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Intelligent urban freight transportation

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Intelligent urban freight transportation

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INTELLIGENT URBAN FREIGHT TRANSPORTATION

by

Yanbo Zhao

A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)

August 2017

Copyright 2017 Yanbo Zhao

Table of Contents
List of Tables ................................................................................................................................. III
List of Figures ............................................................................................................................... IV
Abstract ........................................................................................................................................... V
Chapter 1: Introduction ................................................................................................................... 1
Chapter 2: Positive Train Control with Dynamic Headway ............................................................ 5
2.1 Introduction ...................................................................................................................... 5
2.2 Dynamic Headway System Overview .............................................................................. 7
2.3 Train Dynamic Headway Selection .................................................................................. 8
2.4 Train Dispatching with Dynamic Headway ................................................................... 17
2.5 Evaluation Result ........................................................................................................... 26
2.6 Conclusion...................................................................................................................... 29
Chapter 3: Traffic Signal Control with Truck Priority .................................................................. 30
3.1 Introduction .................................................................................................................... 30
3.2 System Overview ........................................................................................................... 34
3.3 Problem Formulation ..................................................................................................... 35
3.4 Evaluation Results .......................................................................................................... 53
3.5 Conclusion...................................................................................................................... 59
Chapter 4: Routing of Multimodal Freight Transportation ........................................................... 60
4.1 Introduction .................................................................................................................... 60
4.2 Problem Formulation ..................................................................................................... 64
4.3 Solution Technique using COSMO ................................................................................ 72
4.4 Experimental Analysis ................................................................................................... 83
4.5 Conclusion...................................................................................................................... 89
Chapter 5: Conclusion and Proposed Research Directions ........................................................... 90
References ..................................................................................................................................... 92

III

List of Tables

Table 2.1: Train dynamics in evaluation ....................................................................... 28
Table 2.2: Evaluation results of different headway polices .......................................... 28
Table 3.1: OD matrix in evaluation (Unit: trips/hour) .................................................. 56
Table 3.2: Evaluation results (3% Truck) ..................................................................... 57
Table 3.3: Evaluation results (10% Truck) ................................................................... 58
Table 3.4: Evaluation results (20% Truck) ................................................................... 58
Table 4.1: Route characteristics and traffic conditions of simple example .................. 78
Table 4.2: Baseline demand of destinations .................................................................. 86
Table 4.3: Evaluation of different traffic conditions and loads .................................... 88

IV

List of Figures

Figure 2.1: Positive train control with dynamic headway ................................................ 7
Figure 2.2: Headway control loop in a fixed block system ............................................ 10
Figure 2.3: Headway control loop in PTC ...................................................................... 11
Figure 2.4: Acceleration profiles during worst-case stopping scenario ......................... 12
Figure 2.5: Numerical procedure of headway calculation .............................................. 16
Figure 2.6: Headway policy switch due to communication loss .................................... 17
Figure 2.7: Dynamic dispatching solution approach ...................................................... 23
Figure 2.8: Sample track network .................................................................................. 24
Figure 2.9: Dispatching conflict cases............................................................................ 25
Figure 2.10: Selected track network region ...................................................................... 26
Figure 3.1: Architecture of proposed truck signal priority system. ................................ 35
Figure 3.2: COSMO control approach for baseline signal generation ........................... 42
Figure 3.3: Optimization algorithm for multiagent signal control with COSMO .......... 49
Figure 3.4: Active priority cases .................................................................................... 51
Figure 3.5: Selected road network .................................................................................. 55
Figure 3.6: Traffic simulator .......................................................................................... 55
Figure 3.7: Desired acceleration rates of car model (left) and truck model (right) ........ 56
Figure 4.1: Service graph and traffic network ................................................................ 65
Figure 4.2: Framework of proposed freight routing system .......................................... 72
Figure 4.3: COSMO iterative approach for freight routing ........................................... 75
Figure 4.4: Performances of different load balancing algorithms .................................. 79
Figure 4.5: An example road network simulation model ............................................... 84
Figure 4.6: Region of study ............................................................................................ 85
Figure 4.7: Load balancing time increasing of enumeration method ............................. 87
Figure 4.8: Traffic conditions ......................................................................................... 88

V

Abstract

Efficient freight movement is an essential factor not only in urban transportation
but also in social and economic development as well as environmental considerations.
The growth of worldwide trade will significantly increase traffic congestion and air
pollution due to existing congestion in current urban transportation infrastructures
especially in metropolitan areas with major ports such as Los Angeles/Long Beach where
there is a high concentration of both freight and passenger traffics that share the same
infrastructures. In this research, we address some approaches to improve efficiency and
safety of multimodal freight transportation infrastructures by exploring availability of
advanced technologies such as active communication, fast simulation, connected vehicle,
and computational optimization tools, including a dynamic headway system for positive
train control based on active communication to improve rail track efficiency and safety,
an adaptive signal light control system with truck priority to reduce the delay and air
emissions of all vehicles involved at signalized intersections, as well as a multimodal
freight routing system based on co-simulation optimization to reduce freight transport
cost.
In this research, we propose a dynamic headway system for PTC based on active
communications, which we integrate with a dynamic dispatching model in order to
improve track capacity and safety in railway operations. Safety, capacity, and timely
schedules are some of the most crucial objectives in railway operations. Positive train
control (PTC) is a concept whose goal is to improve the safety and efficiency of railway
VI

operations by using advanced information technologies. Information technologies such as
active communications enable the use of a dynamic headway policy, which can increase
the track capacity and improve dispatching efficiency in addition to improving safety.
We develop, analyze and evaluate a traffic light control system for signalized
intersections that takes into account the differences in dynamics and characteristics
between trucks and passenger vehicles. In some cases, giving priority to trucks at
signalized intersections will benefit all vehicles because of elimination of extra delays
generated by slow trucks. In addition, it will lead to lower pollution emissions because of
reducing the number of stop and go maneuvers of higher emission trucks. Instead of
simple mathematical models we use a co-simulation approach that involves a more
accurate simulation model together with an optimization and control procedure to
generate the baseline traffic light sequences for multiple signalized intersections in a road
network. The proposed traffic light control system combines an active control strategy
with a signal priority action decision model to minimize vehicle travel delays by timing
the baseline traffic signals to give priority to trucks when it is to the benefit of all vehicles
involved.
We also present a multimodal freight routing system with hard vehicle availability
and capacity constraints based on a hierarchical COSMO (CO-Simulation Optimization)
approach dealing with optimal control of complex and dynamical systems. The
simulation layer provides the state and cost estimations and predictions for the upper
optimization layer in which we develop a novel load balancing methodology to speed up
the algorithm. The complexity and dynamics of multimodal freight transportation
networks make the optimum routing of freight demand a challenging task. Route
VII

decision-making in a dynamical and complex urban multimodal transportation
environment aims to minimize a certain objective cost relying on the accurate prediction
of the traffic network states and the estimation of the route costs that are not readily
available.
We demonstrate the effectiveness of the proposed systems and approaches by
evaluating them with simulation models and platforms. The simulation results of a rail
network in southern California show the reductions of travel delays and travel time when
using the dynamic headway. The proposed traffic light control system has been evaluated
using a road network adjacent to the twin ports of Long Beach/Los Angeles. The
evaluation results show consistent improvements in reducing the truck traffic delays (5%
to 10%) and the truck stops without satisfying passenger vehicles whose travel time have
also been reduced. A simulation testbed consisting of a road traffic simulation model and
a rail simulation model for the Los Angeles/Long Beach Ports regional area has been
developed and applied to demonstrate the efficiency of the proposed co-simulation
multimodal routing approach in reducing delivery cost and algorithm CPU time.

1

Chapter 1:
Introduction

Efficient freight movement is an essential factor not only in urban transportation but also
in social and economic development as well as environmental considerations. The growth of
worldwide trade will significantly increase traffic congestion and air pollution due to existing
congestion in the urban transportation infrastructure especially in metropolitan areas with major
ports such as Los Angeles/Long Beach where there is a high concentration of both freight and
passenger traffic that share the same infrastructure. The developments of advanced technologies
such as communication, simulation, connected vehicles, and computational optimization tools
make the intelligent control of urban freight transportation possible. In this research, we will
explore the availability of these technologies in improving the efficiency, safety and sustainability
of urban freight transportation network.
This research starts from the railway mode, a dynamic headway system for positive train
control based on deployment of active communication is proposed. The growing demand for
railway capacity to move people and freight puts a lot of pressure on the existing railway
infrastructure to be more efficient and safer. Efficiency of railway implies shorter travel times,
predictable schedules, higher track capacity and reduction of congestion delays under the
constraint of safe operations. Higher capacity can be achieved with higher train speeds and shorter
headways. On the other hand, safety can be improved at the expense of lower capacity by
reducing train speeds and conservative headways that provide the train operator sufficient time to
stop the train in case of emergencies. Positive train control (PTC) aims to address these two
2

conflicting objectives by using advanced technologies [1], [2]. PTC systems employ wireless
communication and global positioning system (GPS) technologies to properly monitor train
separation or headways, avoid possible collisions, enforce speed limits and improve the safety of
wayside workers [3]. Active communications in a PTC system will enable the frequent exchange
of information between control center and trains regarding train dynamics and characteristics in
addition to speed and location for the purpose of preventing potential train collisions [4]–[7]. Such
detailed information can be utilized to come up with smaller yet safer headways by taking into
account leading train location, speed, deceleration/acceleration capabilities, condition of the tracks
etc. In such an environment the train control system receives information from the dispatching
center, wayside devices and leading train regarding speed limits, speed, location and
acceleration/deceleration capabilities and intentions for slowing down or braking to a stop. It uses
this information to compute its optimal safe headway from the leading train ahead or upcoming
track obstacle [4]. Since such headway is changing with time, it is referred to as dynamic
headway.
Then the focus of this research turns to the road mode, a traffic light control system giving
priority to trucks is proposed with the development of advanced communication and connected
vehicle techniques. Most current traffic light controllers generate the signal sequences based on
approaching traffic flows and by treating all vehicles the same. However, in areas where the
volume of trucks is relatively high, the approach of treating all vehicles the same may not be the
best way for signal control as trucks have a detrimental impact on overall traffic flows because of
their slow dynamics, large sizes and large turning radius. A heavy truck takes a longer distance
and time to stop before a red light, accelerate and cross an intersection due to its slow
deceleration/acceleration rates, causing extra traffic delays [30-31]. In addition, trucks consume
3

more fuel and generate more air pollution compared to passenger vehicles. With new sensor,
vehicle-to-vehicle communication and GPS technologies, a traffic light controller could be
informed of the type of approaching vehicles and their characteristics (size, position, dynamics,
speed etc.) [32-34] and take this additional information into account in traffic light controlling.
Meanwhile, the availability of these new technologies offers an opportunity for the development
of improved traffic light control systems, which can distinguish differences between trucks and
passenger vehicles in order to reduce traffic delays, improve intersection safety and lower
pollution emissions.
Finally, we formulate and solve a dynamical multimodal freight routing problem by
exploiting the availability of powerful computational software tools. One of the biggest challenges
for freight transport efficiency in a multimodal environment arises from the fact that the same rail
and road networks are used for moving people in addition to goods which leads to non-
homogeneous traffic. This non-homogeneity has a detrimental impact on the transportation
system performance because of the differences of vehicle sizes and dynamics between passenger
and freight transport. The freight vehicles such as freight trains and trucks take longer distances to
stop and time to accelerate from a stopping position, consume more fuel and generate more air
pollution compared to passenger vehicles. The situation becomes even worse during incidents and
disruptions that lead to network changes such as road or railway closures that require rapid
response and distribution of freight traffic across the multimodal network. Without efficient
management of the multimodal freight transport, the transportation network will face severe
capacity shortages, inefficiencies, and route load imbalances across the network in space and time.
Therefore a more efficient routing system could save transport costs and contribute to
sustainability and efficiency of the entire urban transportation network.
4

In Chapter 2, the dynamic headway system for PTC is described. Chapter 3 introduces the
design and evaluation of traffic signal control system with truck priority. In Chapter 4, we
demonstrate how to use co-simulation optimization approach to solve the multimodal transport
routing problem. We present the conclusion and possible future research directions in Chapter 5.

5

Chapter 2:
Positive Train Control with Dynamic Headway

2.1 Introduction
The growing demand for railway capacity to move people and freight puts a lot of
pressure on the existing railway infrastructure to be more efficient and safer. Efficiency of railway
implies shorter travel times, predictable schedules, higher track capacity and reduction of
congestion delays under the constraint of safe operations. Higher capacity can be achieved with
higher train speeds and shorter headways. On the other hand, safety can be improved at the
expense of lower capacity by reducing train speeds and conservative headways that provide the
train operator sufficient time to stop the train in case of emergencies. Positive train control (PTC)
aims to address these two conflicting objectives by using advanced technologies [1], [2]. PTC
systems employ wireless communication and global positioning system (GPS) technologies to
properly monitor train separation or headways, avoid possible collisions, enforce speed limits and
improve the safety of wayside workers [3]. Active communications in a PTC system will enable
the frequent exchange of information between control center and trains regarding train dynamics
and characteristics in addition to speed and location for the purpose of preventing potential train
collisions [4]–[7]. Such detailed information can be utilized to come up with smaller yet safer
headways by taking into account leading train location, speed, deceleration/acceleration
capabilities, condition of the tracks etc. In such an environment the train control system receives
6

information from the dispatching center, wayside devices and leading train regarding speed limits,
speed, location and acceleration/deceleration capabilities and intentions for slowing down or
braking to a stop. It uses this information to compute its optimal safe headway from the leading
train ahead or upcoming track obstacle [4]. Since such headway is changing with time, it is
referred to as dynamic headway. The dynamic headway should also account for possible loss of
communications due to bad weather or other failures and gracefully and safely revert to a more
conservative headway without putting any of the trains into a dangerous situation. The
performance and reliability of the PTC system with a dynamic headway depends on the reliability
of the active communication system.
In this chapter, we propose a dynamic headway system for PTC which improves safety
and increases track efficiency. It employs an active communication system and is designed
without compromising on reliability, safety and performance. The distinct features of the
proposed system are: 1) A dynamic headway policy based on active communication between the
control center and trains that lead to much smaller headways than existing ones that are based on
brick wall scenarios and fixed-block policies. 2) A backup headway switching policy in case of
loss of communications that gracefully increases headway to the new situation without sacrificing
on safety. 3) A train dispatching system that utilizes the dynamic headway as well as the backup
headway in case of communication failure in order to improve track capacity. The contribution of
the chapter is the development of a dynamic headway policy that is integrated with a train
dispatching system in order to improve train capacity and reduce delays without compromising
safety.
This chapter is organized as follows: In Section 2.2, we introduce the design of the
proposed dynamic headway system; in section 2.3 we present the dynamic headway policy. The
7

impact of headway selection on track capacity is presented in Section 2.4. The proposed system is
demonstrated using a simulated track network in Southern California and the results are presented
in Section 2.5. In Section 2.6 we present the conclusions.
2.2 Dynamic Headway System Overview
In this section, we present an overview of the proposed dynamic headway system and how
it differs from existing systems.

Figure 2.1: Positive train control with dynamic headway

In custom train control systems (without active communication), trains travel along tracks
by obeying wayside signals sent through a track circuit. A discrete fixed block system is used to
keep moving trains apart from each other in order to have enough time to stop in case of
emergencies. The track is divided into fixed physical block sections and a train is not permitted to
enter a front block unless the block is not occupied [8], [9].Wayside signals positioned at
appropriate discrete locations notify the train operator whether the front block is occupied or not.
Future train control systems such as PTC systems can employ active communications as shown in
Figure 2.1, in order to have a frequent bidirectional wireless communication between each train
8

and the dispatching center. Such a technology allows each train to know at each instant of time
the position, speed, acceleration/deceleration characteristics and intentions of the leading train that
shares the same track. This information enables each train to choose its headway dynamically
instead of assuming a static more conservative headway based on a worst case scenario associated
with a fixed-block system. Another improvement in reducing the train headway is the fact that
one of the features of PTC is to intervene in case of emergencies if the train operator fails to act
within reasonable time.
The architecture of the PTC system that uses the proposed dynamic headway consists of
the following three layers: 1) Dispatching layer: In this layer the trains are assigned routes along
the rail network by taking into account their origin and destination as well as their expected
speeds and headway policies. 2) Dynamic headway layer: Each train uses communicated
information from the leading train in the same track and the control center in order to calculate its
dynamic headway. 3) Train physical layer: The train control system maintains the selected
headway, follows speed limit restrictions and responds to commands from the train operator. It
also contains a collision avoidance system whose purpose is to aid the train operator or intervene
in case of emergency in order to prevent a collision. In the following section, we present the
calculation of the dynamic headway and then show how it can be integrated with a dispatching
model.
2.3 Train Dynamic Headway Selection
The headway between two trains is defined as the distance from the front of the following
train to the front of the leading train. For safety purposes, the size of the headway is chosen to be
large enough in order to provide sufficient time and space for the train operator to slow down and
stop the train without a collision. This situation is very similar to that of driving vehicles on
9

roadways except for a major difference: a train operator is not able to see the front train or an
upcoming obstacle on the track, and yet have enough time and space to avoid a collision, due to
the high headways used. Therefore the train operator has to rely on control signals and other
notification signs to decide when and where to slow down or brake to a full stop.
In the early days of railway operations, there was no effective way of detecting the
positions of trains in real time with sufficient accuracy. A simple control method called timetable
policy was adopted to prevent collision by ensuring that there was sufficient headway between
trains [8] and trains traveled according to a strict schedule [9]. The timetable headway was
relatively large putting a limitation on capacity as capacity is inversely proportional to the train
headway. In subsequent years, the fixed block systems were developed and widely applied in
railway operations. The headway size in this system depends on the division of each track into
blocks as well as on the worse-case stopping scenario assumed. For example, a worst-case
scenario may be one where the leading train stops instantaneously at any point in time [10]–
[11][12]. This scenario is referred to as the brick wall scenario because of the fact that the front
track segment occupied by another train can be viewed as a brick wall obstacle by the following
train. It is also a conservative scenario as in practice the obstacle ahead is a moving train, which
takes time and space to come to a full stop. In this case the headway is fixed in terms of blocks by
using wayside signals to alert the train operator to enter or not enter an upcoming block (as Figure
2.2).
10

Figure 2.2: Headway control loop in a fixed block system

For the dynamic headway implementation in PTC we have the following two control
loops: (1) driver control loop; (2) headway selection loop. The driver control loop determines the
train acceleration/deceleration operations based on track speed limits and desired headway. The
headway selection loop calculates the dynamic headway to be followed by the train by taking into
account the following information: 1) communicated characteristics and acceleration/deceleration
intentions of the leading train (target train to follow) based on an active communication system; 2)
its own characteristics and status; 3) condition of tracks, communication delays, train operator
reaction times etc. Since the characteristics of the trains involved vary with time so is the headway
and for this reason is referred to as dynamic headway policy. Figure 2.3depicts these two loops.
The headway selection loop, assumes a worst-case stopping scenario in order to find the
11

minimum headway for avoiding collision. The scenario assumes that the leading train performs an
emergency stopping maneuver using a maximum braking profile (emergency braking) and the
following train responds after a certain delay by applying its service braking profile (as Figure
2.4). In the following subsection we use this scenario to generate the dynamic headway model and
policy.

