A Simulation-Based Dynamic Traffic Assignment Model With Combined Modes

Promet – Traffic&Transportation, Vol. 26, 2014, No. 1, 65-73 65
M. Meng, C. Shao, J. Zeng, C. Dong: A Simulation-Based Dynamic Traffic Assignment Model with Combined Modes
MENG MENG, Ph.D.
E-mail: 10114221@bjtu.edu.cn
1. MOE Key Laboratory for Urban Transportation Complex
Systems Theory and Technology,
Beijing Jiaotong University
No.3 Shang Yuan Cun, Haidian District,
Beijing 100044, China
2. Centre for Infrastructure Systems,
School of Civil and Environmental Engineering,
Nanyang Technological University,
Singapore 639798, Singapore
CHUNFU SHAO, Professor, Ph.D.
E-mail: cfshao@bjtu.edu.cn
MOE Key Laboratory for Urban Transportation Complex
Systems Theory and Technology, Beijing,
Beijing Jiaotong University
No.3 Shang Yuan Cun, Haidian District,
Beijing 100044, China
JINGJING ZENG, M.E.
E-mail: zengjj@ehualu.com
Beijing E-Hualu Information Technology Company Limited
China Hualu Building No.165 Fushiroad,
Shijingshan District, Beijing, China 100043
CHUNJIAO DONG, Ph.D.
E-mail: serena.dongchj@gmail.com
Center for Transportation Research,
University of Tennessee
600 Henley Street, Knoxville, TN37996-4133, USA
Traffic in the Cities
Preliminary Communication
Accepted: Mar. 4, 2013
Approved: Oct. 12, 2013
A SIMULATION-BASED DYNAMIC TRAFFIC
ASSIGNMENT MODEL WITH COMBINED MODES
ABSTRACT
This paper presents a dynamic traffic assignment (DTA)
model for urban multi-modal transportation network by con-
structing a mesoscopic simulation model. Several traffic
means such as private car, subway, bus and bicycle are con-
sidered in the network. The mesoscopic simulator consists of
a mesoscopic supply simulator based on MesoTS model and
a time-dependent demand simulator. The mode choice is si-
multaneously considered with the route choice based on the
improved C-Logit model. The traffic assignment procedure is
implemented by a time-dependent shortest path (TDSP) al-
gorithm in which travellers choose their modes and routes
based on a range of choice criteria. The model is particularly
suited for appraising a variety of transportation management
measures, especially for the application of Intelligent Trans-
port Systems (ITS). Five example cases including OD demand
level, bus frequency, parking fee, information supply and car
ownership rate are designed to test the proposed simulation
model through a medium-scale case study in Beijing Chaoy-
ang District in China. Computational results illustrate excel-
lent performance and the application of the model to analy-
sis of urban multi-modal transportation networks.
KEY WORDS
dynamic traffic assignment, combined modes, mesoscopic
simulation, time-dependent shortest path algorithm
1. INTRODUCTION
The modelling of simulation-based dynamic traffic
assignment (DTA) has witnessed a growing amount of
research attention recently as the management of the
time-dependent traffic flow becomes more and more
important. Most of the simulation-based DTA litera-
tures are concentrated on the single mode modelling,
usually private car or bus. In metropolitan areas, how-
ever, the combined travel mode is becoming more and
more common, where travellers often transfer more
than one time to complete a trip by using at least two
different traffic modes. The ignorance of the transfer
behaviour limits the existing research used in the real-
world application.

66 Promet – Traffic&Transportation, Vol. 26, 2014, No. 1, 65-73
Traffic assignment with combined modes is more
complicated than the assignment of a pure mode trip.
