro

GC2 = general Cost for Ro

t1 = travel time along Route A,

t2 = travel time along PR-153,



= In vehicle time constant coefficient, –0.094,



= Total Cost constant coefficient, –0.002,



= Congestion Index constant Coefficient, –0.009,

ption

cost,

vi =traffic volume for route i,

Ci =capacity for route i,

Cost = in this study refers to gasoline consum

PR-153

ROUTE A







 34200 

















6.5

99.01091.0

























1.5

15500

6.01138.0

V1+V2

Figure



 =

 Congestion Index

The value of coefficients , 2



and 3



were

adopted from previous research et al..

5.2. Link Cost Due to Gasoline Expenses

The “cost” which appears in the utility functions (8) and

(9) refers to the situation where some travelers may

choose the route based on the gasoline consumption. In

this study, it is a cost with respect to gasoline consump-

tion. The study compared Route A and PR-153 using the

link length with respect to average fuel efficiency and

price per gallon. The average fuel efficiency is taken 20

Therefore;

For Route A Link: len

Gasoline cost = 4.15 × r link com-

om-

A over

es by Kato [6]

miles/gallon, while gasoline price was taken as $4.15/

gallon (the gas price when the study was conducted).

gth = 5.00 miles,

5.00/20 = $1.04 pe

ete trip,

For PR-153 Link: length = 5.50 miles,

Gasoline cost = 4.15 × 5.50/20 = $1.14 per link c

plete trip,

Probability of the traveler choosing Route

PR-153 is

AGC GC

P



 (10)

Probability of the traveler choosing PR-153 over

Route A is

153 12

GC GC

P



 (11)

To determine the optimal balance volumes which take

intics and costs,

to account the described road characteris

e following conditions must be fulfilled;





12A 1

+*P 0.0VV V



12 1532

+*P 0.0VV V (12)

The outputs from Equation (12) gives the optimal traf-

fic volume assignment and travel time by taking into

account all variable and utility costs. The equation was

programmed in Matlab for optimizati

on and yielded;

GC1 GC2 V1 (vph) V2 (vph)

−0.95 −0.405 28,000 12,000

Therefore, as a result of Stochastic User Equilibrium

(SUE), the originally traffic assigned to Route A and

PR-153 using O-D study percentage were optimized to

the final assignments as follows:

4. Link travel time and flow formulation along

Route A and PR-153.

D. CHIMBA ET AL. 303

Traffic Assignment

From O-D Survey From SUE Deviation (%)

Route A 24,600 28,000 13.8%

PR-153 15,400 12,000 22%

6. Conclusions

Thaper integrated the findings from origin-destination

(O-Dey and ststic userium in

routeation ste news propo the

townamo, Pu. Thsed nete is

e town were deter-

minedm the O-D surv assignments

on thnew atesed-

ings from O-D survey.

ic Userium was th

to ork uitial volumes assigned

from O-D survey findings. Included in the SUE was tra-

s which is controlled by the free flow

ty, length of the link and si

assignment on new route was i

[1]

ure Travelers to the United States by Income Level,” Jour-

e p

) survochar equilibapproach

reloc

of Co

udy. Th

erto Rico

route i

e propo

sed in

w rou

pected to capture diverted traffic currently using exist-

ing routes. The O-D provided the existing traffic pattern

and characteristics with respect to trip purposes, and the

percentages for internal and external trips. Percentages of

trips from major cities surrounding th

fro

ey. The initial trip

nd existing rous were ba on the find

Stochastr Equilib(SUE) en applied

the netwsing the intraffic

vel time on the link

speed, maximum capacignal

spacing density. Apart from link travel time, the utility

function of SUE contained other link measures of effec-

tiveness such as time spent in the vehicle (in-vehicle time

coefficient), congestion index and cost due to gasoline

consumption (cost coefficient). The gasoline cost consi-

dered vehicle fuel efficient of 20 miles/gallon, gasoline

price of $4.15/gallon and length of the link. All these link

characteristics were used to optimize the traveler choice

of the route.

Traffic assignment from the SUE was slightly different

from those initially assigned using O-D, indicating there

was optimization. The n-

eased by 13.8% from the one assigned using O-D while

assignment on the existing link was reduced by 22%. The

final optimized volumes were within capacity limits for

each link indicating successful optimization. The final

traffic assignment from SUE was used in the new route

design. The findings from this study showed the possible

benefit of integrating O-D with other trip assignment opti-

mization approaches. By integrating O-D survey with opti-

mization algorithms like UE or SUE can result in a well

balanced links which take into account all possible con-

strains.

REFERENCES

S. Jiang, B. Bai, G. Hong and J. O’Leary, “Understanding

Travel Expenditure Patterns: A Study of Japanese Pleas-

nal of Tourism Management, Vol. 25, No. 3, 2004, pp.

331-341.

doi:10.1016/S0261-5177(03)00141-9

[2] H. Alibabai and H. S. Mahmassani, “Dynamic Origin-

Destination Demand Estimation Using Turning Move-

ment Counts,” The 87th Annual Meeting of the Trans-

portation Research Board Proceedings, Washington DC,

2008.