Figure 2.3: Headway control loop in PTC

3.3.1 Basic Dynamic Headway Model
We use Figure 2.4 to compute the minimum distance between the two trains in order to
avoid collision as a result of the deceleration profiles shown in Figure 2.4.
12

a
t
Following Train
Leading Train
a
imax
a
jmax
t
ia
t
ja t
jb
t
jc
t
istop
t
jstop
t
ib
t
jd

Figure 2.4: Acceleration profiles during worst-case stopping scenario

The leading train i and following train j are moving in the same direction on same track
segment k at constant speeds (V
i
and V
j
, ft/sec). At t = 0 (sec) the leading train performs an
emergency stopping maneuver with the maximum deceleration rate a
imax
(ft/sec
2
) and sends a
message to the following train of its intention. t
ia
is the time when the leading train starts
deceleration after a brake delay t
ibrake
and t
ib
is the time when the leading train achieves its
maximum deceleration rate. The following train receives the message that the leading train is
decelerating at time t
ja
.it receives the emergency message from the leading train. The train
operator responds with a delay t
jdriver
to the emergency message at time t
jb
by applying the brakes
for a service deceleration braking a
jmax
. The assumption of service versus emergency
deceleration is again done for the purpose of been conservative. After a brake delay t
ibrake
, the
train j begins to decelerate at time t
jc
and builds its full service deceleration at time t
jd
[16], [17],
[18]. The time t
istop
, t
jstop
is the time that the leading and following trains come to a full stop
13

respectively. Based on the above, we can obtain the deceleration rates of the two trains a
i
(t) and
a
j
(t) in this worst-case stopping scenario as follows.
adjust
max
(0) if
( ) (0) ( ) if <
if
i ia
i k i i ia ia ib
i ib
a t t
a t a a jerk t t t t t
a t t
 

     




(2.1)

adjust
max
(0) if
( ) (0) ( ) if <
if
j jc
j k j j ja jc jd
j jd
a t t
a t a a jerk t t t t t
a t t
 

     




(2.2)
where
adjust
67.2
32.2sin
kk
k
aG
R


brake
max
(0)
ia i
ii
ib ia
i
tt
aa
tt
jerk




driver comm driver jb ja j j
t t t t t    

brake comm driver brake
max
(0)
jc jb j j j
jj
jd jc
j
t t t t t t
aa
tt
jerk
    



a
kadjust
(ft/sec
2
) in (2.1) and (2.2) is used to compensate for the impact of track conditions of
segment k (track grade G
k
and curvature radius R
k
) on braking rates according to [19]; jerk
i
and
14

jerk
j
(ft/sec
3
) are defined as the derivatives of accelerations of the leading and following train
respectively, [20]; t
ibrake
and

t
jbrake
is the response time of the brake system of each train
respectively; t
comm
is the delay of the active communication system; t
jdriver
is the driver reaction
time for the following train. In order to prevent collision the distance between the two trains
should be always greater than the leading train length. The minimum distance between the two
trains in order to avoid collision under the worst case stopping scenario presented above can be
generated by solving the following problem:
 
 
stop
00
stop stop
stop
00
stop stop
min (0)
. . ( ) (0) ( ) ( )
( ) if
( )
( ) if
( ) if
()
( ) if
i j i
t
i i i
i
i i i
t
j j j
j
j i j
x
s t x t x D t D t L
V a d d t t
Dt
D t t t
V a d d t t
Dt
D t t t


  
  
   


















(2.3)
where D
i
(t) and D
j
(t) are the covered distances of leading train and following train respectively;
L
i
(ft) is the length of leading train. The problem can also be written as
 
min (0) max ( ) ( ), 0 +
j i i
x D t D t L 
(2.4)
for all t > 0. An explicit expression for min x(0) can also be derived in terms of the above
integrals.
The calculation of the dynamic headway based on the worst-case stopping scenario of
Figure 2.4 relies on the presence of an active communication system to communicate the
required information. A safety concern is whether a temporary interruption or failure of the
15

active communication system will put any of the trains in a dangerous situation where the train
operator or the PTC system will not be able to prevent a possible collision. In our approach we
account for such a failure as follows: If one train stops receiving information from the active
communication system after a specified time threshold t
fail
(sec), it automatically assumes that a
failure has occurred and begins to decelerate till a longer safety headway is reached as described
in next subsection. One option is to accommodate for the time threshold t
fail
by modifying the
dynamic headway of (2.4) as follows: the dynamic headway H
i,j,k
in terms of distance in units of
space is modified as
H
i,j,k
=minx(0)+L
sm
+V
j
t
fail
(2.5)
and in terms of time headway H
i,j,k
i.e. the time required to cover the headway distance at
constant speed V
j
as
,,
, , fail
min (0)
i j k
sm
i j k
jj
H
xL
ht
VV

  
(2.6)
The margin L
sm
(ft) is an additional distance to compensate for the impact of other
unknown factors especially the measurement error of train positioning and irregular track friction
force. In this paper, we use equations (2.5) and (2.6) to compute the space headway and time
headway respectively. The numerical headway calculation procedure is shown in Figure 2.5
where T
s
is the time step of calculation.
Dynamic Headway Calculation (Train i, Train j, Segment k)
0 t  ,
,,
0
i j k
D 
While ( ) 0
j
vt 
Update the deceleration rates using equations (2.1)-(2.2) and travelled distances of the
two trains at time t;
16

Compute ( ) ( )
ji
D t D t  ;
If ( ) ( )
ji
D t D t  > 0 and
,,
( ) ( )
j i i i j k
D t D t L D    then
Set
,,
( ) ( )
i j k j i i
D D t D t L   
End If
Update
s
t t T 
End While
Return
, , , , fail i j k i j k j sm
H D V t L   
and
, , , ,
( ) /
i j k i j k j
h H t V 

Figure 2.5: Numerical procedure of headway calculation

3.3.2 Headway Policy Switch during Loss of Active Communication
The dynamic headway selection primarily depends on the reliability of the
communication links. If the communication system fails, the headway policy should be
gracefully changed to a more conservative policy, so that a train operator or the PTC system can
handle all likely possible emergency situations. The fixed block can be activated as a backup
system provided that the track circuit and other fixed block related devices are still in place and
available. Suppose two trains are following each other with a dynamic headway H
dyn
when the
following train detects a loss of communication at time t
fail
. It starts decelerating using its service
braking profile as in Figure 2.4 in order to increase the distance to the leading train (see Figure
2.6, the used variables are defined in the text associated with Figure 2.4). At the same time it
notifies the control center, which activates the wayside signals and the backup system of fixed
block headway policy. If the following train has already reached the higher headway H
fixed
corresponding to the fixed block policy at t
jfinish
the two trains will continue operating with fixed
block headway (case 1 in Figure 2.6). Otherwise, if the signals associated with the fixed block
failed to be activated, the following train will come to a full stop at t
jstop
until the communication
connection is reestablished (case 2 in Figure 2.6). When active communication links are
17

reestablished, the transitions back to the shorter dynamic headway can be performed in a very
similar manner.

a
t
Following Train
a
fmax
t
fail t
jb
t
jc
t
jstop t
jd
Headway
t
Case 1
H
dyn
H
fixed
t
fail t
jb
t
jc
t
jstop
t
jfinish
Case 2

Figure 2.6: Headway policy switch due to communication loss

2.4 Train Dispatching with Dynamic Headway
The dynamic headway alone will not bring the expected benefits unless it is properly
utilized in the train dispatching and train network operations. In this section we develop a train-
dispatching scheme that uses the dynamic headway. The goal of train dispatching is to route
18

trains from their origin to destination stations safely. Efforts to solve the train dispatching
problem involves formulating the problem as a mathematical programming problem and
generating the optimal dispatching rules based on train and track network characteristics[21]-
[27]. Genetic algorithm [21][24], branch and bound algorithm [22][26], and greedy heuristics
[25][27] are typical algorithms used to solve the dispatching problem. The branch and bound
algorithm uses the branch & bound procedure to reduce the search space. It guarantees the
calculation of the optimal solution when the train paths are given. However, its search time
increases exponentially when the track network gets larger and/or the number of dispatched
trains increases leading to computational times that limit its practical application.. . Genetic
algorithm is a heuristic search method that routinely searches for new solutions till it finds the
optimum one. Even though it can not guarantee that the optimum solution found is the globally
optimum one it is easy to implement. The genetic algorithm approach however suffers from the
constraint of dimensionality as it cannot handle large-scale problems. Greedy heuristic
algorithms keep evaluating alternative neighbor solutions iteratively in order to find a better
solution. The computing time of greedy algorithms is more reasonable compared to branch and
bound and genetic algorithms for large-scale problems but the solution may be attracted to a
local optimum. Computer simulation is also an effective approach to study train dispatching
[28][29]. In these past efforts, the headway assumed is usually fixed time interval or fixed
number of track segments.
In this section, we propose a train dispatching approach based on the dynamic headway
policy presented in the previous section. The inputs to the train-dispatching problem include the
dispatched train characteristics, track network topology, and active communication distribution
information. The train characteristics include information such as braking system characteristics,
19

maximum speed, length, origin and destination station, planned departure time, and planed dwell
time at intermediate stations, etc. The track network topology is denoted by G = (N, S), where N
is the set of track nodes and S is the set of track segments. A node has no length and denotes the
intersection of track segments. A track segment is the track part connecting two nodes. The
output for the train dispatching is a set of train paths and detailed schedules for each train. One
train path is a sequence of ordered track segments connecting its origin and destination node.
One train schedule is an instruction timetable of train movement, e.g. the arrival and departure
time for the train at all the segments in the train path. The optimum train schedule is found as the
solution of a certain optimization problem formulated and solved as explained below. The
dispatching objective is to minimize the total required travelling time for all dispatched trains to
move from their origin to destination stations. This objective is equivalent to minimizing the sum
of weighted arrival times of all trains to their destination station segment s
i
d
. This objective
function can be expressed as:
,
min
d
i
i
is
iT
wa


(2.7)
subject to the constraints:
,
o
i
o
i
is
ad  for iT  (2.8)
, , , , i k i k i k i k
d a mr md    for ,
i
i T k p    (2.9)
1
1
,,
qq
ii
q
i
i
i s i s
s
L
da
v



for
1
, ,
qq
i i i
i T s s p

   (2.10)
For , , ,and ,
i j c
i j T i j k p p k S       ,
20

, , , , , , j k i j k i k i j k
a Mx a h   
(2.11)
 
, , , , , ,
1
i k i j k j k j i k
a x M a h    
(2.12)
For , , ,and ,
i j c
i j T i j k p p k S       ,
, , , , j k i j k i k
a Mx d 
(2.13)
 
, , , ,
1
i k i j k j k
a x M d   
(2.14)
 
,,
0,1
i j k
x 

where
i, j are the indices of trains, k is the index of segment;
T is the set of trains to be dispatched;
ω
i
is the weight of train i
a
i,k
and d
i,k
is the arrival and departure time of train i in segment k respectively;
s
i
o
and s
i
d
is the origin and destination segment of train i respectively;
d
i
o
is the planned departure time of train i;
P
i
is the set of all segments in the path of train i i.e. a sequence of ordered track segments
connecting the origin and destination node of train i;
mr
i,k
is the minimum travel time for train i to pass a track segment k;
21

md
i,k
is the planned dwell time for train i on segment k;
S
c
is the set of segments covered by the active communication system;
h
i,j,k
and h
j,i,k
is the minimum safety headway between two trains i and j and j, i
respectively at segment k. They are derived using the worse-case stopping scenario described in
Figure 2.6 and do not depend on time;
M is a large positive design number and x
i,j,k
is a binary variable that takes the following
values:. If train i passes track segment k before train j, x
i,j,k
= 1; if train j passes track segment k
before train i, x
i,j,k
= 0; the variable x
i,j,k
is meaningful only when
,and
ij
i j k P P   
.
Inequality (2.8) ensures the departure time constraints: each train is not available and
cannot leave its origin node earlier than its planned departure time.
Inequality (2.9) and (2.10) represent the travelling time constraints. A minimum travel
time mr
i,k
is required for each train i to pass a track segment k. The minimum travel time can be
computed using the minimum available train speed and the segment length. The maximum
available train speed at track segment k is the smaller speed between the maximum train
operation speed mv
i
and segment speed limit v
k
. In addition, a planned dwell time md
i,k
for train i
is required at some segments in its path due to railway application requirements, e.g. interlock
device operation, boarding and unloading. Constraint (2.9) guarantees enough time for each train
i to pass each segment in its path P
i
that should be greater than the sum of the minimum travel
and dwell time. Inequality (2.10) guarantees enough time for each train to pass adjacent
segments s
i
q
, s
i
q+1
in its path P
i
. It defines the minimum time interval for train i to clear the
intersection node of adjacent segments in P
i
.
22

Inequalities (2.11)-(2.14) describe the safety headway constraints to be followed by trains
in the same track travelling in the same direction. e.g. the same track block (either virtual
dynamic block in dynamic headway policy or physical block in fixed block) cannot be occupied
by more than one train. The constraints (2.11) and (2.12) guarantee that there is enough time
headway between trains i and j if two trains i and j are travelling in a segment k within active
communication coverage. h
i,j,k
and h
j,i,k
are derived from the headway selection model in section
III and train speed. The constraints (2.13) and (2.14) guarantee that if two trains i and j are
travelling in a segment where there is no active communication signal, then there is at least one
free track segment between trains i and j.
The dispatching optimization model (2.7)-(2.14) is a mixed integer programming (MIP)
problem. It is clear that the use of the dynamic headway affects the variables a
i,k
and d
i,k
which
lead to a lower cost etc. The time it takes to calculate the optimal train schedule grows
exponentially with the number of trains and the size of the track network, making an exact
solution impractical. The MIP model could find the optimal schedule if the train paths are given.
We use a heuristic approach to search for the optimal train paths and schedule that
involves the use of a genetic and branch & bound algorithm and is depicted in the flowchart of
Figure 2.7. The proposed approach involves two steps: the preprocessing and optimization steps.
The purpose of the preprocessing step is to calculate the following variable values: The segments
covered by active communication are defined according to the given base station locations and
track geometry. The minimum travelling time for each train at each segment is computed based
on the available maximum train speed at the segment, segment length and planned train dwell
time. All available train paths for a given train are specified using the origin and destination
nodes, as well as the network topography.
23

Start
Randomly generate the initial
dispatching solution
Input Trains Track Network
Base Station
Locations
Pre-Processing
Output active communication coverage area,
minimum traveling time,
possible paths for trains
Evaluate the MIP model with
Branch and Bound algorithm
Reach optimal or nearly
optimal solution?
Modify the solution by
reproduction, crossover and
mutation
Output
optimal paths
and schedule

Figure 2.7: Dynamic dispatching solution approach

The optimization step involves the use of a genetic algorithm to solve the optimization
problem. The first step of the genetic algorithm is to define the representation of the population.
In our strategy, the population is defined as the set of uniquely numbered paths for the
dispatched trains. For example in a sample of 12 miles length track network shown in Figure 2.8
there is a total of eight possible paths between stations A and B that are numbered from 1 to 8.
Suppose we have four trains to dispatch from station A to B, a representation of the path
population might be (1, 3, 5, 8), which indicates that the four trains will travel along the path 1, 3,
5, and 8 respectively. Given a population representation that defines a solution of train paths, the
MIP dispatching problem could be solved to evaluate the fitness of this solution whose objective
24

is to minimize the travelling time by searching for optimal train orderings in given paths. We use
the branch and bound algorithm to evaluate the fitness of a given population by solving MIP.