Especially, dynamic combined trip assignment needs
to focus on the mode-route choice problem in the
time-dependent network. It involves mode and route
choice simultaneously in the traffic demand simula-
tor in which travellers choose not only the routes but
the traffic mode at the transfer nodes. The existing
simulation-based DTA models are still limited by the
pure mode trip assumption [1-5]. For instance, the
mainstream traffic planning software DYNASMART
and DYNAMIT regard buses as part of the vehicular
mix, which follow a pre-specified route and departure
schedule. The travel mode assignment is exogenous
to the model which neglects the interaction between
mode choice and trip assignment. Few DTA studies
have been developed with considering the combined
mode problem. Abdelghany [6] proposed an ana-
lytical stochastic DTA model with combined mode in
the multi-modal networks. The model is formulated
as minimization mathematical program with a set of
descriptive constrains. Meanwhile, Abdelghany and
Mahmassani [7] presented a simulation-based DTA
model with combined mode. They captured the inter-
action between mode choice and traffic assignment
in a multi-modal network. However, these two models
just focus on the motor vehicles and regard travel time
as the only factors in road impedance function model.
A simulation-based DTA model with combined modes
is closer to realistic behaviour in mode choice and as-
signment procedures, which should be the future di-
rection of the research.
Four different traffic modes are considered in this
paper including private car, bus, subway, and bicycle.
A simulation-based approach to the dynamic assign-
ment problem is adopted in this work in an attempt
to combine mode and route choice with more realistic
travel time function. The paper is organized as follows.
The simulation framework is presented in Section 2.
Section 3 elaborates about the components of the me-
soscopic vehicle movement simulator. After the travel
time analysis, Section 4 proposes the assignment al-
gorithm and the mode-route choice procedures. Five
sets of simulation experiments are designed in Sec-
tion 5. Computational results illustrate the validity
of the model and provide the basis for management
policies. Finally, the concluding remarks are given in
Section 6.
2. SIMULATION FRAMEWORK
In general, traffic simulation models can be cate-
gorized into three classes: macroscopic, mesoscopic,
and microscopic models [8-10]. A mesoscopic model
is more flexible than macroscopic models for model-
ling travel behaviour, such as route choice, and coars-
er than microscopic models for modelling the entity
movement, such as lane changing. This can effectively
reduce computational complexity and ensure the re-
sults with certain accuracy. Therefore, if the precision
is not very high while dealing with a large-scale net-
work, a mesoscopic simulation model would be the
best choice for the traffic simulation.
The mesoscopic simulation framework is shown in
Figure 1. The inputs in the system are the network infor-
mation and available OD demand. The demand simu-
lator separates the multimodal transportation network
into several traffic layers to represent individual traf-
fic modes. In addition, the demand simulator updates
the traffic disutility at the start of each simulation run.
The supply simulator moves the vehicles on the lane
of the network until the end of simulation time. When
the simulation process is complete, the output is the
distribution of traffic flows which can be used in the
traffic analysis.
Transit Vehicle
Generation
Time-dependent OD
Demand
Mode-route Choice
Time-dependent Shortest
Path Algorithm
Passenger
Assignment
Auto Generation
& Assignment
Traffic Cell
Vehicle Movement &
Network Control
Figure 1 - Simulation framework
3. MESOSCOPIC TRAFFIC SIMULATOR
The flowchart of the mesoscopic traffic simulator is
shown in Figure 2. The vehicle simulator is composed
of five modules: vehicle generation module, traffic cell
module, vehicle speed update module, vehicle loca-
tion update module, and vehicle movement module.
3.1 Vehicle generation module
Time-dependent OD demand is considered in the
simulation. The transit vehicles (bus and subway) fol-
low the pre-determined timetable and routes, while
Vehicle Generation
Traffic Cell Update
Vehicle Speed Update
Vehicle Location Update
Record Running Time & Remove
Simulation Clock Pushing
Time for Terminating?
yes
yes
Leaving Network?
Stop and Output
no
no
Figure 2 - Flowchart of the mesoscopic traffic simulator

the generation of cars and bicycles is a stochastic
procedure. A Poisson distribution is used to represent
the traffic arrival statistical regularity so that the time
headway follows a negative exponential distribution.