[3] H. Spiess, “A Maximum Likelihood Model for Estimat-

ing Origin-Destination Matrices,” Transportation Re-

search, Vol. 21, No. 5, 1987, pp. 395-412.

doi:10.1016/0191-2615(87)90037-3

[4] M. Hazelton, “Some Comments on Origin-Destination

Matrix Estimation,” Transportation Research Part A: Po-

licy and Practice, Vol. 37, No. 10, 2003, pp. 811-822.

doi:10.1016/S0965-8564(03)00044-2

amic Traffic Modeling [5] S. Han, “Dynand Dynamic Sto-

chastic User Equilibrium Assignment for General Road

Networks,” Transportation Research Part B: Methodo-

logical, Vol. 37, No. 3, 2003, pp. 225-249.

doi:10.1016/S0191-2615(02)00009-7

[6] M. Hazelton, “Estimation of Origin-Destination Matrices

from Link Flows on Uncongested Networks,” Transpor-

tation Research, Vol. 34, No. 7, 2000, pp. 549-566.

doi:10.1016/S0191-2615(99)00037-5

[7] K. Jeornsten and S. Wallace, “Overcoming the (Apparent)

Problem of Inconsistency in Origin-Destination Matrix

Estimations,” Tran sportation Science, Vol. 27, No. 4, 1993,

pp. 374-380. doi:10.1287/trsc.27.4.374

[8] H. Lo., N. Zhang and W. Lam, “Estimation

Destination Matrix with Random L

of an Origin-

ink Choice Propor-

tions: A Statistical Approach,” Transportation Research,

Vol. 30, No. 4, 1996, pp. 309-324.

doi:10.1016/0191-2615(95)00036-4

[9] M. Hazelton and M. Gordon, “Estimation of Origin-Desti-

ion,” Trans-

gical, Vol. 32, No.

nation Trip Matrices from Link Counts,” Proceedings of

the 2002 European Transport Conference, London, 2002.

[10] H. Yang and J. Zhou, “Optimal Traffic Counting Loca-

tions for Origin-Destination Matrix Estimat

portation Research Part B: Methodolo

2, 1998, pp. 109-126.

doi:10.1016/S0191-2615(97)00016-7

[11] J. Hu, L. Yang, L. Kong and Y. Yang, “Urban M

Traffic Flow Considering the Influenc

ixed

e by Origin-Desti-

nation of Public Transportation,” Journal of Transporta-

tion Systems Engineering and Information Technology,

Vol. 11, No. 1, 2011, pp. 102-107.

doi:10.1016/S1570-6672(10)60107-9

[12] S. Clark and P. Watling, “Sensitivity Analysis of the Pro-

bit-Based Stochastic User Equilibrium Assignment Mo-

del,” Transportation Research Part B: Methodological,

Vol. 36, No. 7, 2002, pp 617-635.

doi:10.1016/S0191-2615(01)00021-2

[13] Y. Lim and B. Heydecker, “Dynamic Departure Time and

Stochastic User Equilibrium Assignment,” Transportation

Research Part B: Methodological, Vol. 39, No. 2, 2005,

pp. 97-118. doi:10.1016/j.trb.2003.08.003

[14] A. Nielsen, D. Frederiksen and N. Simonsen, “Stochastic

User Equilibrium Traffic Assignment with Turn-Delays

D. CHIMBA ET AL.

304

national Transactions in Opera-

p. 555-568.

in Intersections,” Inter

tional Research, Vol. 5, No. 6, 1998, p

doi:10.1111/j.1475-3995.1998.tb00137.x

[15] M. Hazelton, “Some Remarks on Stochastic User Equi-

librium,” Transportation Research Part B: Methodologi-

cal, Vol. 32, No. 2, 1998, pp. 101-108.

doi:10.1016/S0191-2615(97)00015-5

o-Stage Stochastic

valuation of Count

ation of O-D Ma-

[16] X. Fei and H. S. Mahmassani, “A Tw

Model for the Sensor Location Problem in a Large-Scale

Network,” The 87th Annual Meeting of the Transporta-

tion Research Board Proceedings, Washington DC, 2008.

[17] K. N. Paul and H. K. L. William, “E

Location Selection Methods for Estim

trices,” Journal of Transportation Engineering, Vol. 124,

No. 4, 1998, pp. 376-383.

doi:10.1061/(ASCE)0733-947X(1998)124:4(376)

[18] Highway Capacity Manual, “Transportation Research

pes of Travel Demand Tech-

Trans-

Board,” National Research Council, Washington DC, 2000.

[19] M. G. H. Bell and H. W. K. Lam, G. Ploss and D. Inaudi,

“Stochastic User Equilibrium Assignment and Iterative

Balancing,” Proceedings of the 12th International Sym-

posium on Transportation and Traffic Theory, Berkeley,

1993.

[20] S. Kato, Y. Kaneko and M. Inoue, “Empirical Analysis

on Relationship Between Ty

niques and Estimated User’s Benefit Stemming from

portation Investment,” Journal of the Eastern Asia Society

for Transportation Studies, Vol. 6, 2005, pp. 3937-3947.