1 2
3
4
5
6
7
8 9 10 11 12 13 14
15
17
16
18
19
20
21
22
23
24
25
26
27
28
A
B

Figure 2.8: Sample track network
In summary, the solution strategy is first generating the initial population randomly. Then
evaluate its fitness by solving the MIP problem using the branch and bound method. If the
termination condition is satisfied, the dispatching results are the output of the algorithm.
Otherwise, a new population is generated by reproduction, crossover and mutation operations in
the genetic algorithm.
This dispatching model works well in the case where all trains sharing the same track
segment are travelling in the same direction or with trains traveling in different directions using
distinct segments in the track network. The model cannot guarantee prevention of deadlocks
when trains travelling in opposite directions share the same track segments. Avoiding deadlocks
in this case is hard to formulate in the form of mathematical constraints, therefore a deadlock
prevention mechanism is required to handle the opposite direction dispatching. A deadlock is a
situation that occurs when trains come to an indefinitely waiting state due to the track resources
conflicts [28]. A deadlock state arises when a conflict cannot be resolved. The possible conflicts
during train dispatching are shown in Figure 2.9 [29] and explained below. These conflicts do
25

not include unusual rail operation failures such as abrupt track damage or PTC system
breakdown.
1 2
3
4
5
6
7
8 9 10 11 12 13 14
15
17
16
18
19
20
21
22
23
24
25
26
27 28
A
B
Case 1
Case 2 Case 3

Figure 2.9: Dispatching conflict cases
Case 1 is the situation where multiple trains request the use of the same track at the same
time from same direction. In this situation we can prevent the deadlock by establishing a certain
priority protocol based on some optimal passing sequence. Several algorithms could be used to
determine the train passing sequence: first-in-first-out (FIFO), first-out-first-in (FOFI), and based
on the total travelling time optimization rule. If the total travelling time of all possible orderings
is evaluated, the optimal train sequence could be determined, using the MIP model. Case 2 is the
situation where two trains are travelling in opposite directions in a single track. In order to
prevent this deadlock state, we need to assign different paths or let the trains pass one by one at
different times. Case 3 is the situation where a train has to pass a track segment or stop in a
segment when another train is stopping at the same location, a situation that may arise at a station.
The deadlock state can be avoided if the stopping train could move to the front track. However,
if the stopping train has operational failures a deadlock will also happen. If there is an available
free path to the destination station for each involved train and the destination station has
additional track for them to stop, a deadlock will be avoided. The free status of one path for a
train means all front trains in this path are travelling in the same direction. However this
26

deadlock prevention strategy is very conservative. In order to improve the dispatching efficiency
of opposite travelling we use a feasible checking procedure to check whether a train can use a
segment, an algorithm referred to as the move forward check algorithm [29]. After the feasible
checking, there may be multiple available paths for opposite travelling trains. The total travelling
time of different available options will be evaluated and the option with minimum total travelling
time will be selected. The MIP model and solving procedure can be used in searching for the
optimum option.
2.5 Evaluation Result
We apply the proposed dynamic headway policy on a track network of Union Pacific
Alhambra line simulated using the Arena simulation software. The selected track network is from
Los Angeles Transfer Container Facility (LATC) to Downtown Pomona and the total length is
about 30 miles (Figure 2.10). Two types of trains are considered, freight and passenger trains,
whose characteristics are shown in Table 2.1.

Figure 2.10: Selected track network region
27

Four different daily scheduling scenarios are evaluated from low traffic to high traffic
demand. The average number and type of trains per day dispatched from LATC to Pomona, and
vice versa for each scenario 1 to 4 are listed below. The train arrivals are assumed to follow a
Poisson processes with the daily average arrival rates as specified above.
1) 5 passenger trains and 3 freight trains
2) 10 passenger trains and 5 freight trains
3) 15 passenger trains and 10 freight trains
4) 20 passenger trains and 15 freight trains
We compare the performance of the network based on our dynamic headway policy with
that based on the fixed headway policy for all the scenarios under consideration. For fixed
headway policy, the track network has 32 blocks whose lengths are from 0.4 mile to 2 miles based
on the network topology. In the fixed headway policy each block can only be occupied by at most
one train. In the dynamic headway policy, the algorithm of section 2.3 decides the headway
distance between trains. The dispatching algorithm presented in Section 2.4 is used to determine
the train routes for all scenarios. Table 2.2 shows the tested average delays and traveling time for
all scenarios where the delay is the difference between tested traveling time and the free traveling
time, i.e. the traveling time when there are no other trains in the same network. The table shows
clearly the impact of dynamic headway on the average delay and travel time compared to the
fixed block headway. In all cases, both the average delay and traveling time of trains are
improved. The reduction of average delay is at least 57% while the average traveling time is
reduced by more than 35% among all simulated scenarios. The improvements are much more
28

pronounced when there are more train arrivals, which suggests that the dynamic headway will be
very effective in reducing congestion by improving track network capacity.
Table 2.1: Train dynamics in evaluation
Train
Type
Length
(ft)
Max
Velocity
(ft/min)
Acceleration
Rate
(ft/min2)
Deceleration
Rate
(ft/min2)
Freight 6000 6160 1584 1584
Passenger 1000 6952 2112 2112

Table 2.2: Evaluation results of different headway polices
Case
Average Delay (min) Average Traveling Time (min)
Fixed
Headway
Dynamic
Headway
Improvement
Fixed
Headway
Dynamic
Headway
Improvement
1 5.7 2.1 63% 63.1 40.1 36%
2 7.5 3.2 57% 64.2 41.5 35%
3 15.4 6.8 55% 73.2 45.0 38%
4 23.8 10.0 57% 82.1 48.3 41%

29

2.6 Conclusion
In this chapter, we propose a dynamic headway system for positive train control using an
active communication system. We show how the dynamic headway can be incorporated in a
dispatching model that minimizes the total travel time. Since the dynamic headway relies on
active communications we also address the situation of temporary or permanent communication
loss. We demonstrated the results using a rail network in Southern California by showing
significant reductions in travel times due to the use of dynamic headway.
30

Chapter 3:
Traffic Signal Control with Truck Priority

3.1 Introduction
Signalized intersections in a transportation network aim to control and optimize traffic
flows by reducing traffic delays, avoiding unnecessary vehicle stops and preventing long waiting
queues at intersections. Most current traffic light controllers generate the signal sequences of
green and red light based on approaching traffic flows without distinguishing different classes of
vehicles. In areas where the volume of trucks is relatively high, the approach of treating all
vehicles the same may not be the best way for signal control as trucks have a detrimental impact
on overall traffic flows because of their slow dynamics, large sizes and large turning radius. A
heavy truck takes a longer distance to stop before a red light and also takes longer time to cross an
intersection after a stop due to its slow deceleration and acceleration, causing extra traffic delays
[30-31]. In some cases, it may be more beneficial to all vehicles involved to extend the green light
in order for an approaching heavy truck to cross the intersection without going through a slow
stop and go maneuver which may generate extra delays for other vehicles following the truck. In
addition, trucks consume more fuel and generate more air pollution compared to passenger
vehicles. Therefore, giving truck priority could also reduce air pollution and fuel consumption,
which has a beneficial impact on environment. With new sensor, communication and GPS
technologies, a traffic light controller could be informed of the type of approaching vehicles and
31

their characteristics (size, position, dynamics, speed etc.) [32-34] and take this additional
information into account in traffic light control in order to reduce traffic delays, improve
intersection safety and lower pollution emissions.
Existing bus signal priority systems have similarities with truck priority systems however
there is a significant difference in priority objectives. In the case of bus priority, the bus is given a
priority in order to minimize the bus delays sometimes at the expense of other vehicles. In the
case of truck priority, the objective is to give trucks priority only when other vehicles are not
affected even benefited. Previous bus priority systems involve two main strategies: passive and
active. The passive approach assigns longer green time to prioritized directions based on the
knowledge of traffic flows and patterns from historical data and sensor measurements, such as
traffic volumes, average vehicle speeds, vehicle compositions in all directions and turns [35][36].
On the other hand, active priority requires real-time detection of approaching vehicles and
bidirectional communications between vehicles and signal controllers for the subsequent priority
request-response solution [34][37]. For bus priority applications, reference [38] proposes a
framework of integrating passive with active priority in order to realize bus priority. Reference
[39] presents a bus priority system assuming that the bus arrival time is a random variable with
certain stochastic characteristics.
Although the concept of truck priority is similar to the bus priority systems that are
currently in use in many cities, truck signal priority still requires a dedicated system due to the
following reasons: 1) The control objectives of bus priority and truck priority systems are
different. In the case of bus priority, the objective is to minimize the delays of buses, by taking
into account factors associated with bus schedules and/or the demand of bus passengers, whereas
in the case of truck priority, the objective of giving truck priority is to benefit not only trucks but
32

also all vehicles involved; 2) The arrival rates of trucks are much higher than that of buses,
especially in areas near ports, warehouses, markets, etc.; 3) The routes and schedules of trucks are
not fixed as buses; 4) The priority level of trucks is lower than that of buses, allowing more
flexibility in taking into account the impact to overall traffic.
Past research on truck priority involves a prototype system for truck detection using video
sensors developed in [32] and applied to traffic light control in [60]. The potential benefits of
truck priority are demonstrated in [61] and [62] with evaluations at actual isolated intersections.
Reference [63] proposes a signal priority system with connected vehicle technology that can be
applied to truck signal priority at more than one intersection. Other approaches, which may
support truck traffic light priority, include the adaptive signal control systems (ATCS) such as
LHOVRA [40], Optimized Policies for Adaptive Control (OPAC) [41] [42], and Real-time
Hierarchical Optimizing Distributed Effective System (RHODES) [43]. LHOVRA can support
limited signal priority in isolated intersections with road vehicle detectors. The OPAC system can
give priority to certain vehicles such as emergency vehicles if they are operating on restricted
lanes, placing limitations on the priority vehicles. Most of the adaptive signal control systems are
based on a Model Predictive Control (MPC) methodology and the priority is realized by assigning
different weights according to vehicle classes. However, the prediction of future traffic flows
using explicit mathematical models such as in the MPC methodology is often inaccurate due to
the time-variant and nonlinear nature of traffic flows especially in road networks with multiple
signalized intersections. The optimization techniques and approaches proposed for traffic light
control with and without priority include fuzzy logic [44], neural networks [45], cell transmission
models [46] [47], dynamic programming [48], Genetic Algorithm [49] [50] and Q-learning [51]
33

[52]. Some of these optimization techniques involve the search of optimal signal sequence based
on future traffic prediction and can also be used for truck priority systems.
Most of the past efforts that support traffic light control with vehicle priority are model-
based approaches. However, the complexity of traffic flows and vehicle interactions at road
networks with intersections especially at large scaled networks may not be accurately captured by
simple mathematical models of the type used with MPC techniques. The availability of fast
computers and software tools opens the way for new approaches that go beyond the limitations of
simple mathematical models. The flows of the traffic network can be better predicted using
simulation models that are more complex and can capture phenomena that cannot be model with
simple mathematical equations. These simulation models can also be integrated with control and
optimization techniques to provide better and more robust decisions in real time.
In this chapter, we integrate traffic flow simulation models with optimization and control
tools in an approach referred to as CO-SiMulation Optimization (COSMO) control in order to
generate the signal sequence which gives truck priority when necessary. We replace simple
explicit mathematical models with more complicated and far more accurate simulation models for
traffic prediction. The features of the proposed COSMO truck priority system include:
1) A COSMO approach is used to generate the optimal baseline signal in which simulation
models are used to predict the corresponding traffic flows and costs that are used to generate the
optimum traffic light sequences;
2) A multi-agent design is used to deal with scalability issue;
3) A priority request evaluation model is proposed to determine whether the priority
requests from trucks are permitted or refused.
34

The proposed system is evaluated using microscopic traffic simulations of a road network
adjacent to the Long Beach/Los Angeles port. The simulation results demonstrate that the
proposed traffic light control system with truck priority reduces the travel time of trucks 5% to
10% without affecting the travel time of passenger vehicles, and reduces the number of truck
stops that has additional benefits in reducing emissions and fuel consumption.
This chapter is organized as follows: Section 3.2 presents the framework of proposed
system and Section 3.3 gives the problem formulations. Section 3.4 shows the evaluation results
of the proposed system for a road network in the Long Beach/Los Angeles port area for different
volumes of trucks. The conclusions are given in section 3.5.
3.2 System Overview
Figure 3.1 shows an overview of the proposed truck signal priority system. Our proposed
approach is divided into two parts: baseline signal generation and real-time active control.
The first part deals with the baseline signal sequence of a network of signalized
intersections using the proposed COSMO approach assuming that all vehicles are communicating
with the traffic light controller of the approaching intersections. The objective of this approach is
to minimize the overall delay of all involved vehicles by taking into account the different classes
of vehicles namely passenger vehicles and trucks.
The second part deals with the fine turning of the traffic light sequence generated by the
first part in order to minimize the sum of the waiting queue sizes of controlled intersections by
extending or deducing the green time of some phases based on real-time truck arrivals. We refer
to this part as the active control part. In the following sections we present our problem
formulation and proposed approach.
35

Figure 3.1: Architecture of proposed truck signal priority system.
3.3 Problem Formulation
3.3.1 Problem Formulation of Baseline Signal Generation
Consider a road network with N signalized intersections and M links. A link is defined as a
stretch of the road segment that has a specified direction of traffic flow connecting with the
intersection. Therefore, the value of M is less than N where  is the maximum number of links
connecting with one intersection. The control input at time t for the road network with N
signalized intersections is the collection of the traffic signal inputs of these intersections at time t
i.e.
 
12
( ) ( ), ( ),..., ( )
T
N
U t u t u t u t  (3.1)

36

where ()
i
ut is the traffic signal status for all signal heads for the ith intersection at time t. Our
control objective is to find U(t) that minimizes a given cost function C over the time t to t + T
p

where T
p
> 0 is the selected time horizon.
We assume that all vehicles keep reporting their position, speed and class (i.e. truck,
passenger vehicle, etc.) to the traffic light controller of the approaching intersection. Let x
i
(t) be
the flow of vehicles (no. of vehicles/unit time) in link i at time t then
  ( ) ( ) ( ) 1 ( ) ( )
i i i i i
x t p t x t p t x t    (3.2)
where p
i
(t) denotes the percentage of trucks and 1 - p
i
(t) is the percentage of passenger and other
vehicles besides trucks in the flow of link i at time t.
Let X(t) = [x
1
(t) , x
2
(t), …, x
M
(t)]
T
denote the vector of the flows in all M links at time t and
let P(t) = [p
1
(t) , p
2
(t) , …, p
M
(t)]
T
and V(t) = [v
1
(t), v
2
(t), …, v
M
(t)]
T
be the corresponding vectors
of truck percentage and vehicle speed of link flows respectively at time t. The future link flows
are a nonlinear and time varying dynamical function of past flows, speed, truck percentage, and
traffic signal sequences selected at time t. That is,
  ( 1) ( ), ( ), ( ), ( ),
X
X t f X t P t V t U t t  (3.3)
  ( 1) ( ), ( ), ( ), ( ),
V
V t f X t P t V t U t t  (3.4)
  ( 1) ( ), ( ), ( ), ( ),
P
P t f X t P t V t U t t  (3.5)
where f
X
, f
V
, and f
P
, are the dynamical functions of traffic flow, flow speed and truck percentage
respectively.
For link i define its average flow, average vehicle speed, and average truck percentage
over the time t to t + T
p
, as follows:
37

 
1 p
tT
ii
t
p
x x d
T




(3.6)
   
 
p
p
tT
ii
t
i tT
i
t
v x d
v
xd
  






(3.7)
   
 
p
p
tT
ii
t
i tT
i
t
p x d
p
xd
  






(3.8)
The travel delay for a vehicle is the additional travel time experienced by the vehicle, i.e.
the time difference between actual travel time and ideal free-flow travel time. Then the total travel
delay TD
i
i.e. the sum of delay of all vehicles on link i over the prediction horizon can be
computed by:
max
11
i i i
ii
TD L x
vV




(3.9)
where L
i
is the link i length, V
maxi
is the link speed, i.e. the speed limit for the link i.
The problem of finding the optimal traffic light by minimizing total travel delay is
formulated by the following optimization problem,
   
1
min 1
M
i i i i
i
C p TD p TD 

  

(3.10)
subject to
max
0
ii
vV  (3.11)
01
i
p  (3.12)
0
ii
x Cap  (3.13)
38

and (3.3) – (3.9) (3.14)
for i = 1, …, M
given X(t), P(t), V(t)

(3.15)
In objective cost function (3.10), the first term is the weighted truck delay and the second
term is the passenger car delay where  > 1is a predefined value to denote the truck weight in
computing delay of overall traffic flows. The value of  gives relative priority to the links with
higher truck volumes since the lower truck speed will generate more traffic delay and pollution
emissions than cars. The constraints (3.11) and (3.12) are constraints for flow speed and truck
percentage. The constraints (3.13) are the link capacity constraint.
As indicated in (3.10)-(3.15), the solution of the optimization problem requires the
knowledge of the nonlinear and unknown functions given by (3.3), (3.4) and (3.5). One typical
approach to deal with this complexity is to use a simplified mathematical model to describe the
traffic dynamics of (3.3), (3.4), and (3.5) then solve the simplified optimization problem, as done
in most of the literature. Assume that the implicit simple models of (3.3) – (3.5) are given, then
the average traffic flow, speed, and truck percentage could be expressed as functions of the
intersection signal inputs over the prediction horizon, () Ut which consists of the phase lengths
for all signal groups in the controlled road network.
 
,
( ), ( ), ( ), ( )
i X i
x f X t P t V t U t  (3.16)
 
,
( ), ( ), ( ), ( )
i V i
v f X t P t V t U t  (3.17)
 
,
( ), ( ), ( ), ( )
i P i
p f X t P t V t U t  (3.18)
39

where
i
f ,
i
g
and
i
h
are the revised dynamical functions of average traffic flow, flow speed, truck
percentage of link i respectively.
With dynamical functions (3.16)-(3.18), the original optimization problem (3.10)-(3.15)
can be rewritten as follows:
 
()
min ( )
Ut
C U t

(3.19)
where the feasible set  is defined by constraints (3.11)-(3.14):
 
 
 
max
max
0 ( ), ( ), ( ), ( )
0 ( ), ( ), ( ), ( ) 1
()
0 ( ), ( ), ( ), ( )
given ( ), ( ), ( ), , , , 1,...,
ii
i
ii
ii
g X t P t V t U t V
h X t P t V t U t
Ut
f X t P t V t U t Cap
X t P t V t V Cap i M 








 




(3.20)
The dual function of optimization problem has the form:
   
 
   
1, max
2, 3,
()
1
4, 5, 6,
inf ( ) 1
i i i
M
D i i i i i
Ut
i
i i i i i
gV
L C U t h f C
g h f

  
  

 

     


  


(3.21)
where
 
1,1 6,
,...,
M
    .
By the dual theorem, we have
*
( ) arg max ( )
D
U t L

  (3.22)
By solving the unconstrained optimization problem (3.22), we obtain the optimal solution
*
() Ut
applied from time t. In next control period when new traffic flow information is detected,
the optimal input will be found by repeating the same methodology as above.
40

Since the computation complexity of problem (3.19)-(3.20) increases exponentially with respect
to the number of controlled intersections N and the control horizon T
p
, it becomes difficult to find
the optimal solution in a feasible time when the number of intersections or the control horizon is
large. Therefore the metaheuristic algorithms are widely used to search a suboptimal solution in a
reasonable computational time. The typical metaheuristic algorithms have population-based
family algorithms [49][50][58], Q-learning algorithms [51][52], or Trajectory search family
algorithms [53][54], etc.
a) Population-based family algorithms: the general scheme of population-based
algorithms is shown as follows:
Step 1): Create an initial solution population including J possible solutions for the problem.
 