3.2 Traffic cell update module
Vehicles are formed into many groups in the sim-
ulation, which are called traffic cells in MesoTS (Me-
soscopic Traffic Simulator) [11]. Each traffic cell is
composed of vehicles which have the same traffic
dynamics, such as traffic speed, vehicle position. The
composition of the traffic cell varies with the changes
of vehicle speed or position. The model defines first a
standard distance DD (e.g. 60 m) to control the merg-
ing and splitting of traffic cells. The judge distance is
the gap distance between the last vehicle in the lead-
ing traffic cell and the first vehicle in the following traf-
fic cell (see dkj and dji in Figure 3). When the vehicles
are on the same segment, if the distance between two
traffic cells is less than DD, these two traffic cells are
merged into a larger traffic cell as shown by cell i and j
in Figure 3-(a). Otherwise, if the distance between two
vehicles in a traffic cell is greater than DD, this traffic
cell is split into two cells as cell j in Figure 3-(b), where
these two vehicles are the lead vehicle and the tail ve-
hicle, respectively.
3.3 Speed update module
The speed update module updates the speed of
each vehicle in the traffic cells by two traffic modes
[12-13]: cell-following model calculates the speed of
the lead vehicle in a traffic cell; speed-density model
calculates the speed of the tail vehicle in a traffic cell.
The lead vehicle speed in the traffic cell can be ob-
tained as follows:
,
,
v
v
v v
d DD
d DD
1
max
max
ij
i i j
ij
ij
0 1
$
m m
=
+ -
^ h
) (1)
where vij is the cell-following speed of the lead vehicle
in traffic cell i travelling in direction j; vmax is the free
flow speed in the segment; vj0 is the speed of the tail
vehicle in the leading traffic cell j; i
m is a scalar equal
to /
d DD
ij .
The tail vehicle speed in the traffic cell can be ob-
tained as:
,
v v v v
k
k
1
min max min
i
jam
i
0 = + - -
a b
^ c
h m
; E (2)
where vi0 is the speed of the tail vehicle in traffic cell i;
ki is the vehicle density in traffic cell i, which is equal to
the total vehicle length in the traffic cell divided by the
total segment length occupied by the traffic cell; kjam
is the jam density of the segment, which is usually set
to 1; vmin is the minimum traffic speed of the segment,
which is usually set to 0; a, b are the indefinite param-
eters, usually set as .
1 8
a = , .
5 0
b = [11].
The others vehicles in the middle of the traffic cell
are calculated by a linear interpolation based on their
speed:
,
min
v v v v v
k
k
1
min max min
ij
n
ij
jam
n
= + - -
a b
l l
^ c
h m
; E
) 3 (3)
where vij
n
is the speed of the Nth
vehicle in traffic cell i
towards direction j; kn is the traffic density from the Nth
vehicle to the end of the road. In order to make sure
that k k
i n
2 , al, bl are different with a, b in Equation
(1), typically set as .
1 5
a =
l , 3
b =
l in the normal traf-
fic condition.
3.4 Position update module
The vehicle position in the next time step is the cur-
rent position plus the travelled distance. If a bus sta-
9
10 8 k
6 5
7 j
3 1
4 i
2
d > d
kj min
d > d
kj min
d < d
ji min
d > d
ji min
9
10 8
6 5
7 j
3 1
4 i
2
k
(a) Merge
(b) Split
Figure 3 - Merging and splitting of traffic cells

tion is located along this link, after leaving the station
the bus may clash with the last vehicle. To avoid this,
the model takes the minimum position between the
last vehicle position and the simulation position as the
updated position.
A channelized section of a certain length is set
for each segment in the simulation. Each channel-
ized lane corresponds to a different turning direction,
where a specific mode-route choice is determined.
Once a vehicle moves near the intersection and into a
channelized lane, it is not allowed to change its turning
direction until it is in the downstream section. Vehicles
in different lanes have no influence on each other.
