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
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.
C
opyright © 2012 SciRes. JTTs

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
ij
T

Trips from other cities to Coam
ji
To

The proportion trip among all surveyed vhicles is
given by;
Proportion of internal trips to total survey, Pii
e
;
11
11 111 
1


  ij ji ii
ij jii
TT T
ii
T
P (1)
ii nn
Proportion of outbound external trips to total survey, Pij;
11
11 111 
1


 
ij jiii
TT
T
ij
ij nn
ij jii
T
P (2)
Proportion of inbound external trips to total survey, Pji;
11
11 111 
1


 
ij ji ii
TTT
ji
ji nn
ij jii
T
P (3)
Both trip proportionand sii P, ij P
j
i
P
e ex
are ut
termination of the trip thisting and proposed
routs.
fond b
C
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:


0
ii
fcu

 for all
i
PERCENTAGE TRIPS BY PURPOSE
52%
22%
13% 13%
0%
5%
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
i
f
q
 and
where,
0
i
f
i
f
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
an
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-
d
speed limits, link lengths and sdensity along each
gment utiureau of Puads (BPR) [19].
ei
R oute i
i
cis th
uis th
dqis the combined flow
lution to the above condition
n equivalent optimization p

0
Min zd
i
v
i
i
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 


 
0
vd
i
v
ii ii
i
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,
i
 t = travel time for route i,
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
0C
1tt
b
V
a





(5)







0
0
L
tS  (6)
Combining Equations (5) and (6) gives;
0
1
b
LV
ta
SC












(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
se
to Pr-14 to
do
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
1
10.09110.3134200
V
t







with Initial V1 =24,600 vpd
PR-153;
5.0
2
20.138 10.3815500
V
t







with Initial V2 =15,400 vpd.
5
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
2
1
11123
1
**Cost* *
v
GC tt
C
 

 


1
(8)
2
2
21223
2
**Cost* *
v
2
t t
C
 

 

 (9)
where
ute 1,
ute 2,
GC
GC1 = general Cost for Ro
GC2 = general Cost for Ro
t1 = travel time along Route A,
t2 = travel time along PR-153,
1

= In vehicle time constant coefficient, –0.094,
2

= Total Cost constant coefficient, –0.002,
3

= 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
1
99.01091.0
1V
t














1.5
15500
2
6.01138.0
2V
t
V1+V2
V1+V2
Figure
2
v

*
ii
t
C
 =
i  Congestion Index
The value of coefficients , 2

and 3

1

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-
pl
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
1
12
e
ee
GC
AGC GC
P

 (10)
Probability of the traveler choosing PR-153 over
Route A is
2
153 12
e
ee
GC
GC GC
P

 (11)
To determine the optimal balance volumes which take
intics and costs,
th
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
ex
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
cr
[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
e
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.
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