1
( ) ,..., ( )
J
U t U t (3.23)
where ()
j
Ut is the jth solution.
Step 2): Compute the corresponding fitness i.e. cost function value of each individual
solution in the current population, get
 
()
j
C U t for j = 1, ..., J.
Step 3): Generate new population with mutation and crossover operations based on
 
()
j
C U t for j = 1, ..., J;
 
1
( ) ,..., ( )
J
U t U t  (3.24)
Step 4): If the stop criterion is not fulfilled, go to step 2; otherwise compute the fitness of
new individuals and output the best individual solution.
41

The main disadvantage of population-based algorithm is that a large number of iterations
are required for one converging process, especially when the number of the controlled
intersections increases.
b) Q-learning algorithms such as algorithms in [51][52]. Q-learning decides new
solutions based on updating and improving optimal mapping Q between traffic flow states and
corresponding control inputs from continuous observations of old solution costs.
     
( 1)
( ), ( ) ( ), ( ) min ( 1), ( 1)
U
Q X U Q X U Q X U

      

   

(3.25)
where  is a predefined discount factor and 01   .
Then for a new observed traffic state () Xt , select
 
*
()
( ) arg min ( ), ( )
Ut
U t Q X t U t  (3.26)

Q-learning method is powerful when the states of traffic flows are relatively stable but this
method is not powerful for dynamic traffic flows since Q-learning method needs a long
converging process.
c) Trajectory search family algorithms: Typical methods include pattern search method,
simulated annealing, Tabu search, hill climbing method, etc [53][54]. A typical procedure can be
expressed as:
Step 1): Create an initial solution () Ut

for the problem, set
*
() Ut  () Ut

(3.27)
Step 2): Generate a neighbor solution set ()
Neig
Ut based on current solution then find the
best solution in the set ()
Neig
Ut , get
42

 
( ) ( )
( ) arg min ( )
Neig
U t U t
U t C U t


 (3.28)
Step 3): If
   
*
( ) ( ) C U t C U t

 then
*
( ) ( ) U t U t


Step 4): If the stop criterion is not fulfilled, go to step 2; otherwise output current
optimal
*
() Ut .
Our approach called COSMO control approach goes beyond the simple model based
approaches by using real time simulation models to capture the dynamics, nonlinearities,
interactions, and other phenomena of traffic flows that cannot be adequately described by simple
models.
3.3.2 COSMO Control Approach for Baseline Signal Generation
The proposed Co-SiMulation Optimization control approach is referred as COSMO
control approach as shown in Figure 3.2.

Figure 3.2: COSMO control approach for baseline signal generation
The main parts of this approach include:
a) Network Simulation Models
The simulation model captures vehicle dynamics and interactions and is far more accurate
than simplified mathematical models. For the simulation models, many microscopic and
43

macroscopic traffic modeling tools could be used as the traffic flow simulators in COSMO. For
any simulation models, the first step to run simulations is to create the network model of the road
network. In this step, the network elements such as road links, intersections, signal heads, and
signal controllers are added in the simulation models according to the practical road network.
Once the traffic network is ready, the next step is to configure the vehicle flows to start
simulations. The traffic flow data (flow, truck percentage, and speed) will be detected and set into
the simulators. After running simulations, the evaluation tools of simulation models collect
simulated results and then the corresponding cost values are computed for the optimization
algorithm. In this paper we use VISSIM, a microscopic and behavior based simulator to model the
agent network traffic flows accurately [56]. However, Instead of the microscopic simulation
model a macroscopic simulation model based on the commercial software VISUM could also be
used for complex networks as it is computationally faster.
b) Optimization Algorithm
We apply a metaheuristic algorithm to find the optimal baseline signals which are tested
using the simulation model in an iterative manner till a stopping criterion is satisfied in which
case the final solution is applied to the actual traffic light. The iterative procedure of the COSMO
approach involves the following steps:
Step1): Create an initial solution.
In this part, the revised control input () Ut is a list of time length of signal phases for
controlled intersections. The sequence of signal state will be generated based on phase by phase
from time t until new control input is generated. The initial cycle length is 60 seconds for all
intersections. We assume that there is no overlap interval between any two signal phases in a
44

given intersection. For each phase, its initial phase length is decided by the traffic flows and
capacities of links in the phase direction. We let S
k
denote the sum of link traffic flows in the
directions of phase k and Cap
k
denote the sum of link capacities in the directions of phase k at
an intersection.
where link is in direction of phase
ki
i
S X i k

 


where link is in direction of phase
ki
i
Cap Cap i k

 


Then for each phase k, its time length in a cycle is:
1
k
k
k
k
k
k
S
Cap
T Cycle
S
Cap


 





(3.29)
where T
k
is the initial phase time length of phase k in seconds and Cycle is the given cycle length.
For each intersection i, we compute the phase time in the initial signal sequence
0
()
i
ut at time t
using (3.29).
Step 2): Select following algorithm parameters:
UB: the maximum number of iterations of the algorithm;
 ≥ 1 is the increasing scalar for iteration step size;
0 <  <1: the deceasing scalar for iteration step size;

0
is the initial step size;
 is the smallest step size.
45

Step 3): For each iteration k, new solutions are generated and the optimal solution that
improves the most cost is selected as follows:
(1) Direction vector generation
A set of J feasible direction vectors denoted by d
k
is generated for new signals. For each
direction vector, its size is the total number of phases of all intersections and its elements are
selected randomly from {-1, 0, 1}, indicting {reducing, keeping, and increasing} the current phase
time respectively.
 
12
, ,...,
k k k k
J
d d d d  (3.30)
where
k
j
d is the jth direction vector.
(2) New signal generation
New signals are generated by the direction vectors and current step size 
k
.
()
kk
kj
U t d  for j = 1,…,J (3.31)
where ()
k
Ut is the optimal solution found in iteration k.
For example, if the direction vector elements for an intersection i signal sequence are
[1,0,…,-1]
T
, which means to add the current time length of phase 1, keep the current time length
of phase 2, …, and reduce current the time length of last phase. If current step size 
k
is 5 seconds,
then the new phase time in signal sequence will be
 
12
( ) 5, ( ),..., ( ) 5
i
P
T t T t T t
  
 .
(3) Optimal direction selection
The traffic simulation models are used to evaluate these new solutions to predict the traffic
flows and corresponding costs. In order to speed up the algorithm, the parallel simulation
46

structure is applied i,e, new J solutions are evaluated independently with J simulation models at
the same time. After simulations, the optimal direction that decreases most cost function value is
found.
 
*
arg min ( )
kk
j
k k k
kj
dd
d C U t d

   (3.32)
(4) Optimal solution updating
If the found optimal direction cannot decrease the cost, i.e.
   
*
( ) ( )
k k k
k
C U t d C U t    ,
the current optimal solution will not be updated and the step size is decreased using the scalar .
   
1kk
U t U t

 (3.33)
1kk


   (3.34)
Otherwise, the optimal solution will be replaced and the step size will be increased using
the scalar .
1*
( ) ( )
k k k
k
U t U t d

   (3.35)
1kk


   (3.36)
c) Stop Criteria
The algorithm will stop and output current optimal signal phase lengths when one of the
following stop criteria achieves:
(1) When the iteration number achieves the predefined upper bound, i.e. k = UB, or
(2) The step size in one iteration is less than the predefined the minimum step size, i.e.
k
  .
47

d) Signal controller
The signal controller generates the signal inputs as baseline signal sequence for
intersections based on the phase time lengths in final solution. The yellow and all-red intervals are
added into each phase to guarantee intersection safety.

3.3.3 Scalability of COSMO Approach
The proposed COSMO approach faces computational difficulties for large network since
the simulators need longer time to run simulations for large road network and the optimization
algorithm also requires a longer convergence process. In order to handle the scalability issue, the
large scaled road network could be divided into n multiple subnetwork and the multi-agent control
technique is used in solving the optimal signal problem in COSMO approach.
Consider a road network with S subnetworks and each subnetwork is controlled by one
agent. Let
s
L be the set of links in subnetwork s and ()
s
Xt 1,..., sS  denote the observed local
traffic flow of subnetwork s at time t. Then ( ) : ( )
s
s
X t X t  denotes the union of the local flows of
all agents which is also the global flow of the road network at time t. Let ()
s
Ut denote the control
input of the agent controller j i.e. the baseline signal sequence for all signalized intersections in
the jth subnetwork. ( ) : ( )
s
s
U t U t  denotes the union of all control inputs at time t that is also the
control input for the whole road network.
During the control process, each agent controller s keeps observing its local traffic flow
()
s
Xt and seeking the optimal signal sequence ()
s
Ut for its intersections using its subnetwork
traffic simulators. In addition, agent controllers keep communication with neighbor agents to
48

share their traffic flows and control inputs. Then each agent controller has the information
()
s
Mt

that includes traffic flow and the current control inputs of neighborhood agents. The usage of the
shared information is due to the fact that the traffic flows in one subnetwork not only determined
by its own intersection signals but also the flows and intersection signals of its neighborhood
subnetworks.
The signal optimization problem for a single agent controller is converted into the
following problem:
 
()
min 1
s
s
s
i i i i
Ut
iL
C p TD p TD 

  

(3.37)
subject to
 
( 1) ( ), ( ), ( ), ( ), ( ),
s s s s s s s
X
X t f X t p t V t U t M t t  (3.38)
 
( 1) ( ), ( ), ( ), ( ), ( ),
s s s s s s s
V
V t f X t p t V t U t M t t  (3.39)
 
( 1) ( ), ( ), ( ), ( ), ( ),
s s s s s s s
P
P t f X t p t V t U t M t t  (3.40)
and (3.11) – (3.14)
where
s
C ,
s
P , and
s
V are the total delay, truck percentage vector at time t, and vehicle speed
vector at time t of subnetwork s agent respectively.
s
X
f ,
s
V
f and
s
P
f are the nonlinear dynamical
system functions for subnetwork s.
An optimization algorithm as in Figure 3.3 is used to solve the above agent optimization
problem. The procedure of optimization is the same as in previous section as each agent
broadcasts its traffic states and control inputs to neighboring agents when optimality is reached.
49

Initialization at k = 0:
Create initial solution
,0
()
s
Ut ; Evaluate the value of objective cost function
with agent simulators, get
 
,0
()
s
C U t ; Broadcast the initial signal sequence and
current link flows to neighboring agents;

Select algorithm parameters:
UB, [1, ), (0,1), and       .
For each searching iteration k, do the following:
1) Determine new search direction vector randomly, get
12
, ,...,
k k k k
J
d d d d  

;
2) For all search directions 1,2,..., jJ  :
Compute directional search step
kk
j k j
sd  ;
Evaluate
 
,
()
s s k k
j
C U t s  with simulation models if
,
()
s k k
j
U t s  is
a feasible input;
End for
3) Select  
,
arg min ( )
k
j
s s k k
kj
s
s C U t s  among all feasible inputs;
4) If
   
,,
( ) ( )
s s k k s s k
j
C U t s C U t 
   
, 1 , s k s k
U t U t

 and update step size
1kk


  
Else
Update
1kk


   and
, 1 ,
( ) ( )
s k s k k
j
U t U t s

 ;
Broadcast the new signal sequence
,1
()
sk
Ut

and link flows generated by
,1
()
sk
Ut

to neighboring agents;
5) If
1 k


 or k = UB, stop optimization algorithm and return
*1
( ) ( )
k
U t U t

 ;
End for

Figure 3.3: Optimization algorithm for multiagent signal control with COSMO

3.3.4 Active Control Part
Consider a signalized intersection whose index is k with L approaching links where L is
less than  i.e. the maximum number of connecting links for one intersection. Let U
k
(t) be the
optimal baseline signal sequence from first part at time t. Assume all approaching vehicles
communication their position, speed and class to the intersection controller, the waiting queue
50

sizes i.e. the numbers of waiting vehicles of all L approaching links could be estimated based on
vehicle speed and position that is denoted by q
k
(t) i.e.
 
12
( ) ( ), ( ),..., ( )
T
k k k kL
q t q t q t q t  (3.41)
where q
kl
(t) is the waiting queue size of the lth approaching link of intersection k at time t, and L
is the number of approaching links for intersection k.
In addition, the truck percentage vector of intersection waiting queues ()
k
q
pt will also be
obtained and
12
( ) ( ), ( ),..., ( )
k k k kL
T
q q q q
p t p t p t p t  

(3.42)
 
( ) ( ) ( ) 1 ( ) ( )
kl kl
kl q kl q kl
q t p t q t p t q t    (3.43)
where ()
kl
q
pt is the truck percentage in waiting queue size of the lth approaching link at time t.
When a truck approaches an intersection, it reports its arrival and applies for a priority
passing to the intersection signal controller at the same time. After the signal controller receives
the request, it predicts the arrival time of the truck. This arrival time is an important parameter
determining whether the optimal baseline signal needs to be adjusted in order to let this truck pass
without stopping. If the traffic light is green when the truck arrives in intersection then the signal
does not need to be changed if let the truck pass (case 1 in Figure 3.4). Otherwise, an adjustment
of current signal sequence is required for the truck. This adjustment depends on the truck arrival
time and the future traffic light state at this arrival time: In case of the arrival time of the truck is
ahead of the starting time of its passing phase, the controller needs to start the green state earlier
in order to give a priority passing (case 2 in Figure 3.4). In case of that the arrival time of the
51

truck is after the ending of its passing phase, the controller needs to extend the green interval of
the truck passing phase (case 3 in Figure 3.4) to give priority for this truck.

Phase 1 Phase 2 …...
Phase 1 Phase 2 …...
Phase 1 Phase 2 …...
time
Case 1 – No Action
Case 2: Early Green
Case 3 – Green Extension
t T
ϕ1
Phase 1 Phase 2 …...
Optimal Baseline Signal
T
ϕ2

Figure 3.4: Active priority cases
Giving priority for trucks in one phase or direction has a negative impact on traffic flows
of other directions. Therefore, the signal adjust amounts in priority actions should be limited
within a threshold value (THV) to reduce the impact of priority actions. In this paper, the phase
ending time will be selected from three discrete values T
j
, T
j
– THV, and T
j
+ THV that are three
cases in Figure 3.4. Assume that there are J phases over current time t to t + T
a
where T
a
is the
control horizon of the active priority algorithm.
The control input of active part a
k
(t) for this intersection is the priority decision for J
future phases in the control horizon,
 
12
( ) ( ), ( ),..., ( )
T
k k k kJ
a t a t a t a t  (3.44)
where ()
kj
at is the action decision of phase j of intersection k at time t and its possible values of
include 0 (no action), -1 (early green) or 1 (green extension).
52

 
 
0, No action, =
( ) 1, = max ,
1, = min ,
jj
kj j j
j j a
TT
a t T T THV t
T T THV t T






  





(3.45)
Our control objective is to minimize a given cost function R over the selected time horizon
T
a
by selecting optimal a
k
(t) at time t. This cost function R in active part is selected as a weighted
sum of waiting queues of L approaching links for the controlled intersection. We give priority to
the link whose waiting queue has trucks using different queue weights.
()
1
min = ( ) ( )
a
k
L
tT
kl kl
t at
l
R w t q d 




(3.46)
 
( ) ( ) 1 ( )
kl kl
kl q q
w t wp t p t    (3.47)
where w
kl
(t) is the weight of queue in lth link at time t. w is a predefined weight of truck with
respect to passenger car in waiting queues.
The problem constraints of problem (3.46) include
  ( 1) ( ) ( ) ( ), ( ), ( ),
kl kl l l kl k k
q q X q U a             (3.48)
max
0 ( 1)
kl kl
qq     (3.49)
0 ( 1) 1
kl
q
p     (3.50)
( ) {0, 1,1 }
k
at (3.51)
for l = 1, 2, …, L,  =t,…,t+T
a
-1.
where (3.48) is the queue prediction model and µ
l
is the queue leaving rate with respect to priority
action and current optimal signal, constraint (3.49) makes sure that the queue size cannot exceed
53

its maximum size q
maxkl
, and constraint (3.50) defines the feasible value set of action vector
elements.
In this part, we use the below simple function to determine the priority action input.
 