3.5 Capacity constraints
The model calculates the average time headway in
each update phase. The average time headway deter-
mines the time at which vehicles can move into the
segment:
t t
Q
1
n n 1
= +
- (4)
where tn is the earliest time for the next vehicle enter-
ing the segment; tn 1
- is the time for the last vehicle
entering the segment; Q is the real capacity of the
segment, Q qQ
= r , in which Q
r is the traffic capacity in
one direction; if the intersection is control-signalized,
g is the green/cycle ratio; if the intersection is unsig-
nalized, g is the delay coefficient [14]. If a bus stop is
located along a particular segment, Q
r for this segment
should be reduced in order to represent the bus stop-
ping effect.
A vehicle is allowed into a link only if the simula-
tion time is greater than or equal to tn; otherwise, the
vehicle queues at the node. Meanwhile, the model will
check the vehicle count in the network while updating.
If the end of the last traffic cell reaches the link bound-
ary, no vehicle is allowed into this segment.
4. TIME-DEPENDENT SHORTEST PATH
ALGORITHM
The total simulation time is divided into several
time intervals. Each time interval is also divided into
certain iterative phases according to the system ini-
tialization. The model updates the path travel time at
the beginning of each iterative phase, finds the short-
est path with the k-shortest path algorithm, and finally
assigns the traffic flow based on an improved C-Logit
model.
4.1 Travel utility function
To facilitate the interface of the mode choice mod-
el with the shortest path calculation, the generalized
cost is expressed in units of time (minutes). The result-
ing systematic utility equations are:
.
U C s
0 04722
Sin k
od
=- ^ h (5)
. .
U C s
2 169 0 04722
Com k
od
=- - ^ h (6)
. .
U C s
0 598 0 04722
Tra k
od
=- - ^ h (7)
where Sin = single-car travel mode, Com = combined
car and transit travel mode, Tra = Transit travel mode;
U is the travel utility; C s
k
od
^ h is the generalized traf-
fic cost of path k in time s. Parameters in the above
equations are calibrated by the survey results from the
Beijing Huilongguan residential area.
The travel cost is updated only in the new time in-
terval to reduce the calculation. The generalized travel
cost contains many factors like travel time, travel cost,
travel distance, and so on. Assuming these factors are
independent for each link, the generalized traffic cost
can be expressed as
C s C s
k
od
ak a
od
d
=
^ ^
h h (8)
where ak
d equals 1 if link a lies on path k, otherwise
0; C s
a
od
^ h is the traffic cost of the link a in time s. The
considered travel time and travel cost, C s
a
od
^ h can be
expressed as:
C s T s M s
a
od
t a m a
~ ~
= +
^ ^ ^
h h h (9)
where T s
a^ h is the travel time of link a in time s; M s
a^ h
is the travel cost of link a in time s; t
~ and m
~ are the
weights respectively. The details about the two compo-
nents are discussed further in the text.
Running in an independent space, a subway link is
affected little by external circumstances. Travel time for
a subway is regarded as a deterministic value equal-
ling the subway’s runtime adding the waiting time. The
travel time for a bus includes the bus run time and the
delay time at the bus station which is determined by
the number of travellers getting on and off the bus.
The link travel time for the bicycle and the pri-
vate car is the mean time for many vehicles passing
through. Let tn
k
denote the mean travel time for all ve-
hicles passing through the link at iterative phase n in
time interval k, and let Tn
k
1
- denote the mean travel
time after the previous iterative phase n 1
- in the
same time interval. The link travel time for the bicycle
and the private car can be updated by:
T T
n
t T
1
n
k
n
k
n
k
n
k
1 1
= + -
- -
^ h (10)
The model decides the set of alternative mode-
route choice at the beginning of the next iterative
range according to the updated link travel time Tn
k
. If
no vehicle has passed through the link in a certain it-
erative phase, the link travel time is not updated; if
there are vehicles passing through the link, the mean
link travel time equals the total travel time for all pass-
ing vehicles on the link divided by the total number
of vehicles. Moreover, one case that may arise at the
onset of the simulation is that no vehicle arrives at a
link in the whole time interval, and then the link travel

time is equal to the link length divided by the link free-
flow speed.
4.2 Mode-route Choice Model
The nodes in the multi-modal networks can be of
two types: route-choice node and non-route-choice
node. Route-choice nodes are the nodes which con-
nect several downstream nodes, in which the mode-
route choice may be changed. Non-route-choice nodes
are the nodes which connect only one downstream
node with the same traffic mode, in which the travel
route cannot be chosen. Therefore, the model only
needs to make mode-route choices at the route-choice
nodes in the simulation, thereby reducing the calcu-
lation process. Moreover, the route-choice node can
be manually set in a large network for increasing ef-
ficiency.
After calculating the shortest path in the network,
the travel route can be determined by a nested logit
model. Mode-route choice in the simulation is as-
sumed to follow the Stochastic User Equilibrium (SUE)
principle. The mode-route choice probability is deter-
mined by absolute deviation of the path travel time in
the C-Logit model as follows:
exp
exp
P s
bU s CF
bU s CF
k
od
k
od
k
k K
k
od
k
od
=
- -
- -
!
^
^
^
h
h
h
6
6
@
@
/
(11)
where P s
k
od
^ h is the probability for choosing path k in
time s; U s
k
od
^ h is the traffic utility of path k in time s; b
is a non-negative parameter; CFk is the common factor
of path k, and the formulation from Cascetta [15] is
introduced herein as follows:
ln
CF
C C
C C
k
k
od
q
od
k
od
q
od
q Kod
t
=
+
!
v
e o
= G
/ (12)
where t and v are non-negative parameters.
In the real world, however, travellers are more con-
cerned about the relative deviation of the path travel
time. Therefore, the C-logit model is modified as fol-
lows:
exp
exp
P s
b
U s
U s
CF
b
U s
U s
CF
k
od
od
q
od
k
q K
od
k
od
k
od
=
- -
- -
!
^
^
^
^
^
h
h
h
h
h
=
=
G
G
/
(13)
where U s
od
^ h is the average traffic utility.
4.3 Time-dependent K-shortest path algorithm
The assignment procedure in each iterative phase
is achieved by a multi-objective shortest path algo-
rithm. The k-shortest path algorithm [16] is an exten-
sion of the typical Dijkstra algorithm to calculate the
set of the shortest travel time paths between every
origin-destination pair. The primary advantage of this
approach is that it can obtain more than one short-
est path, and determine the distinct set of the short-
est path numbers according to different criteria. The
procedure proposed herein is extended by Kihara et
al. [17] as follows:
Step 0: Initialization. Set time interval TI=1, itera-
tive phase IP=1;
Step 1: Calculate the shortest path which has the
least travel time between the original node
and the destination node by Dijkstra’s Algo-
rithm;
Step 2: Remove all links which belong to Step 1
from the network;
Step 3: Repeat Step 1 and Step 2 k-times, and then
k link-disjoint paths are obtained. If the Di-
jkstra’s algorithm cannot be executed as
the links are all removed, the shortest path
in this IP is founded. The traffic flow can be
assigned based on the mode-route choice
model;
Step 4: If the iterative phase matches the final it-
erative phase in this time interval, TI=TI+1,
else IP=IP+1 and go to Step 1;
Step 5: If the time interval reaches the final time
interval, the algorithm is terminated, else
TI=TI+1 and go to Step 1.
5. EXPERIMENTS AND ANALYSIS
Five sets of simulation experiments were designed
to illustrate the performance and application of the
model. A medium-scale network was used in these ex-
periments as shown in Figure 4, which is an area in the
Chaoyang District in Beijing. The network consists of 5
subway lines (as bold blue lines) with 39 stations (as
yellow nodes), and 188 road links with 122 nodes. The
subway lines overlap with the roads on the same loca-
tions, but in two different layers. A bus line is taken into
consideration only if it has at least four stations in the
study area. Hence, 18 bus lines with 51 stations were
selected as shown in Figure 5. As explained before, a
bicycle link is the road link between an origin /destina-
tion node and a subway station. The bicycle and bus
networks are introduced here for illustrative purposes
only, and do not correspond to available service (which
does not affect the examination of the model).