0, when signal is red for link
, when signal is green for link and ( ) 0
( ), when signal is green for link and ( ) 0
l l kl
l kl
l
lq
X l q
  



  




(3.52)
where is
l
 the average link flow when the signal for that link is green for nonempty link queue,
that is obtained by averaging the detected queue leaving volumes during previous green intervals.
The solving algorithm for the problem (3.46)-(3.51) is straightforward when T
a
is a short
time horizon. After evaluating all possible combinations of action vector, the optimal action input
could be found. The total number of possible combinations is 3
J
.
3.4 Evaluation Results
In this section we use a network example to demonstrate the proposed traffic light control
with truck priority based on the COSMO approach. The microscopic traffic simulator VISSIM is
used to model traffic flows on the selected traffic network.
3.4.1 Set-up of Evaluation Platform
A simulation platform is developed to implement and evaluate the proposed truck priority
system based on VISSIM simulator. The priority control algorithms are implemented in
MATLAB/C++ and integrated with the simulator via COM (Component Object Model) interface
[56]. The traffic simulator is set up to collect the following information for the control algorithms:
1) Data Collection Points are placed to measure the vehicle volumes, compositions and
speeds of link flows every one minute during simulation;
54

2) Queue Counters are used to monitor the queue length at intersections every one second
during simulation;
3) Vehicle Information is to collect the real-time desired vehicle information such as type,
speed, location, etc.;
4) Detectors are used to simulate the vehicle detection function using induction loops,
track circuits or cameras;
5) Network Performance Evaluation is used to get the network level simulation
performances such as average delay, vehicle speed, and number of vehicle stops;
6) Vehicle Record: We use the CMEM (Comprehensive Model Emission Model) [57]
vehicle emission model to calculate fuel consumption and emissions with the outputted vehicle
record file containing vehicle dynamics information including vehicle IDs, speed profiles, and
acceleration profiles after simulations to compare the average vehicle emissions and fuel
consumption of different scenarios.
The selected road network is circled by Pacific Coast Hwy, N Wilmington Blvd, W
Anaheim St and N Avalon Blvd that consists of more than 100 intersections in total and 15 of
which are signalized (see Figure 3.5). The 15 signalized intersections are controlled by three
agents and each agent controls five intersections. A microscopic traffic simulator of the selected
road network has been implemented in VISSIM (see Figure 3.6).
55

1
2
3
4
5
6
7
8
9 10
11
12
13
14
15

Figure 3.5: Selected road network

Figure 3.6: Traffic simulator

3.4.2 Evaluation Scenarios
We evaluated our proposed algorithms when the traffic flow in the road network is the
average daily flow in table I and the truck volume is 3%, 10%, and 20% of the overall flow
respectively. The OD (Origin Destination) matrix is estimated from the daily flow by dividing the
trip demands between ten different zones in the road network.
56

Table 3.1: OD matrix in evaluation (Unit: trips/hour)

Destination
1 2 3 4 5 6 7 8 9 10
Origin
1 0 0 25 20 5 0 680 0 0 0
2 0 0 3 3 3 3 3 3 0 0
3 3 2 0 0 0 0 0 0 0 20
4 2 0 0 0 0 0 0 10 5 5
5 5 5 0 0 0 0 0 20 0 0
6 0 0 0 0 0 0 0 20 0 0
7 670 0 0 0 0 0 0 30 10 10
8 50 10 10 10 30 50 10 0 0 0
9 0 0 0 5 45 5 0 0 0 0
10 10 0 25 5 5 5 5 0 0 0

We used two types of vehicles typical cars and trucks for the traffic demands. The
distributions of their desired acceleration rates are show in Figure 3.7.

Figure 3.7: Desired acceleration rates of car model (left) and truck model (right)
We evaluated two different controllers with same proposed COSMO approach in addition
to the traditional fixed time controller. The parameters in the COSMO are: the prediction time
horizon T
p
= 20 min, UB = 10,  = 2,  = 0.5,  = 2 sec. In controller 1 without truck priority, the
57

cost function in baseline signal generation part is the sum of travel delay of all vehicles without
considering differences between trucks and passenger cars, i.e.  = 1. In controller 2 with truck
priority, the cost function in baseline signal generation is weighted sum of travel delay of cars and
delay of trucks. Since the percentage of trucks is less than that of passenger cars, we give priority
to trucks in the second controller by setting  = 10. Both controller 1 and 2 have the same active
part on reducing intersection waiting queue and the predefined weight of one truck is w = 2.
3.4.3 Evaluation Results
Tables 3.2-3.4 summarize the evaluation results of three controllers (fixed time, controller
1, and controller 2) when the truck ratio is 3%, 10%, and 20% of the overall traffic flows
respectively. The evaluation time is one hour for all three truck ratios. The environmental impact
in the tables such as fuel usage, CO2 emission and NOx emission are computed using vehicle
emission models CMEM (Comprehensive Model Emission Model) in [57].
Table 3.2: Evaluation results (3% Truck)

Controller
Fixed Time
Controller 1
W/out Passive
Priority
Controller 2 W/
Passive Priority
Avg. Delay/Veh (sec) 85.4 51.5 49.3
Avg. Delay/Car
(sec)
85.1 52.2 49.1
Avg. Delay/Truck
(sec)
88.1 63.3 55.5
Avg. Stops/Veh 3.84 2.76 2.73
Avg. Stops/Car 3.93 2.77 2.74
Avg. Stops/Truck 3.8 2.50 2.49
Fuel Trucks (g/km) 452.0 362.2 354.7
Fuel cars (g/km) 137.8 95.6 93.2
Fuel all veh. (g/km) 163.6 117.3 115.0
CO2 Emis. All (g/km) 427.9 325.5 316.8
NOx Emis. All (g/km) 1.01 0.80 0.76

58

Table 3.3: Evaluation results (10% Truck)

Controller
Fixed Time
Controller 1
W/out Passive
Priority
Controller 2 W/
Passive Priority
Avg. Delay/Veh (sec) 89.0 52.7 49.3
Avg. Delay/Car
(sec)
88.7 51.6 48.2
Avg. Delay/Truck
(sec)
91.8 62.7 59.3
Avg. Stops/Veh 4 2.72 2.67
Avg. Stops/Car 4.09 2.70 2.65
Avg. Stops/Truck 3.9 2.85 2.82
Fuel Trucks (g/km) 470.9 377.3 369.5
Fuel cars (g/km) 143.6 99.6 97.1
Fuel all veh. (g/km) 170.5 138.3 132.6
CO2 Emis. All (g/km) 445.8 361.6 346.9
NOx Emis. All (g/km) 1.06 0.86 0.82

Table 3.4: Evaluation results (20% Truck)

Controller
Fixed Time
Controller 1
W/out Passive
Priority
Controller 2 W/
Passive Priority
Avg. Delay/Veh (sec) 93.4 53.8 50.3
Avg. Delay/Car
(sec)
93.1 51.8 48.8
Avg. Delay/Truck
(sec)
96.3 62.5 56.8
Avg. Stops/Veh 4.22 2.73 2.65
Avg. Stops/Car 4.31 2.68 2.66
Avg. Stops/Truck 3.96 2.95 2.62
Fuel Trucks (g/km) 494.4 396.1 387.9
Fuel cars (g/km) 150.7 104.5 101.9
Fuel all veh. (g/km) 179.0 128.3 125.7
CO2 Emis. All (g/km) 468.0 356.0 346.6
NOx Emis. All (g/km) 1.11 0.88 0.84

59

The following benefits have been shown in Tables 3.2-3.4: 1) Both controllers with
COSMO approach improve the network performance by reducing the delay (about 28% to 45%)
and vehicle stops (about 30%) as well as reducing fuel consumptions and emissions of CO2 and
NOx compared to the fixed time controller which is the commonly used controller. The
improvements are more significant when the truck volume is 20%. 2) Compared to controller 1
without priority, controller 2 with truck priority provides further improvements in the truck delay
(about 5% to 10%) without satisfying passenger vehicles whose travel time and number of stops
have also been reduced. The fuel consumption and air pollution emissions of all vehicles involved
have been reduced as a result of reducing vehicle delay and unnecessary stops. In summary,
giving truck priority could benefit all vehicles involved and has a positive impact on environment.
3.5 Conclusion
In this chapter, we proposed a truck traffic light priority system and demonstrated its
application in a practical road network. The system integrates the advantages of co-simulation
optimization approach and active truck priority strategy to achieve better transportation
performance in improving traffic delays, reducing fuel consumption and air pollution emissions in
comparison to fixed time and no-priority strategies. The system is evaluated using a microscopic
traffic simulation and its performance improvements have been demonstrated. The evaluation
results show that giving truck priority in traffic light control could benefit all vehicles involved in
reducing their travel time and number of stops, as well as reducing the fuel consumption and air
pollution emissions .

60

Chapter 4:
Routing of Multimodal Freight Transportation

4.1 Introduction
The growth of worldwide trade has significantly increased traffic congestion and air
pollution due to existing congestion in the urban transportation infrastructure especially in
metropolitan areas with major freight ports such as the Los Angeles/Long Beach Ports where
there is a high concentration of freight traffic. One of the biggest challenges for freight transport
efficiency in such a multimodal environment arises from the fact that both freight and passenger
traffic share the same infrastructure for moving people in addition to freight goods which leads to
non-homogeneous traffic. This non-homogeneity has a detrimental impact on the urban transport
performance because of the differences of vehicle sizes and dynamics between passenger and
freight vehicles. The freight vehicles such as freight trains and heavy trucks take longer distances
to stop and time to accelerate from a stopping position, consume more fuel and generate more air
pollution compared to passenger vehicles. The situation becomes even worse during incidents and
disruptions that lead to network capacity reduction such as road incidents or railway closures that
require rapid response and redistribution of freight traffic across the multimodal network. Without
efficient management of the freight transport, the whole transportation network will face severe
capacity shortages, inefficiencies, load imbalances, and will have a negative environmental
impact across the network in space and time. Therefore a more efficient freight routing system
61

can not only save freight delivery time and cost but can also contribute to improve mobility,
efficiency and sustainability of urban transportation systems.
Due to the important role of freight transport, numerous researchers have addressed the
issue of multimodal freight transportation especially in multimodal network modeling as well as
routing and scheduling of freight traffic [64-90]. Jourquin and Beuthe presented a multimodal
freight model based on a digitized geographic network [64]. Southworth and Peterson developed a
multi-layer intermodal shipment model in [65]. The intermodal freight transport model between
rail and road has been described in [67-69]. Moreover, Russ et al. and Yamada et al showed the
application of routing and scheduling techniques in multimodal freight network design [89][90].
As a fundamental issue in routing and scheduling algorithms, the shortest route problem has been
studied by many researchers [70-76]. Modesti and Sciomachen applied a link utility measure
approach to solve the multiobjective shortest route problem [70]. Lozano and Storchi considered
the impact of modal transfer costs when finding the shortest multimodal route [71]. The shortest
route problem in a dynamic and stochastic multimodal network was studied in [72] and [73].
Speed-up techniques have also been analyzed including Core-Based routing [74], label-setting
and label-correcting methods [75] and the improved label setting algorithm [76]. These shortest
route algorithms can satisfy the routing requirement of a small amount of demand since the
routing decision has a limited impact on the network state because the interaction between the
loaded traffic and current traffic is not significant. For a large amount of demand that may change
the network state and cost, optimization techniques have been commonly used to solve the
multimodal routing and scheduling problem with a formulation of a simplified network state and
cost model such as in [77-81]. Guelat and Florian proposed a linear approximation algorithm to
solve the multimodal and multiproduct freight assignment problem [77]. Castelli et al. used a
62

Lagrangian-based heuristic procedure to solve the freight scheduling problem [78]. Ham, Kim and
Boyce showed the application of Wilson’s iterative balancing method in interregional multimodal
shipment planning [79]. Zografos et al. developed a dynamic programming based algorithm for
multimodal scheduling based on a shortest route algorithm [80]. Moccia et al. solved a
multimodal routing problem with timetables and time windows by integrating a heuristic
methodology with the column generation algorithm [81]. The main difficulty is that these
approaches use mathematical models which may not be able to find a closed form solution when
applied to complex networks such as large scale multimodal freight networks that exhibit
nonlinear states and costs.
The availability of fast computers and software tools open the way for new approaches
that go beyond the limitations of network complexity. The traffic flows and states can be better
predicted using simulation models that are more complex and can capture phenomena that cannot
be formulated with simple models. Some researchers tried to solve the multimodal routing and
scheduling problem from the aspect of user equilibrium and dynamic traffic assignment using
simulation based methods as in the unimodal road routing and scheduling problem [82-88]. The
common idea of user equilibrium based traffic assignment is to search the traffic flow iteratively
until the trip costs for the same demands are equal and the costs of the used routes are less than
the costs of the other unselected routes. Peeta and Mahmassani formulated and developed a
simulation model based method for the dynamic user equilibrium problem given fixed demand
[82]. The proposed simulation based method was also applied in multimodal transport [83]-[85].
The user equilibrium among supply and demand has been also studied in which trip costs from all
suppliers to the same destination are in equilibrium [86][87]. Other solution algorithms such as
cross entropy based [88] and gap-based [83][100] methods were proposed to give better
63

performance than the method of successive average (MSA) that is widely used for user
equilibrium problems. The system optimal routing problem can also be solved by the above
algorithms by using the marginal costs of the routes in the equilibrium solution instead of the trip
costs [82][99]. Due to the fact that the number of routes increases exponentially in the size of the
transportation network, it is computationally prohibitive to evaluate the marginal costs of all
possible routes by running simulations. The marginal costs of the routes can be estimated
approximately from the link states of the simulation model [82]. Besides the computational issues
associated with using the simulation based user equilibrium approaches to the system optimal
problem, there are other difficulties in applying these approaches for optimal system based freight
routing. First, the equilibrium of routes may not be able to be achieved in some cases where
vehicle availability and hard capacity constraints exist. These types of constraints need to be
added in the freight model especially when considering the rail mode of transport since there are a
limited number of trains available for dispatching on a particular day and the rail network has
capacity for a finite number of trains before deadlock occurs. Second, the coordination of
suppliers has not been considered in most previous approaches where it is typically assumed each
OD conducts their own route augmentation and load balancing separately. Although the
interaction of different suppliers are included and evaluated in the simulation models, it may lead
to a suboptimal solution within a given amount of iterations. Russ et. al. [89] proposed the idea of
coordination among suppliers in route augmentation to achieve better system benefits during load
balancing.
The contributions of this chapter are as follows. First, we formulate a freight routing
problem of a multimodal network in which hard vehicle availability and capacity constraints exist
in portions of the transportation network. Moreover, we propose a hierarchical COSMO (CO-
64

SiMulation Optimization) control approach as a means to deal with the optimal control of
complex and dynamical systems such as a multimodal transportation network. Finally, we
propose a novel loading balancing methodology that coordinates the routes for multiple shippers.
In computational experiments using data from the Ports of Los Angeles and Long Beach we show
the convergence speed of our load balancing methodology is faster than other approaches in the
literature.
The chapter is organized as follows. Section 4.2 gives the problem formulation. Section
4.3 demonstrates how to solve the formulated multimodal routing problem with the proposed
COSMO approach. Section 4.4 shows the experimental results of the proposed approach on
portions of the transportation network in Southern California. Finally conclusions are discussed in
Section 4.5.
4.2 Problem Formulation
A multimodal freight transportation network can be represented as a directed graph
consisting of a set of nodes (N ) with a set of directed arcs (A) connecting the nodes. A node in the
transportation network can be an intersection, rail station, port terminal etc. An arc in the
transportation network can be one segment of a roadway or railway track. Both passenger and
freight traffic start and end at certain network nodes. Let I and J be the sets of origin nodes and
destination nodes respectively. Both I and J are a subset of N.
In this chapter we deal with the routing of freight traffic that is container flow between
origin nodes and destination nodes. In practice, the available freight vehicles are constrained
between some nodes. For example, the available number of trains is limited between two rail
stations. Therefore, a multimodal service graph G is proposed to formulate the freight routing
65

problem. The service graph is also represented as a directed graph consisting of a set of service
nodes (NS) with a set of directed service links (L). The set NS is a subset of N consisting of all
origin and destination nodes as well as other nodes that can be used as interchange nodes of
different types of freight vehicles such as port terminals, truck depots, and rail stations. A link in
the service graph is served by a unique type of vehicle (e.g., road trucks or rail trains). Therefore,
the freight service graph can be seen as an abstracted upper layer of its corresponding physical
transportation network. Figure 1 shows an example of a service graph and traffic network where
node A and node B are the origin node and destination node respectively. The traffic network with
eight nodes can be abstractly represented by a service graph with four nodes including nodes A, B,
and the two rail nodes.
Road
Node
Rail
Node
Service
Link
Road
Node
Rail
Node
Road
Arc
Rail
Arc
Service Graph
Traffic Network
A
A
B
B

Figure 4.1: Service graph and traffic network
66

The overall freight routing problem has two levels of decisions. The demand routing
decision of the service graph is the allocation of freight demand among the service graph nodes
under the freight vehicle availability and capacity constraints to deliver the container demand
from the origin nodes to the destination nodes. The decision of the transportation network is then
the vehicle dispatching solution which is the assignment of the freight vehicles to the physical
transport paths. The routing decisions in the service graph that minimize the total cost depend on
the transportation network dynamics (e.g., traffic congestion, arc travel time etc). Moreover, the
transportation network dynamics are impacted by the service graph decision since the travel time
and congestion of a road segment or rail segment is determined by the traffic volumes.
We are trying to solve the routing decision of freight demand across the service graph and
traffic network between the origin and destination nodes to find the optimal distribution of goods
that minimizes the total delivery cost. The analysis time horizon is discretized into |K| time
intervals to formulate the problem. The notations that are used throughout the paper are defined as
follows:
i The index of an origin node, i I;
j The index of a destination node, j J;
k The index of a time interval, k K where K = {0, 1, …, |K|};
l The index of a link in service graph G, l L;
R
i, j
The set of all feasible routes from an origin i to a destination j;
r The index of a route from an origin i to a destination j;
67

, ij
d The total demand in the number of containers from an origin node i to a
destination node j;
 
.
r
ij
Xk The freight demand in units of containers using service route r with a departure
time k;
 
l
xk The number of containers using link l at time k;
 
l
uk The vehicle availability in the number of freight vehicles of link l at time k;
 
l
vk The vehicle capacity of link l in units of containers per freight vehicle at time k;
 
,
r
ij
Sk The average service cost per container on route r from node i to node j at time k
consisting of the non-travel time vehicle cost  
,
r
ij
Ck and the cost of route travel time  
,
r
ij
Tk ;
P
l
The set of all feasible vehicle paths consisting of arcs of the same transport mode
as service link l;
p The index of a vehicle path in the transportation network for service link l, p  P
l
;
 
p
l
ck The non-travel time vehicle cost of a vehicle path p for service link l at time k;
 
p
l
tk The travel time of a vehicle path p for service link l at time k;
 
p
l
yk The number of containers using path p for demand of service link l at time k;
 
a
zk The traffic volume of transportation network arc a at time k;
 
a
wk The travel time of transportation network arc a at time k;

68

The freight routing problem of the service graph that considers vehicle availability and
capacity constraints can be expressed as follows:
     
       
,
,
,,
, , ,
min
ij
ij
rr
i j i j
k K i I j J r R
r r r
i j r i j i j
k K i I j J r R
TC X S k X k
C k T k X k 
   
   


   
   
(4.1)
subject to the following constraints:
 
,
,,
, for ,
ij
r
i j i j
k r R
X k d i I j J

    

(4.2)
   
,
, , , ,
, for ,
ij
r
i j l r k l
i I j J r R k
X x k l L k K



   
    
   
(4.3)
    0 ( ) for ,
R
l l l
x k u k v k l L k K       (4.4)
 
,
0
r
ij
Xk  (4.5)
given
, ij
d , ( ), ( ),
ll
u k v k for , , , i I j J l L k K      (4.6)
Equation (4.1) is the problem objective that minimizes the total cost TC to deliver the
demand where X is the routing decision consisting of the distribution of freight demand on all
possible routes in the service graph.
r
 is the value of travel time of route r. Equation (4.2)
represents the demand conservation constraint. Equation (4.3) is the link demand model where
, , ,
1
l r k 
  when the demand of route r with departure time  uses service link l at time k.
Otherwise,
, , ,
0
l r k 
  . Equation (4.4) is the vehicle availability and capacity constraints where L
R

is the set of service links where vehicle constraints exist. In this paper, we only consider the
69

vehicle availability constraints existing in links served by the rail mode but the proposed approach
can also be extended for a more general problem where constraints exist on all service modes.
Since the explicit forms of the cost functions in the problem objective are not available directly
due to the nonlinearities and complex variable interactions, traffic network simulation models are
used to estimate the service graph states and costs for more accurate routing decisions.
In a traffic network, the freight vehicles are used to deliver the container demand on the
service graph using different vehicle paths. The demand of containers on link l determines the
demand of freight vehicles for the transportation network based on the service mode (rail, road,
etc.) and freight vehicle capacity.
Let
       
1 2 | |
, ,...,
A
Z k z k z k z k

 

be the vector of traffic volumes on the
transportation network arcs 1 to |A| at time k. Then the relationship of the traffic volume on arc a
with the departure of the freight traffic and other parameters in the network can be expressed as a
nonlinear dynamical equation:
         
1 , , , , for ,
a a a a
z k f z k q k Y k k a A k K       (4.7)
where

   :,
p
ll
Y k y k l L p P

     

(4.8)
In (4.7), f
a
is a nonlinear and time-dependent function of the traffic volume of arc a. The
impact of the traffic volumes from the adjacent arcs at time k is denoted by q
a
(k) and Y(k) is the
vector of departure freight traffic from all the origin nodes at time k as in (4.8). Since z
a
(k) and
q
a
(k) contain the impact of the previous departure container traffic before time k (i.e., Y( ) for  
< k), only Y(k) is included in equation (4.7). The arc volumes in the transportation network are
70

time-dependent due to various factors such as time-dependent passenger traffic, network changes,
accidents and incidents.
Let
       
1 2 | |
, ,...,
A
W k w k w k w k

 

be the vector of travel time (unit: t) of arcs 1 to
|A| at time k. The arc travel time is a function of the arc volume at time k which

is time-dependent
because of the impact of the time-dependent passenger traffic, network incidents and railway
dispatching decisions. The travel time of an arc is dependent on not only the arc flow but also on
the flows of the other arcs therefore,
     
, , for W k g Z k k k K    (4.9)
Let  
p
l
tk be the travel time of a path p if a freight vehicle departs from the origin node on
service arc l at time k. Assume a path p contains arcs
,1 ,
...
p
p p N
aa  where N
p
is the total
number of arcs on this path p. Define  
, pn
p
a
ek as the entering time at arc
,
p
pn
a for a freight vehicle
using path p with a departure time of k from the origin. Then the path travel time can be computed
as follows:
   
 
,,
1
p
p n p n
pp
p
N
p
l a a
n
t k w e k



(4.10)
where
 
,1
,
p
a
e k k  (4.11)
     
 
, +1 , , ,
,
for 1,..., 1
p n p n p n p n
p p p p
a a a a
pp
e k e k w e k
nN


(4.12)
71

Then the vehicle dispatching problem in the transportation network given the service
graph decision can be expressed as follows:
        min
l
p p p p
l l l l
k K l L p P
c k t k y k 
  

  
(4.13)
where
p
l
 is value of vehicle travel time of path p for service link l.
The problem constraints consist of (4.7) – (4.12) and
   , for ,
l
p
ll
pP
y k x k l L k K

    

(4.14)
  0 for , ,
l
p
l
y k l L p P k K        (4.15)
given X  (4.16)
The objective function (4.13) is the total cost of the transportation network generated by
the freight demand which is equal to TC if X is a feasible solution for problem (4.1-4.6).
Constraints (4.14) and (4.15) are the constraints for demand balancing for each service link. The
feasible set  in (4.16) is defined by constraints (4.2-4.6). Since the explicit forms of the
dynamical functions in (4.7-4.9) are difficult to mathematically express directly due to the
nonlinearities and complex traffic interactions, we use simulation models to replace the
mathematical functions to generate more accurate arc traffic volumes and travel times. For freight
vehicles using the road mode, the problem can be seen as a system optimal traffic assignment
problem. For the subnet of freight vehicles using the rail service mode, the problem can be seen as
a train dispatching problem. The resulting service link costs are used to update the route service
cost variables in (4.1) with a similar method as in (4.10-4.12) which reconstructs the travel time of
a path as the sum of travel times of the transportation arcs belonging to this path.
72

4.3 Solution Technique using COSMO
4.3.1 Framework of the Solution Technique
Service Graph Optimization
Vehcilet Demand
Service Graph Route
State & Cost
N O
N 1
N 2
N 3
N 4
N 5
N D
Physical Transportation Network
Simulation Models
Simulation-based Cost Evaluation
Simulation-based
Dynamic Assignment
For Road Network
Dynamic
Dispatching For Rail
Network
Vehicle Assignment
Traffic Network
State
Interface Layer
Traffic Network Sensing Vehicle Routing Decison
Optimization
Algorithm

Figure 4.2: Framework of proposed freight routing system
We use a system with hierarchical design as in Figure 4.2 to solve the formulated freight
routing problem considering vehicle availability and capacity constraints based on the COSMO
73

approach. The proposed system has the following layers above the physical transportation
network.
1) Interface layer: This layer connects the physical traffic network and the upper routing
optimization layers. It involves the sensing of the physical transportation network parameters
achieved by the various techniques including GPS (global positioning system), V2I (vehicle to
infrastructure) & V2V (vehicle to vehicle) communication, sensor detection of the traffic status
and incidents, etc. All the collected data are fed into the simulation model which reconfigures
itself to match the measurements to provide accurate state and cost prediction data for the upper
optimization layer. In addition, the vehicle routing decision is transferred to the physical network
after the optimization is carried out.
2) Simulation models: Since the transportation network dynamics are difficult to express
as simple mathematical models, the simulation models are used to capture the main characteristics
and dynamics of the multimodal transport network under the impact of the service graph routing
decisions, passenger traffic and network changes (network incidents, road closures, etc.).
3) Simulation-based cost evaluation: This part is used to estimate the link/route state and
cost information which is required by the service graph optimization algorithm. The system
optimal dynamic assignment is used to find the optimal paths of the trucks on the road
subnetwork. Then, the trip time and costs of the trucks are collected for updating the cost of the
service graph links served by the road mode. A train dispatching algorithm is used to find the best
schedule of freight trains that minimizes the total cost without generating deadlocks by
considering the impact of the passenger trains. The schedule of freight trains is used to update the
cost of the service graph links served by the rail mode.
74

4) Service graph optimization: This part controls the whole optimization process. The
optimization algorithm searches new candidate routing decisions that can reduce the total cost
until the stopping criteria are satisfied. The stopping criteria includes the maximum number of
iterations is reached or the change in the total cost is less than a predefined value between two
consecutive iterations. Once the stopping criterion is satisfied the final solution consisting of the
decision in the service graph as well as the dynamic assignment and dispatching results in the
simulation-based cost evaluation layer are sent to the actual transportation network to implement
the routing decisions.
4.3.2 Optimization Algorithm
The optimization problem (4.1-4.6) can be relaxed to the form with penalty functions as
follows:
         
min , ,
R
l l l l l
kKlL
J X TC x k u k v k 
 


(4.17)
subject to constraints (4.2), (4.5-4.6) where
l
 is the penalty factor of link l and
l
 is the service
link penalty function depending on the freight on the link, and the link vehicle availability and
capacity levels. According to the KKT (Karush-Kuhn-Tucker) conditions, the necessary
conditions for a minima of problem (4.17) are all used routes for the same group of demand share
the same route marginal cost which is less than the marginal costs of the other unused routes. The
marginal cost of a service route is defined as the partial derivative of the revised total cost J(X)
with respect to the route load. The incremental penalty algorithm [101] is applied to solve
problem (4.1-4.6) where hard constraints exist by solving the relaxed problem (4.17) repeatedly.
The procedure of the incremental penalty algorithm is:
75

Step 0: Choose initial penalty factors
0
l
 for
R
lL  and set master iteration round to n =
0;
Step 1: Find an optimal solution of the relaxed problem (4.17) with given values of
,
nR
l
lL   by the iterative COSMO approach using the idea of column generation [98] as shown
in Figure 4.3. Considering the fact that it is difficult to find the explicit functional form of TC, the
marginal costs with respect to feasible service routes cannot be obtained directly. The method
that leads to the best cost evaluation is to run the simulation models repeatedly by adding one unit
of demand to this route and then check the change in costs. However, it is impracticable to
enumerate the routes due to the fact that the number of possible routes grows exponentially with
respect to the service graph size. An alternative way is to estimate the route marginal costs with
the updated service link states and costs from the simulation-based cost evaluation layer.

Figure 4.3: COSMO iterative approach for freight routing
Therefore, the procedure for solving the relaxed problem (4.17) given the penalty factors
and functions using the COSMO approach is:
Step 1.1: Set the initial solution
76

In the nth round of the master procedure, set the iteration counter m = 0 and update the
link cost function with penalty factors ,
nR
l
lL   . Assign the freight demand according to the
previous round routing decision as the initial solution
(0)
X .
(0)
, ij
R is the set of the used routes.
Step 1.2: Update the service link states using the simulation models
Set the current demand routing decision
() m
X as the traffic demand of the transportation
network simulation models and conduct system optimal dynamic assignment of trucks and
optimal train dispatching to obtain the marginal costs of the service graph links. After the cost
evaluation, the marginal costs of the used vehicle paths belonging to the same service link are in
equilibrium. Then the marginal cost  
l
MC k for a service link at time k can be estimated by the
marginal cost of the vehicle paths plus the derivative of the penalty value, i.e.
 
       
 
,,
l l l l l
l
l
x k u k v k
MC k
xk
 


(4.18)
In this research, we use        
2
max{ ,0}
l l l
x k u k v k  as the derivative of the link penalty
value. We give the details of how to obtain the service link marginal cost  
l
MC k in the
following section.
Step 1.3: Route augmentation (Column generation)
With the revised service link marginal cost as in (4.18), find service routes that can reduce
the revised total cost J(X) using the shortest route algorithm. The new route is augmented in the
available route set. The time-dependent shortest route algorithms in references [71-74] can be
applied to find the shortest routes.
Step 1.4: Check for Convergence
77

Check whether the convergence criteria are satisfied. The used stopping criteria in this
paper is the cost difference between successive iterations is less than a predefined threshold or the
maximum number of iterations has been reached. If one of the criteria is reached, go to Step 2 of
the main procedure. Otherwise, go to step 1.5 for load balancing.
Step 1.5: Perform load balancing
For an OD pair having a route with less marginal cost, conduct load balancing by
redistributing the freight load from the current used routes to the new found route then return to
step 1.2 to continue the optimization algorithm. The load balancing algorithm starts from
constructing an auxiliary solution
  m
Aux
X for example all-or-nothing assignment, i.e. the demand of
an OD pair is loaded to the service route with minimum marginal cost. Then the new routing
decision can be generated by selecting a proper step size
 
[0,1]
m
  ,
         
 
1 m m m m m
Aux
X X X X 

   (4.19)
There are many ways to determine the step size in (4.19), such as the enumeration method
i.e. redistributing only one unit of demand which is the most conservative step size, the MSA
method [82, 84], the revised MSA method, and the optimal step size method in Frank-Wolfe
algorithm [102] etc. The enumeration method has a very slow convergence despite the fact that it
is guaranteed to find the optimal step size. One issue with the MSA group methods is that the step
size only depends on the iteration without considering the current solution quality. Another issue
is that they may exhibit solution oscillations around the hard constraints when the values of the
penalty factor are large for the problem in this chapter.
In the optimal step size method, the step size is determined by solving a linear searched
problem as follows.
78

 
 
       
   
[0,1]
arg min
m
m m m m m
Aux
J X X X



   (4.20)
The linear search optimal step size is computationally intensive because running
simulation models is required to conduct the cost evaluation J in (4.20). As an alternative
approach, a discrete set of predefined candidate step sizes is selected and evaluated in order to
speed up the algorithm; however, the step size optima is not guaranteed.
We compare three different step size selection algorithms (i.e., enumeration as in Abadi et
al. [88], MSA, and the optimal step size approach using (4.20)) on a simple example. There are
three possible routes connecting one OD pair whose characteristics and conditions during three
time intervals (one-hour each in length) are shown in Table 4.1.
Table 4.1: Route characteristics and traffic conditions of simple example
Time Interval Route Length (mile)
Capacity
(veh/hour)
Current
Demand
(veh/hour)
Travel Time
(min)
1
1 12 1100 1200 24
2 10 1000 1000 18
3 11 1050 1500 31
2
1 12 1100 1000 20
2 10 1000 950 17
3 11 1050 1100 21
3
1 12 1100 800 17
2 10 1000 900 17
3 11 1050 700 15

The number of vehicles between this OD pair is 1200 and the total cost is the sum of the
travel times in minutes of all the vehicles. Figure 4.4 shows the convergence of the three step size
algorithms. The x-axis is the iteration number and the y-axis is the total cost for that iteration.
The required numbers of iterations to stop for the three algorithms are about 750 for the
enumeration algorithm of Abadi et al., 20 for the MSA algorithm, and 6 for the optimal step size
79

algorithm. Therefore, the optimal step size method provides the best convergence speed although
the three algorithms find the same optimal total cost.
1 2 3 4 5 6 7
2
2.5
3
3.5
4
4.5
5
x 10
4

(a) (b) (c)
Figure 4.4: Performances of different load balancing algorithms
a) Enumeration Algorithm in Abadi et al. [88]; b) MSA Algorithm; c) Optimal Step Size
Algorithm
A common issue with the above load balancing algorithms is that all OD pairs are
considered in the same way when selecting the step sizes, leading to slow convergence for
multimodal routing when vehicle availability and capacity are considered. In order to speed up the
solving algorithm, we propose the following revision algorithm to give priority to some suppliers
or OD pairs in the step size selection. The step sizes of the different OD pairs are determined with
respect to the potential cost reduction that is evaluated approximately by the standard deviation of
the marginal costs of the used routes. Therefore,
   
 
 
,
, max
( , )
,
( , )
min ,
ij mm
ij
ij
ij
ij
d
d

  











(4.21)
80

where
max
 is the upper bound of the step size and
 
, ij
d  is the standard deviation of the marginal
cost of all the used routes by demand d
i,j
.
Step 2: Compute        
,,
n
l l l l
x k u k v k  in the current solution.
If        
, , 0, for
nR
l l l l
x k u k v k l L     , terminate the algorithm because the problem solution
is found;
Step 3: Update the penalty factors as follows then set n = n + 1 and go to step 1;
       
       
1
if , , 0
if , , 0
n n n n
l l l l l l l
n
l
nn
l l l l l
x k u k v k
x k u k v k
  



   






(4.22)
where 0
n
l
 is the increasing scalar to update the penalty factor of link l at round n. In the
experimental study of this chapter, we select
0
10
l
  and =0.001
n
l
 .
4.3.3 Marginal Cost of the Service Link
Assume we have a current container vehicle dispatching solution Y, the marginal cost of a
vehicle path demand can be computed by the following equation:
 
 
       
 
     
 
 

l
l
p p p p
l l l l
k K l L p P p
lpp
ll
p
l p p p p p
l l l l l p
k K l L p P l
c k t k y k
TC
MCP k
y k y k
tk
c k t k y k
yk


   


  
   
   



 

   
 
  
  
(4.23)
where  
p
l
MCP k


 is the change in the total cost in (4.13) if  
'
'
'
p
l
yk is changed by one unit of a
container. The first two terms are the cost of the current path and the last term is the cost change
due to the impact on the arc travel time which can be computed approximately using the outputs
of the simulation models. By the derivative chain rule and equations (4.10),
81

 
 
 
 
 
 
 
 
 
 
,,
,, ,
,
,
1
1

p
p n p n
pp
p
p
p n p n pn pp p
pn
p
p
pn
p
N p
aa
l
pp
n
ll
N
aa a
a p
n
al
w e k
tk
y k y k
z e k w
ek
z y k

 

 



 
 

 


(4.24)
The term  
a
a
w
k
z


in (4.24) is the change in the arc travel time at time k when the arc
vehicle volume changes by one vehicle. It can be approximately estimated using the simulated arc
traffic volume  
a
zk and arc capacity at time k.
For a road segment, the travel time derivative can be obtained using the fundamental
diagram of traffic flow [91] with the observed arc volume and density. The travel time derivative
can also be determined using a road travel time model such as the Bureau of Public Roads (BPR)
function in [92] or other estimated functions in [93]. Take the BPR function as an example,
_
1
a
a
a a free a
a
z
wt
cap




   




(4.25)
where
a
w is the arc travel time,
_ a free
t is the arc free-flow travel time,
a
z is the arc vehicle volume
and
a
cap is the arc capacity for vehicles. 0, 0
aa
  are model parameters that can be estimated
from historical data. The arc travel time derivative in (4.25) can be computed by the following
equation,
 
 
 
 
1
_ a a a free a a
a a a
t zk w
k
z cap k cap k










for , a A k K     (4.26)

82

For the railway segments, considering the impact of the passenger train schedule and the
freight dispatching decisions, the travel time of a rail arc is not an explicit function so the
corresponding travel time derivative cannot be computed by a uniformed model. Therefore, the
travel time with respect to the number of rail arcs are estimated from running the rail simulation
models repeatedly or using historical operations data. Lu et. al. provide a detailed description of
how to find the schedule of freight trains by dispatching passenger and freight trains without
deadlocks in [94].
Ignoring the arc interactions to simplify the problem computation, we get,
 