It is assumed that no traveller would be willing to
transfer more than twice in one trip. Five travel modes
are available for all travellers: private car, park and
ride (P&R), one bus line, bus to transit (bus or sub-
way), bicycle to transit (bus or subway). The propor-
tions for five travel modes and the average travel time
(minute) are recorded as the output results. Travellers
head to the CBD area (the upper part of the network)
from all other zones. All travellers are generated over

20 minutes of the peak period between 12 zones. The
iterative phase is 0.5 seconds, and the time interval is
5 minutes. All travellers are assumed to have pre-trip
information on available alternatives, and have the ac-
cess to use a car and a bicycle (own or rent). The free
flow speed and minimum speed of the road are set as
60 km/h and 15 km/h;62 signalized intersections are
assumed to operate under vehicle-actuated two-phase
control, the green ratio is set as 0.45; 60 unsignalized
intersections are set as follows: no control (20 inter-
sections), stop sign control (25 intersections) and yield
sign control (15 intersections). The frequency of the
subway is 15 vehicle/hour. The bus ticket is 1 yuan.
Other parameters are: 18
p = yuan/hour, .
b 3 3
= ,
.
0 5
t
~ = , 1
t = , 2
v = .
The first set of experiments studies the effect of
the different congestion levels. Four OD demand lev-
els are considered in the experiments with regard to
the spatial distribution, the OD trip desires, morning
peak travel pattern. In this experiment, the traffic in-
formation is fully provided, the bus frequency is 12
buses/hour, and parking fee is 6 yuan. Table 1 shows
the effect of the network congestion on mode split
and average travel time. With the increase in network
congestion, more travellers will prefer the transit travel
mode and the combined travel mode. For example, the
proportion of car travel trips decreases from 63.0% for
9,000 OD demand to 60.6% for 15,000 OD demand.
Similarly, the one bus line travel mode increases from
3.5% for 9,000 OD demand to 4.6% for 15,000 OD de-
mand. With the increase of OD demand, transit travel
trip is more attractive than car trip. Meanwhile, the
increase of OD demand also adds the average travel
time nearly in a linear pattern. The average travel time
for the highest OD demand increases by 48.5% com-
pared to the lowest level.
The effect of imposing parking fee on private car
travellers is examined in the second set of experi-
ments. The parking fee which ranges from ¥0 to ¥12 is
applied to all final destinations in the network. In this
experiment, the traffic information is fully provided, the
bus frequency is 12 buses/hour, and the OD demand
is 13,000, the parking fee at transfer node is ¥2. A
private car traveller who transfers to subway or bus to
complete their trip must pay the parking fee and the
transit ticket. Parking fee is assumed to charge for the
entire parking time in one day. The simulation results
are listed in Table 2. It shows that with the increase
of the parking fee, the proportion of private cars is
sharply reduced, while the proportion of park and ride
rises in a certain range, and other travel modes have
Figure 4 - Road network Figure 5 - Bus network

not changed much. When the parking fee is ¥0, the
proportion of cars is the highest (75.8%); when the
parking fee is ¥9, the proportion of cars is about 50%,
when the parking fee is ¥12, the proportion of cars to
subway is nearly 40%. Therefore, in this case, if the
management objective for the proportion of cars is
less than 50%, the parking fee should be set at more
than ¥9.00, fewer travellers will choose the car trip be-
cause of high money cost at the destination. On the
other hand, the increase of the parking fee at the final
destination adds to the attractiveness of transit trip
and the combined trip as the advantage of the traffic
cost. Travellers would avoid high parking fees at their
destination to change their travel mode. For example,
the proportion of park-and-ride rises more than twice
from 13.4% to 29.7%, and one bus line trip rises more
than three times from 3.6% to 14.5%. Meanwhile, the
increase of parking fee also adds to the average travel
time as the transfer time and the delay time of transit
increase.
The effect of bus frequency is examined in the third
set of experiments. The bus frequency which ranges
from 3 buses/hour to 15 buses/hour is assumed to
apply to all bus lines in the network. In this experiment,
the traffic information is fully provided, the parking fee
is ¥6.00, and the OD demand is 13,000. The simula-
tion results listed in Table 3 show that with the increase
of the bus frequency, a slight increase in the transit
share is observed. For example, when the bus frequen-
cy increases from 3 buses/hour to 12 buses/hour, the
private car trips drop by 15.0%, the park-and-ride trips
double to 25.3%, and the one-bus line trip increases
almost 3 times to 3.9%. The increase in bus frequency
to 15 buses/hour does not lead to a significant change
in the travelling mode share, but most of the shift trips
choose the one-bus line as the advantage of saving
the transfer time. Therefore, considering the invested
funds, the best bus frequency should be set at about
nearly 12 buses/hour. Meanwhile, the increase of bus
frequency reduces the average travel time as both the
transfer time and the delay time of transit become
smaller.
The fourth set of experiments examines the effect
of traffic information on the travel mode choice. Five
cases are considered in the experiments: full infor-
mation, no car transfer information, no bus transfer
information, no bicycle transfer information, and no
all-transfer information. The traffic information is as-
sumed as the only accessibility for travellers to other
traffic modes. Without transfer information, travellers
Table 1 - Effect of OD demand on travel mode split and traffic assignment
OD demand 9,000 11,000 13,000 15,000
Private Car 63.0% 62.7% 61.5% 60.6%
Park and Ride 24.0% 24.1% 25.3% 25.5%
One Bus Line 3.5% 3.7% 3.9% 4.6%
Bus to Transit 3.0% 3.2% 3.1% 3.2%
Bicycle to Transit 6.4% 6.3% 6.2% 6.1%
Average travel time (min) 16.01 19.34 20.55 23.78
Table 2 - Effect of parking fee on travel mode split and traffic assignment
Parking Fee 0 3 6 9 12
Private Car 75.8% 70.2% 61.5% 51.3% 40.3%
Park-and-Ride 13.4% 17.5% 25.3% 26.6% 29.7%
One Bus Line 3.6% 3.8% 3.9% 8.9% 14.5%
Bus to Transit 2.1% 2.8% 3.1% 6.8% 8.9%
Bicycle to Transit 5.1% 5.7% 6.2% 6.4% 6.6%
Average travel time (min) 20.29 20.38 20.55 20.87 21.21
Table 3 - Effect of bus frequency on travel mode split and traffic assignment
Bus Frequency 3 6 12 15
Private Car 76.5% 63.5% 61.5% 59.0%
Park–and-Ride 14.0% 24.2% 25.3% 25.9%
One-Bus Line 1.3% 3.4% 3.9% 5.5%
Bus to Transit 2.0% 2.4% 3.1% 3.5%
Bicycle to Transit 6.2% 6.4% 6.2% 6.1%
Average travel time (min) 20.86 20.75 20.55 19.97

have no opportunity to change their travel mode. The
parking fee is ¥6.00, the bus frequency is 12 buses/
hour, and the OD demand is 13,000. The simulation
results listed in Table 4 show that full information en-
sures the best performance of the network. When the
car transfer information is not provided, the traveller
who drives the car has no opportunity to transfer to
other traffic mode; the private car trip increased from
61.5% to 86.5%, and the average travel time increased
from 20.55 minutes to 21.07 minutes. Similarly, when
the bus transfer information is not provided, the one-
bus line trip will immediately increases from 3.9% to
6.2%; other travel modes do not change so much.
The average travel time will increase more than the
case in which there is no car transfer information from
20.55 minutes to 22.98 minutes. The case in which
no bicycle transfer information is provided, other mode
shares also increase a little. Finally, if no transfer infor-
mation is provided, most of the travellers choose the
private car trip, and the average travel time increases
as the traffic congestion aggravates.