 
 
 
   
,, ,,
,
,,
1
, and
0, otherwise
p n p n p p p n p n pp pp
pn
p
aa p n p n a a
a
p
l
z e k a a e k e k
v k t
yk






  




 


(4.27)
Finally, the marginal cost of a vehicle path in (4.23) can be approximately computed by,
     
 
 
 
 
 
 
'
,
,,
' ,
,
1
1

for , ,
p
pn
p
p n p n
pp
p pn
p
pn
p
p p p p
l l l l
N
a
pp
l l a a
n a
la
l
MCP k c k t k
w
y e k e k
z
v e k t
l L p P k K










   
   





     






  

        

(4.28)
Since the first and second terms in (4.28) are decomposable with respect to the arcs, the
marginal costs of the used paths belonging to the same service link will be in equilibrium by
running a dynamic assignment algorithm. Then the marginal cost for a service link can be
approximately estimated by the resulting vehicle path marginal cost, i.e.
   , for ,
p
ll
MC k MCP k l L k K


         (4.29)
83

4.4 Experimental Analysis
This section shows the experiments of the proposed approach on a regional transport
which covers the LA/LB Ports and surrounding area. The simulation models used in the COSMO
approach consist of a macroscopic road network model and a rail simulation model. We use the
macroscopic traffic simulator VISUM [103] to develop the road network model in Figure 4.5 to
achieve fast network state predictions computationally. The simulator parameters including lane
number, length, speed limit and road capacity etc. are configured based on a practical
transportation network. The inputs including passenger and freight traffic for the road network are
expressed as the number of trips between zones that are the origins and destinations within the
road network. We assume that the trucks can only carry one container in the model so the number
of truck trips between each OD pair will be the number of containers to be delivered. Historical
passenger traffic data of year 2012 that are obtained from the Southern California Association of
Governments (SCAG) are used to tune the simulation models. Since the data is only available for
a portion of the arcs in the selected region, dynamic traffic assignment is used to estimate volumes
for the other network arcs.
For the rail simulator, we use the railway simulation system of Lu et al. in [95] developed
based on the ARENA simulation software. The rail simulator is used to evaluate the dynamical
train movements for a complex rail network. The track network is divided into different segments
based on their speed limits, length, and locations. Then, an abstract track graph is constructed with
these segments. The inputs for the rail simulator are the passenger and freight train schedules
including their planned departure times, origin stations, and destinations. Then the train
movements in the track network are simulated to calculate the travel times and delays of all
involved trains.
84

Figure 4.5: An example road network simulation model
The integration of the two models has been realized by sharing the OD demands and
simulation outputs. The road network simulator sends the freight traffic that will be delivered
through trains to the rail simulator. Then, the rail simulator creates the freight train schedule
based on the train capacity and simulates the train movements with the planned passenger trains
together to output the predicted train arrival times. After receiving the outputs of the rail simulator,
the road network simulator will generate the necessary truck flows to dispatch containers from the
rail stations to their final destinations. Both the simulation models and optimization program were
run on a desktop computer with 3.10GHz CPU and 8.0G memory.
We evaluated the routing between six main destinations (D1 – D6) and three terminals (A,
B, C) in the region with different demands as shown in Figure 4.6. The average weight of all the
containers is assumed to be 25 tons and the transportation costs per unit (price/ton-mile) are
assumed to be 8 cents for the road network and 3 cents for the railway network [97]. Three
85

shippers communicate their demand and current routing decision to a coordinator who runs the
COSMO approach to generate new route decisions by minimizing the overall cost that is defined
by the transportation cost plus the travel time cost. The baseline amount of delivery demand for
each shipper is 1020 containers. The demands of the six destinations are provided in Table 4.2.
We assume that the freight trains have a capacity of 50 containers and the port terminals and two
rail stations are located near the destinations.

Figure 4.6: Region of study
The numbers of available freight trains from the terminals to the two rail stations are:
 Terminal A to station 1: 6 trains;
 Terminal B to station 1: 2 trains;
 Terminal C to station 1: 4 trains;
 Station 1 to station 2: 10 trains.
Coordinator

C

B

A
SC SC
Rail Station 1

Rail Station 2
SC
D1
D2 D3
D4
D5 D6
86

Table 4.2: Baseline demand of destinations
Destination 1 2 3 4 5 6
Supply from A 0 60 400 0 0 560
Supply from B 0 390 0 0 630 0
Supply from C 350 0 0 600 70 0
Total Demand 350 450 400 600 700 560

Four step size selection algorithms are compared: 1) Enumeration method in which the
step size is the most conservative; 2) MSA with priority in which the step size is computed by
equation (4.21) where
 
  1/ 1
m
m   ; 3) Optimal step size selection in which the step size is
found by model (4.20); 4) the new proposed algorithm – optimal step size selection with priority
in which the step size is found by model (4.10) and equation (4.21). Since the custom MSA
method faces oscillation issues for large penalty parameters leading to the algorithm to not
converge within a reasonable time, we do not include its performance in this chapter.
Figure 4.7 shows a plot of the CPU time in unit of seconds of one load balancing step of
the enumeration method as a function of the demand size. The x-axis is the multiplicative factor
of the default demand load and the y-axis is the CPU time in unit of seconds for load balancing to
compute the marginal costs of the used routes in equilibrium. As shown in Figure, the CPU time
keeps increasing with respect to the demand. As a result, the loading balancing with enumeration
method becomes very slow to solve the problem with hard vehicle constraints as the demand load
increases. We evaluated the CPU time of cases with hard vehicle constraints under normal traffic
87

conditions. When the demand loads are 1.0 and 2.0 times of the default values, more than 13 and
22 CPU hours are required until convergence respectively. When the demand load is 2.5 times the
default values, the enumeration method was not able to converge to a solution within one day.

Demand load
CPU time (sec)

Figure 4.7: Load balancing time increasing of enumeration method
Table 4.3 summarizes the average costs and CPU time of the three load balancing methods
for seven different road traffic cases and demand loads. We do not include the enumeration
method in these set of experiments due to its slow convergence speed. In cases 1 to 4, four
different road traffic conditions are compared by fixing the demand to the baseline demand: 1)
normal traffic in which the road traffic is set as the daily average traffic volumes; 2) widely
congested traffic in which the network level road passenger traffic is increased by 50%; 3) partial
congested traffic in which the traffic in one segment of freeway 405 is congested as shown in
Figure 4.8 a); 4) traffic under incidents in which the lane closures are introduced at two locations
on the main freeways I-710 and I-110 causing the capacities of the two freeway segments to be
88

reduced by a half as in Figure 4.8 b). Cases 5 to 7 are the different demand loads (0.5, 2.0, and 2.5
times the baseline demand) under the normal traffic condition.

Figure 4.8: Traffic conditions
a) 405 freeway congestion and b) freeway capacity reduction due to lane closure
Table 4.3: Evaluation of different traffic conditions and loads
Case
MSA with Priority Optimal Step
Optimal Step with
Priority
Avg. cost
(dollar)
Time
(sec)
Avg. cost
(dollar)
Time
(sec)
Avg. cost
(dollar)
Time
(sec)
1 48.34 28810 48.02 4051 48.39 1827
2 65.61 50571 66.34 8647 66.43 5214
3 48.62 38651 48.35 2345 48.61 1824
4 66.20 39900 67.04 6305 67.13 5441
5 43.40 19415 43.38 508 43.56 162
6 60.19 41568 61.18 9931 61.14 4187
7 68.32 90465 68.99 13045 68.72 11690

89

As shown in Table 4.3, although in most cases the load balancing algorithm with the MSA
method generates a slightly better routing solution in reducing the total cost, its CPU time is much
higher, which limits its practical application. The load balancing algorithm with the optimal step
size selection has a much quicker convergence than the MSA method. Compared to the optimal
step size method without priority case, the proposed load balancing algorithm combining the
optimal step size selection and supplier priority can save from 10% to 68% on the CPU time. In
summary, the proposed load balancing with priority algorithm provides the best convergence
performance in reducing the computation time while providing nearly the same total costs
compared to the other methods.

4.5 Conclusion
In this chapter, we proposed a regional freight routing system in which a hierarchical Co-
Simulation Optimization control methodology is proposed to deal with hard vehicle availability
and capacity constraints. By using a multimodal transport testbed adjacent to the Los
Angeles/Long Beach Ports, the performances of the different step size algorithms in the load
balancing stage were compared and the evaluation results showed that the proposed algorithm
considering priority can speed up convergence.

90

Chapter 5:
Conclusion and Proposed Research Directions

In this work, we proposed some completed systems for multimodal urban freight transport
to improve safety, mobility and efficiency of overall traffic system with adoption of advanced
techniques. In particular, we developed:
 a dynamic headway system in positive train control based on active communication
that improved track capacity without sacrificing rail operation safety;
 an adaptive traffic signal control system considering truck priority that reduced travel
time and air pollution;
 a regional freight routing system in which a hierarchical Co-Simulation Optimization
control methodology is proposed to deal with hard vehicle availability and capacity
constraints.
The main directions for future research are as follows:
 Time window policy impact analysis. The presented multimodal routing algorithm
could be extended to include time based variables to model time window constraints
to represent any possible due dates or time incentive policies. Adding time window
constraints will increase the problem size and complexity but have the potential
benefit of significantly reducing the search space. The impact analysis of time
window policy could be implemented based on new proposed algorithms that could
solve the multimodal routing problem under time window in an efficient manner. The
91

objective of policy study is to explorer the optimal policy to determine transport
delivery time windows to reduce transport cost, relieve road traffic congestions, and
make full usage of multimodal transportation network capacity considering dynamical
demand, traffic condition, and vehicle availability and operation regulations.
 Distributed optimization/learning algorithm for COSMO approach. To apply the
COSMO approach in a large urban area requires fundamental contributions to the
distributed design of optimization/learning algorithms to search optimal decision for
the large scaled problem under dynamic and stochastic environment. Problem
decomposition approaches and decentralized system design will be applied to tackle
the issue of scalability. In addition, the optimization/learning algorithms for large-
scale, nonlinear programming problems with special structures will be studied.
 Incorporation with real-time urban data. The co-simulation approaches overcame the
modeling limitation but did not answer the issue of online optimization under future
uncertainties. With developed theories and analysis tools to use the vast amount of
historical and real-time data, it might be possible to make efficient control decisions
by taking advantage of multi-source real time data in the face of complexity and
uncertainty of urban environment. How to take advantage of big data development to
support connected/autonomous vehicle control and urban transport management is
still an important and interesting research direction.
92

References
[1] M.Hartong, R.Goel,andD.Wijesekera, “Communications based positive train control
systems architecture in the USA,” in Proc. IEEE 63rd Veh. Technol. Conf., 2006, pp.
2987–2991.
[2] R.Lindsey, “Positive train control in North America,” IEEE Veh. Technol. Mag., vol. 4,
no. 4, pp. 22–26, Dec. 2009.
[3] American an Railway Engineering and Maintenance-of-Way Association (AREMA),
Lanham, MD, USA, “Meeting the communication challenges for positive train control,”
in Proc. AREMA Annu. Conf. Expo., Chicago, IL, USA, 2009.
[4] W. P. Siriwongpairat and T. K. Himsoon, “Design and modeling of communications
system for interoperable positive train control,” in Proc. IEEE Int. Workshop Comput.
Aided Modeling, Anal. Design Commun. Links Netw., 2010, pp. 31–35.
[5] T. Hammi, N. B. Slimen, V. Deniau, J. Rioult, and S. Dudoyer, “Comparison between
GSM-R coverage level and EM noise level in railway environment,” in Proc. 9th Int.
Conf. Intell. Transp. Syst. Telecommun., 2009, pp. 123–128.
[6] G. L. Mayhew and D. S. Long, “Contribution of vehicle location technology to transit
headway minimization,” in Proc. IEEE 43rd Veh. Technol. Conf., May 1993, pp. 356–
359.
[7] L. Chen and T. Tang, “Research on the influence of communication delay on safety
location of train in communication based train control (CBTC),” in Proc. IEEE Intell.
Veh. Symp., Jun. 2009, pp. 940–944.
[8] E. Goddard, “Overview of signalling and train control system,” in Proc. 9
th
Inst.
Eng.Technol. Professional Develop. Course Elect. Traction Syst., 2008, pp. 336–350.
[9] M. H. Walshaw, “Railway signalling,” J. Inst. Elect. Eng., vol. 6, no. 72, pp. 723–725,
Dec. 1960.
[10] Y. Ding, Y. Bai, F. Liu, and B. Mao, “Simulation algorithm for energy efficient train
control under moving block system,” in Proc. World Congr. Comput. Sci. Inf. Eng.,
2009, vol. 5, pp. 498–502.
[11] D. Emery, “Reducing the headway on high-speed lines,” in Proc. 9th Swiss Transp. Res.
Conf., 2009, pp. 1–12.
[12] Y. Nie, J. Geng, and J. Ma, “Influence of phase separation upon headway of trains of
passenger-dedicated line,” in Proc.3
rd
Int. Conf. Transp. Eng., 2011, pp. 1257–1262.
[13] Y. Goto, H. Furusawa, M. Araki, and T. Fukuda, “A safe traffic speed control in AHS,”
in Proc. IEEE Int. Conf. Intell. Transp. Syst., 1999, pp. 459–464.
[14] M. Miyachi, “The new ATC system using the digital transmission for super high speed
operation on the Shinkansen lines,” in Proc. Int. Conf. Develop. Mass Transit Syst., Apr.
1998, pp. 68–73.
93

[15] G. Hann, “Incremental train control system,” IEEE Veh. Technol. Mag., vol. 5, no. 4, pp.
50–55, Dec. 2010.
[16] S. G. Wei, B. Cai, J. Wang, and J. Wang, “Research and analysis of ETCS controlling
curves model,” in Proc. 3rd Int. Conf. Adv. Comput. Theory Eng., 2010, vol. 2, pp. 178–
181.
[17] H. Yamazaki, Y. Marumo, Y. Iizuka, and H. Tsunashima, “Driver model simulation for
railway brake systems,” in Proc.4th IET Int. Conf. Railway Condition Monit., 2008, pp.
1–6.
[18] Y. Zhang, Z. Liu, H. Cheng, and Y. He, “The study on electric–pneumatic transfer
control of the train brake system,” in Proc. IEEE Int. Conf. Intell. Comput. Intell. Syst.,
2010, vol. 3, pp. 388–392.
[19] Guide for the Calculation of Braking Distances for Rail Transit Vehicles, IEEE,
Piscataway, NJ, USA, 2009.
[20] J. Baek and C. Lee, “The simulation of train separation control algorithm by movement
authority using beacon,” in Proc. 4th Int. Conf. Fuzzy Syst. Knowl. Discov., 2007, vol. 3,
pp. 717–720.
[21] P.Li, A.Nie, L.Jin, and F.Wang, “Study on intelligent train dispatching,” in Proc. IEEE
Intell. Transp. Syst. Conf., 2001, pp. 948–953.
[22] M.B.Kham and X.Zhou,“Stochastic optimization model and solution algorithm for
robust double-track train-timetabling problem,” IEEE Trans. Intell. Transp. Syst., vol.
11, no. 1, pp. 81–89, Mar. 2010.
[23] S. Sacone and S. Siri, “A planning approach for freight transportation operations in
railway networks,” in Proc. IEEE Int. Conf. Autom. Logistics, 2008, pp. 2633–2638.
[24] S. Mu and M. Dessouky, “Scheduling freight trains traveling on complex networks,”
Transp. Res. B, Methodol., vol. 45, no. 7, pp. 1103–1123, Aug. 2011.
[25] P. Wang et al., “Real-time train scheduling and control based on model predictive
control,” in Proc. 2nd WRI Global Congr. Intelli. Syst., 2010, pp. 47–50.
[26] M. A. Shafia, M. P. Aghaee, S. J. Sadiadi, and A. Jamili, “Robust train timetabling
problem: Mathematical model and branch and bound algorithm,” IEEE Trans. Intell.
Transp. Syst., vol. 13, no. 1, pp. 307–317, Mar. 2012.
[27] A. D’Ariano, M. Pranzo, and I. A. Hansen, “Conflict resolution and train speed
coordination for solving real-time timetable perturbations,” IEEE Trans. Intell. Transp.
Syst., vol. 8, no. 2, pp. 208–222, Jun. 2007.
[28] C. Mu, Z. Wang, and T. Xiao, “A platform for simulation of railway network operation
scheduling,” in Proc. IEEE Int. Conf. Intell. Process. Syst., 1997, vol. 2, pp. 1342–1346.
[29] Q. Lu and M. Dessouky, “Modeling train movements through complex rail networks,”
ACM Trans. Modeling Comput. Simul., vol. 14, no. 4, pp. 48–75, Jan. 2004.
[30] N. J. Garber, L. A. Hoel, Traffic & Highway Engineering, 4th edition, Cengage
Learning, June 2008, ch. 3.
94