The last set of experiments examines the effect of
car ownership ratio on the travel mode choice. Five
cases of car ownership ratio are considered in the
experiments: 100%, 80%, 60%, 40%, and 20%. The
travellers who do not have a car can only choose the
bus or bicycle trip. In this experiment, the traffic in-
formation is fully provided, the parking fee is ¥6.00,
and the OD demand is 13,000. The simulation results
listed in Table 5 show that as the car ownership ratio
decreases, the public travel trips rise sharply. With the
decrease of car trips, the degree of traffic congestion
is reduced, which leads to the conclusion that the trav-
ellers who have cars will prefer car trips over public
trips. Moreover, the decrease in car ownership will
save the average travel time at first, as the car travel
time decreases. However, when the car ownership ra-
tio decreases to a certain level, the average travel time
will increase with the limitation of the public running
schedule. In our case, the average travel time is the
least when the car ownership ratio is 80%.
6. CONCLUSION
DTA is an important issue in ATMS (Advanced Traf-
fic Management System) and ATIS (Advanced Traveler
Information Systems). Detailed research into DTA prob-
lem is helpful for traffic planning and management.
This paper presents a simulation-based DTA model
considering combined travel modes. The framework
consists of a multi-modal supply network and a me-
soscopic demand simulator. On the supply side, four
traffic modes are included in the urban transportation
network: private car, subway, bus and bicycle. On the
demand side, the interaction between mode-route
choice and traffic assignment is taken into account
in a nested improved C-Logit model. The traffic as-
signment procedure is achieved by a time-dependent
shortest-path algorithm.
Five experiments were designed to illustrate the
performance and application of the model in the
transportation management. These experiments illus-
trate the significance of combining the mode choice
and route choice in the DTA framework and also verify
the efficiency of the time-dependent-shortest path al-
gorithm in the dynamic traffic assignment problem.
Five sets of experiments show that the increase of
OD demand makes the transit trip more attractive,
but increases the average travel time; imposing high
parking fee contributes to improving the proportion of
transit trip; the frequency of the bus service will appeal
to the travellers to shift their travel mode, but not in
Table 4 - Effect of information supply strategies on travel mode split and traffic assignment
Traffic Information Full No Car Transfer No Bus Transfer No Bicycle Transfer No All Transfer
Private Car 61.5% 86.5% 62.5% 64.2% 94.7%
Park-and-Ride 25.3% -- 25.4% 27.7% --
One-Bus Line 3.9% 4.3% 6.2% 4.4% 5.3%
Bus to Transit 3.1% 3.4% -- 3.7% --
Bicycle to Transit 6.2% 6.0% 5.9% -- --
Table 5 - Effect of car ownership ratio on travel mode split and traffic assignment
Car Ownership Ratio 100% 80% 60% 40% 20%
Private Car 61.5% 52.6% 42.6% 29.6% 15.6%
Park-and-Ride 25.3% 19.2% 13.4% 8.5% 4.1%
One-Bus Line 3.9% 8.3% 13.3% 18.6% 24.8%
Bus to Transit 3.1% 6.4% 10.4% 14.7% 18.9%
Bicycle to Transit 6.2% 13.6% 20.4% 28.5% 36.6%

the-more-the-better way; the traffic information service
level influences the traffic assignment which should
be provided completely and timely; the car ownership
ratio has direct impact on the travel mode split, and
proper car ownership ratio would contribute to saving
the travel time. All the sets of experiments are well ap-
plied in the real traffic management with the proposed
simulation-based DTA model.
Further research is planned for improving the algo-
rithm efficiency in large-scale networks and calibrating
the parameters with real data. Time-dependent short-
est path algorithm tends to run fairly slowly, especially
when a large network is involved. Intelligent algorithms
(IA) have an excellent ability in searching for the glob-
ally optimal solution, and can be a direction in later
studies. The use of the model to examine the appli-
cation of APTS/ATIS and management measures are
worth continuing the study.
ACKNOWLEDGEMENT
The work described in this paper is supported by
three research grants from the National Basic Re-
search Program of China (No. 2012CB725403),
the National Natural Science Foundation of China
(51178032, 51338008), the Fundamental Research
Funds for the Central Universities (2013YJS047), and
also supported by World Capital Cities Smooth Traffic
Collaborative Innovation Center.
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A Simulation-Based Dynamic Traffic Assignment Model With Combined Modes

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