[31] Traffic Engineering Handbook, 5th Edition, Institute of Transportation Engineers,
Washington DC, 2000, ch. 3.
[32] N. Saunier, T. Sayed, C. Lim, “A prototype system for truck signal priority using video
sensors,” 2009 Annual Conference and Exhibition of the Transportation Association of
Canada - Transportation in a Climate of Change, pp. 1-16, Oct. 2009.
[33] J. Bonneson, D. Middleton, K. Zimmerman, H. Charara, M. Abbas, “Intelligent
detection-control system for rural signalized intersections”, Aug. 2002.
[34] C. Liao, G.A. Davis, “Bus signal priority based on GPS and wireless communications
phase 1 – simulation study, Department of Civil Engineering”, University of Minnesota,
July 2006.
[35] W. Ma, X.Yang, “A passive transit signal priority approach for bus rapid transit
system,” 2007 IEEE Conference on Intelligent Transportation Systems, pp. 413-418.
[36] F. Li, D. H. Wang, J. Wang, and S. Jin, “An approach of transit passive priority with
transit phase overlapped at intersection of arterial signal progression,” 2008 IEEE
Conference on Intelligent Transportation Systems, pp. 729-733.
[37] N. Hounsell and B. Shrestha, “A new approach for co-operative bus priority at traffic
signals”, IEEE Transaction on Intelligent Transportation Systems, vol. 13, no. 1, pp. 6-
14, 2012.
[38] W. Mang, X. Yang, “Design and Evaluation of an Adaptive Bus Signal Priority System
Based on Wireless Sensor Network”, 2008 IEEE Conference on Intelligent
Transportation Systems, pp. 1073-1077.
[39] X. Zeng, Y.Zhang, K.N. Balke, and K. Yin, “A real-time transit signal priority control
model considering stochastic bus arrival time” IEEE Transaction on Intelligent
Transportation Systems, vol. 15, no. 4, pp. 1657-1675, 2014.
[40] A. Peterson and T. Bergh, Report 1991:51E “LHOVRA A traffic signal control strategy
for isolated junctions”, Swedish National Road Administration.
[41] L. C. Liao, “A review of the optimized policies for adaptive control strategy (OPAC)”,
California PATH working paper, UCB-ITS-PWP-98-9.
[42] Farhad Pooran, “OPAC adaptive engine Pinellas County Deployment”, Baltimore
Regional Traffic Signal Forum, 2011.
[43] P. Mirchandani, L. Head, “A real-time traffic signal control system: architecture,
algorithms, and analysis”, Transportation Research Part C, pp. 415-32, 2001.
[44] Y. Tian, Z. Li, D. Zhou, J. Song, D. Xiao, “Interactive signal control for over-saturated
arterial intersections using fuzzy logic,” 2008 IEEE Conference on Intelligent
Transportation Systems, pp. 1067-1072.
[45] X. Kuang, L. Xu, “Real-time traffic signal intelligent control with transit-priority,”
Journal of Software, vol. 7, no. 8, pp. 1738-1743, 2012.
[46] T. Pohlmann, B. Friedrich, “Online control of signalized networks using the cell
transmission model,” 2010 IEEE Conference on Intelligent Transportation Systems, pp.
1-6.
95

[47] S. Timotheou, C. G. Panayiotou, M. M. Polycarpou, “Towards distributed online
cooperative traffic signal control using the cell transmission model,” 2013 IEEE
Conference on Intelligent Transportation Systems, pp. 1737-1742.
[48] T. Li, D. Zhao, J. Yi, “Adaptive dynamic programming for multi-intersections traffic
signal intelligent control,” 2008 IEEE Conference on Intelligent Transportation Systems,
pp. 286-291.
[49] M. Mesbah, M. Sarvi, and G. Currie, “Optimization of transit priority in the
transportation network using a genetic algorithm”, IEEE Transaction on Intelligent
Transportation Systems, vol. 12, no. 3, pp. 908-919, 2011.
[50] J. Stevanovic, A. Stevanovic, P. Martin, and T. Bauer, “Stochastic optimization of
traffic control and transit priority settings in VISSIM”, Transportation Research Part C,
16, pp. 332-349, 2008.
[51] S. EI-Tantawy, B. Abdulhai, “Multi-Agent Reinforcement Learning for integrated
network of adaptive traffic signal controllers (MARLIN-ATSC),” 2012 IEEE
Conference on Intelligent Transportation Systems, pp. 319-326.
[52] S. Araghi, A. Khosravi, M. Johnstone, and D. Creighton, “Q-learning method for
controlling traffic signal phase time in a single intersection,” 2013 IEEE Conference on
Intelligent Transportation Systems, pp. 1261-1265.
[53] R. M. Lewis, V. Torczon, “Pattern search algorithms for bound constrained
minimization,” SIAM Journal on Optimization, vol. 9, no. 4, pp. 1082-1099, 1999.
[54] X.Y. Ge, Z.C. Li, W.H.K. Lam, and K. Choi, “Energy-Sustainable Traffic Signal
Timings for Congested Road Network with Heterogeneous Users”, IEEE Transactions
on Intelligent Transportation Systems, vol. 15, no. 3, pp. 1016-1025, 2014.
[55] H.S. Chang, M. C. Fu, J. Hu, S. I. Marcus, Simulation-based Algorithms for Markov
Decision Processes, Springer, March 2007.
[56] VISSIM – COM User Manual, PTV Vision, 2011.
[57] M. Barth, G. Scora, and T. Younglove, “Estimating emissions and fuel consumption for
different levels of freeway congestion”, Transportation Research Record: Journal of the
Transportation Research Board, no. 1664, pp. 47-57, 1999.
[58] B. Yelchuru, S. Fitzgerel, S. Murari, etc. “AERIS – Applications for the environment:
Real-time information synthesis eco-signal operations operational scenario modeling
report”, December 2014.
[59] C. Osorio, M.Bierlaire, “A simulation-based optimization framework for urban
transportation problems”, Operations Research, vol. 61, no. 6, pp. 1333-1345, 2013.
[60] N. Saunier, W. Kang, “Truck signal priority”, 2009 ITE Quad Conference.
[61] R. A. Plum, “Truck priority evaluation”, Minnesota Department of Transportation, Jan.
2012.
[62] M. Mahmud, “Evaluation of truck signal priority at n Columbia blvd and Martin Luther
King Jr. blvd intersection”, Civil and Environmental Engineering Master’s Project
Report, Portland State University, 2014.
96

[63] D. Kari, G.Wu, M. J. Barth, “Eco-friendly freight signal priority using connected
vehicle technology: a multi-agent systems approach”, IEEE Intelligent Vehicles
Symposium, pp. 1187-1192, June, 2014.
[64] B. Jourquin, M. Beuthe. Transportation Policy Analysis with a Geographic Information
System: The Virtual Network of Freight Transportation in Europe. In Transportation
Research Part C, Vol. 4, No. 6, 1996, pp. 359-371.
[65] F. Southworth, B. E. Peterson. Intermodal and International Freight Network Modeling.
In Transportation Research Part C Vol. 8, 2000, pp. 147-166.
[66] D. Rondinelli, M. Berry. Multimodal Transportation, Logistics, and the Environment:
Managing Interactions in a Global Economy. In European Management Journal, Vol.
18, No. 4, 2000, pp. 398-410.
[67] P. Nijkamp, A. Reggiani, W. F. Tsang. Comparative Modelling of Interregional
Transport Flows: Applications to Multimodal European Freight Transport. In European
Journal of Operational Research, Vol. 155, 2004, pp. 584-602.
[68] P. Arnold, D. Peeters, I.Thomas. Modeling a Rail/Road Intermodal Transportation
System. In Transportation Research Part E. Vol. 40, 2004, pp. 255-270.
[69] C. Macharis, Y. M. Bontekoning. Opportunities for OR in Intermodal Freight Transport
Research: A Review. In European Journal of Operational Research, Vol. 153, 2004, pp.
400-416.
[70] P. Modesti, A. Sciomachen. A Utility Measure for Finding Multiobjective Shortest
Routes in Urban Multimodal Transportation Networks. In European Journal of
Operational Research, Vol. 111, 1998, pp. 495-508.
[71] A. Lozano, G. Storchi. Shortest Viable Route Algorithm in Multimodal Networks. In
Transportation Research Part A. Vol. 35, 2001, pp. 225-241.
[72] K. F. S. Abdelghany. Stochastic Dynamic Traffic Assignment for Intermodal
Transportation Networks with Consistent Information Supply Strategies. Dissertation of
The University of Texas at Austin, 2001.
[73] S. Demeyer, P. Audenaert, M. Pickavet, and P. Demeester. Dynamic and Stochastic
Routing for Multimodal Transportation Systems. IET Intelligent Transportation Systems,
Vol. 8, No. 2, 2014, pp. 112-123.
[74] T. Pajor. Multi-Modal Route Planning. Thesis of Universitat Karlsruhe. 2009.
[75] Lu Liu. Data Model and Algorithms for Multimodal Route Planning with Transportation
Networks. Dissertation of Technische Unversitat Munchen, 2010.
[76] D. Kirchler. Efficient Routing on Multi-modal Transportation Networks. These of
DOCTEUR DE L'ECOLE POLYTECHNIQUE, 2013.
[77] J. Guelat, M. Florian, T. G. Crainic. A Multimode Multiproduct Network Assignment
Model for Strategic Planning of Freight Flows. In Transportation Science. Vol. 24, No.
1, 1990, pp. 25-39.
[78] L. Castelli, R. Pesenti, W. Ukovich. Scheduling Multimodal Transportation Systems. In
European Journal of Operational Research, Vol. 155, 2004, pp. 600-613.
97

[79] H. Ham, T. J. Kim, D. Boyce. Implementation and Estimation of a Combined Model of
Interregional, Multimodal Commodity Shipments and Transportation Network Flows. In
Transportation Research Part B. Vol. 39, No. 1, 2005, pp. 65-79.
[80] K. G. Zografos, K. N. Androutsopoulos. Algorithms for Itinerary Planning in
Multimodal Transportation Networks. IEEE Transactions on Intelligent Transportation
Systems, Vol. 9, No. 1, 2008, pp. 175-184.
[81] J. Moccia, J. Cordeau, G. Laporte, S. Ropke, M. Valentini. Modeling and Solving a
Multimodal Transportation Problem with Flexible Time and Scheduled Services. In
Networks, Vol. 57, 2011, pp. 53-68.
[82] S. Peeta, H. S. Mahmassani. System Optimal and User Equilibrium Time-dependent
Traffic Assignment in Congested Networks. In Annals of Operations Research, Vol. 60,
No. 1, 1995, pp. 81-113.
[83] H. S. Mahmassani, K. Zhang, J. Dong, C. C. Lu, V. C. Arcot, E. Miller-Hooks.
Dynamic Networks Simulation-Assignment Platform for Multiproduct Intermodal
Freight Transportation Analysis. In Transportation Research Record, No. 2032, 2007,
pp. 9-16.
[84] X. Zhou, H. S. Mahmassani, K. Zhang. Dynamic Micro-assignment Modeling Approach
for Integrated Multimodal Urban Corridor management. In Transportation Research
Part C. Vol. 16, 2008, pp. 167-186.
[85] C. C. Lu, H. S. Mahmassani, X. Zhou. Equivalent Gap Function-based Reformulation
and Solution Algorithm for the Dynamic User Equilibrium Problem. In Transportation
Research Part B, Vol. 43, No. 3, 2009, pp. 345-364.
[86] J. E. Fernandez, J. D. Cea, A. Soto. A Multi-modal Supply-demand Equilibrium Model
of Predicting Intercity Freight Flows. In Transportation Research Part B. Vol. 37, 2003,
pp. 615-640.Z.C. Li, W. H. Lam, S.C. Wong, and A. Sumalee. An Activity-based
Approach for Scheduling Multimodal Transit Services. In Transportation, Vol. 37, 2010,
pp. 751-774.
[87] T. Y. Ma, J. P. Lebacque. Dynamic System Optimal Routing in Multimodal Transit
Network. In Transportation Research Record, No. 2351, 2014, pp. 76-84.
[88] A. Abadi, P. A. Ioannou, M. M. Dessouky. Multimodal Dynamic Freight Load
Balancing. IEEE Transactions on Intelligent Transportation System, Vol. 17, No. 2,
2016, pp.356-366.
[89] B. F. Russ, T. Yamada, J. T. Castro, and H. Yasukawa. Optimising the Design of
Multimodal Freight Transport Network in Indonesia. In Journal of the Eastern Asia
Society for Transportation Studies. Vol. 6, 2005, pp. 2894-2907.
[90] T. Yamada, B. F. Russ, J. Castro, and E. Taniguchi. Designing Multimodal Freight
Transport Networks: A Heuristic Approach and Applications. In Transportation Science,
Vol.43, No. 2, 2009, pp. 129-143.
[91] N. Geroliminis; C.F. Daganzo. Existence of Urban-scale Macroscopic Fundamental
Diagrams: Some experimental findings. In Transportation Research Part B, Vol. 42, No.
9, 2008, pp. 759-770.
98

[92] Traffic Assignment Manual. U.S. Department of Commerce, Bureau of Public Roads,
1964.
[93] G. A. Davis, H. Xiong. Access to Destinations: Travel Time Estimation on Arterials.
Technical Report MN/RC 2007-35, University of Minnesota, 2007.
[94] Q. Lu, M. Dessouky, and R.C. Leachman, Modeling Train Movements Through
Complex Rail Networks, ACM Transactions on Modeling and Computer Simulation,
Vol. 14, 2004, pp. 48-75.
[95] D. J. Forkenbrock. Comparison of External Costs of Rail and Truck Freight
Transportation. In Transportation Research Part A, Vol. 35, No. 4, 2001, pp. 321-337.
[96] Bar-Gera, H., Boyce, D., 1999. Route flow entropy maximization in origin-based traffic
assignment. In: Proceedings of the 14th International Symposium on Transportation and
Traffic Theory, pp. 397–415.
[97] Shu Lu, Yu (Marco) Nie, Stability of user-equilibrium route flow solutions for the
traffic assignment problem, Transportation Research Part B: Methodological, Volume
44, Issue 4, May 2010, Pages 609-617,
[98] J. Desrosiers and M. E. Lübbecke, “A Primer in Column Generation,” Column Gener.,
vol. 3, pp. 1–32, 2005.
[99] W Shen, Y. Nie, and H. Michael Zhang, “Route-based System Optimal Dynamic Traffic
Assignment Model: Formulations and Solution Methods”, IEEE Conference on
Intelligent Transportation Systems, pp. 1298-1303, 2006.
[100] O. Verbas, H.S. Mahmassani, M. F. Hyland, “Gap-based transit assignment algorithm
with vehicle capacity constraints: Simulation-based implementation and large-scale
application”, Transportation Research Part B: Methodological, Vol. 93, pp. 1-16, 2016.
[101] Fukushima, M., “Restricted generalized Nash equilibria and controlled penalty
algorithm”, Computational Management Science (2011) 8: 201-218.
[102] Frank, M.; Wolfe, P. (1956). "An algorithm for quadratic programming". Naval
Research Logistics Quarterly. 3: 95-110.
[103] VISUM 11.5 User Manual, PTV Group, 2010.

Abstract (if available)

Abstract Efficient freight movement is an essential factor not only in urban transportation but also in social and economic development as well as environmental considerations. The growth of worldwide trade will significantly increase traffic congestion and air pollution due to existing congestion in current urban transportation infrastructures especially in metropolitan areas with major ports such as Los Angeles/Long Beach where there is a high concentration of both freight and passenger traffics that share the same infrastructures. In this research, we address some approaches to improve efficiency and safety of multimodal freight transportation infrastructures by exploring availability of advanced technologies such as active communication, fast simulation, connected vehicle, and computational optimization tools, including a dynamic headway system for positive train control based on active communication to improve rail track efficiency and safety, an adaptive signal light control system with truck priority to reduce the delay and air emissions of all vehicles involved at signalized intersections, as well as a multimodal freight routing system based on co-simulation optimization to reduce freight transport cost. ❧ In this research, we propose a dynamic headway system for PTC based on active communications, which we integrate with a dynamic dispatching model in order to improve track capacity and safety in railway operations. Safety, capacity, and timely schedules are some of the most crucial objectives in railway operations. Positive train control (PTC) is a concept whose goal is to improve the safety and efficiency of railway operations by using advanced information technologies. Information technologies such as active communications enable the use of a dynamic headway policy, which can increase the track capacity and improve dispatching efficiency in addition to improving safety. ❧ We develop, analyze and evaluate a traffic light control system for signalized intersections that takes into account the differences in dynamics and characteristics between trucks and passenger vehicles. In some cases, giving priority to trucks at signalized intersections will benefit all vehicles because of elimination of extra delays generated by slow trucks. In addition, it will lead to lower pollution emissions because of reducing the number of stop and go maneuvers of higher emission trucks. Instead of simple mathematical models we use a co-simulation approach that involves a more accurate simulation model together with an optimization and control procedure to generate the baseline traffic light sequences for multiple signalized intersections in a road network. The proposed traffic light control system combines an active control strategy with a signal priority action decision model to minimize vehicle travel delays by timing the baseline traffic signals to give priority to trucks when it is to the benefit of all vehicles involved. ❧ We also present a multimodal freight routing system with hard vehicle availability and capacity constraints based on a hierarchical COSMO (CO-Simulation Optimization) approach dealing with optimal control of complex and dynamical systems. The simulation layer provides the state and cost estimations and predictions for the upper optimization layer in which we develop a novel load balancing methodology to speed up the algorithm. The complexity and dynamics of multimodal freight transportation networks make the optimum routing of freight demand a challenging task. Route decision-making in a dynamical and complex urban multimodal transportation environment aims to minimize a certain objective cost relying on the accurate prediction of the traffic network states and the estimation of the route costs that are not readily available. ❧ We demonstrate the effectiveness of the proposed systems and approaches by evaluating them with simulation models and platforms. The simulation results of a rail network in southern California show the reductions of travel delays and travel time when using the dynamic headway. The proposed traffic light control system has been evaluated using a road network adjacent to the twin ports of Long Beach/Los Angeles. The evaluation results show consistent improvements in reducing the truck traffic delays (5% to 10%) and the truck stops without satisfying passenger vehicles whose travel time have also been reduced. A simulation testbed consisting of a road traffic simulation model and a rail simulation model for the Los Angeles/Long Beach Ports regional area has been developed and applied to demonstrate the efficiency of the proposed co-simulation multimodal routing approach in reducing delivery cost and algorithm CPU time.

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Asset Metadata

Creator Zhao, Yanbo (author)

Core Title Intelligent urban freight transportation

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Publication Date 07/14/2017

Defense Date 06/23/2017

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag freight transportation,multimodal routing,OAI-PMH Harvest,traffic signal priority,train headway

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Ioannou, Petros (committee chair), Bogdan, Paul (committee member), Dessouky, Maged (committee member)

Creator Email yanbozha@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c40-398134

Unique identifier UC11266384

Identifier etd-ZhaoYanbo-5511.pdf (filename),usctheses-c40-398134 (legacy record id)

Legacy Identifier etd-ZhaoYanbo-5511.pdf

Dmrecord 398134

Document Type Dissertation

Rights Zhao, Yanbo

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA