Real time path planning based on hybrid-vanet-enhanced transportation system

1664 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 64, NO. 5, MAY 2015
Real-Time Path Planning Based on
Hybrid-VANET-Enhanced Transportation System
Miao Wang, Hangguan Shan, Member, IEEE, Rongxing Lu, Member, IEEE,
Ran Zhang, Xuemin (Sherman) Shen, Fellow, IEEE, and Fan Bai
Abstract—Real-time path planning can efficiently relieve traffic
congestion in urban scenarios. However, how to design an efficient
path-planning algorithm to achieve a globally optimal vehicle-
traffic control still remains a challenging problem, particularly
when we take drivers’ individual preferences into consideration.
In this paper, we first establish a hybrid intelligent transporta-
tion system (ITS), i.e., a hybrid-VANET-enhanced ITS, which
utilizes both vehicular ad hoc networks (VANETs) and cellular
systems of the public transportation system to enable real-time
communications among vehicles, roadside units (RSUs), and a
vehicle-traffic server in an efficient way. Then, we propose a
real-time path-planning algorithm, which not only improves the
overall spatial utilization of a road network but reduces average
vehicle travel cost for avoiding vehicles from getting stuck in con-
gestion as well. A stochastic Lyapunov optimization technique is
exploited to address the globally optimal path-planning problem.
Finally, the transmission delay of the hybrid-VANET-enhanced
ITS is evaluated in VISSIM to show the timeliness of the proposed
communication framework. Moreover, system-level simulations
conducted in Java demonstrate that the proposed path-planning
algorithm outperforms the traditional distributed path planning
in terms of balancing the spatial utilization and drivers’ travel
cost.
Index Terms—Hybrid VANETs, path planning, spatial utiliza-
tion, travel cost.
I. INTRODUCTION
TRAFFIC congestion, as an important societal problem, has
received considerable attention. The 2007 Urban Mobility
Report [1] stated that traffic congestion causes nearly 4.2 billion
hours of extra travel every year in U.S.; the extra travel almost
accounts for 2.9 billion extra gallons of gasoline. Although
many existing advanced personal navigation devices have func-
tionalities of providing an optimal end-to-end path [2], [3],
Manuscript received February 10, 2014; revised April 28, 2014; accepted
June 6, 2014. Date of publication July 2, 2014; date of current version May 12,
2015. This work was supported in part by a research grant from the Natural
Science and Engineering Research Council (NSERC) of Canada, by a research
grant from General Motors, and by the Zhejiang Provincial Natural Science
Foundation of China under Grant LY12F01021. The review of this paper was
coordinated by Prof. Y. Qian. (Corresponding author: H. Shan.)
M. Wang, R. Zhang, and X. Shen are with the Department of Electrical
and Computer Engineering, University of Waterloo, Waterloo, ON N2L 3G1,
Canada.
H. Shan is with the Department of Information Science and Electronic
Engineering, Zhejiang University, Hangzhou 310027, China.
R. Lu is with Communication Engineering School of Electrical and Elec-
tronics Engineering, Nanyang Technological University, Singapore 639798.
F. Bai is with ECI Lab, General Motors Global RD, Warren, MI 48092 USA.
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TVT.2014.2335201
traffic congestion problems in intelligent transportation systems
(ITSs) have not been fully resolved; on the contrary, conven-
tional approaches still face a number of technical challenges.
For example, Google Maps involve existing networks (e.g.,
Global Position System, Wi-Fi, cellular networks, etc.) for in-
dividual path planning to avoid the traffic congestion. However,
the provided services are very costly, and more importantly,
they cannot make quick response to an emergency caused by
an accident/incident. The essential reason for this imperfection
lies in lack of real-time traffic information. Thus, to enhance
the adaptability of path planning, it is indispensable to study
how to efficiently collect and further exploit the real-time traffic
information for path planning and traffic congestion avoidance.
First, to collect the real-time traffic information, the emerging
vehicular ad hoc networks (VANETs) can provide an ITS
system with enhanced communication capabilities for cost
effective and real-time traffic information delivery [4]. Both
vehicle-to-vehicle (V2V1
) and vehicle-to-roadside-unit (V2R)
communications [6] are supported in VANETs to efficiently
collect/report traffic updates from/to vehicles as well as road-
side units (RSUs) [7]. As a result, the collected real-time traffic
information can be utilized for freeway-traffic-flow manage-
ment [8], individualized vehicle path planning [9], and vehicle
localization [10]. However, most of the related works assume
that the incorporated VANETs have sufficiently small deliv-
ery delay for real-time information collection. As VANETs
rely on short-range multihop communications, the end-to-end
transmission delay cannot be neglected in some scenarios.
Therefore, evaluations should be conducted to study how the
end-to-end transmission performance of vehicular communi-
cations affects the performance of path planning in different
scenarios and how to design the transmission mechanisms to
reduce the delay when delay cannot be neglected.
Second, to exploit the obtained real-time traffic information,
many algorithms are designed to discover optimal paths for
individual vehicles [11], [12]. However, individual path plan-
ning may lead to new congestion if performed uncoordinatedly.
To smooth the overall network flow, many works plan optimal
paths from a global perspective for a group of vehicles simul-
taneously [13], [14]. However, most existing globally optimal
path-planning algorithms focus on the network-side perfor-
mance improvement and neglect the drivers’ preferences (e.g.,
shorter travel length or time). Since the replanning decisions
1On February 3, 2014, the U.S. Department of Transportation’s National
Highway Traffic Safety Administration announced that it will begin taking steps
to enable V2V for vehicles to talk to each other and ultimately avoid crashes
altogether by exchanging basic safety data [5].
0018-9545 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
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WANG et al.: REAL-TIME PATH PLANNING BASED ON HYBRID-VANET-ENHANCED TRANSPORTATION SYSTEM 1665
are made to avoid congestion and balance the traffic rather than
discover optimal paths for individuals, some vehicles may pay
additional cost (e.g., a longer traveling length). Therefore, algo-
rithms should be designed to jointly consider the balance of the
network traffic and the reduction of average vehicle travel cost.
To this end, we propose a real-time global path-planning
algorithm that exploits VANET communication capabilities to
avoid vehicles from congestion in an urban environment. Both
the network spatial utilization and vehicle travel cost are con-
sidered to optimally balance the overall network smoothness
and the drivers’ preferences. Specifically, the contributions of
this paper are threefold.
• First, to facilitate the application of real-time path
planning, we propose a hybrid-VANET-enhanced ITS
framework, exploiting both the VANETs and the public
transportation system. Based on the proposed hybrid ITS
framework, a multihop message forwarding mechanism
is designed to collect the real-time traffic information
or the emergent warning messages, which usually have
strict delay bounds. A theoretical analysis on the end-to-
end transmission delay performance of the mechanism is
presented as well.
• Second, we design a real-time global path-planning algo-
rithm to not only improve network spatial utilization but
also reduce average vehicle travel cost per trip. A low-
complexity algorithm is developed based on Lyapunov
optimization to make real-time path planning decisions.
With the proposed path-planning algorithm, the tradeoff
between the overall network spatial utilization and drivers’
preferences can be well balanced.
• Finally, the transmission performance of the hybrid
VANETs is first evaluated under different vehicle densities
via VISSIM, and then, extensive simulations validate the
effectiveness and efficiency of the proposed path-planning
algorithm. The results confirm that our proposed path-
planning algorithm is able to find alternative paths for
vehicles to bypass congestion areas while reducing the
average travel cost in an efficient, timely, and coordi-
nated way.
The remainder of this paper is organized as follows.
Section II provides related works on path planning. The system
model is discussed in Section III. Section IV presents the
transmission mechanism in the proposed architecture and the
corresponding performance analysis. A real-time path planning
problem is formulated in Section V, followed by algorithm
design in Section VI. Section VII demonstrates the performance
of our proposed path-planning algorithm by simulations. Fi-
nally, Section VIII concludes this paper.
II. RELATED WORKS
Traffic congestion, caused by unbalanced traffic flow or a
sudden accident/incident, can cause late arrivals and additional
cost for drivers and becomes a major problem in the trans-
portation. However, this cost due to traffic congestion can be
reduced by route navigation or path planning with congestion
avoidance. For example, the paths of vehicles can be replanned
with the shortest-path-based GPS navigation [15], the accident
duration prediction [16], and the route reservation in advance
[17]. However, these approaches cannot make quick response
to an emergency or congestion due to a sudden accident since a
timely update on the traffic condition is lacking. Thus, the real-
time traffic information becomes indispensable to support the
vehicular real-time path-planning algorithm.
To collect time-varying traffic-condition information, most
existing works in conventional ITS usually rely on cellular
systems or loop detectors. In [18]–[21], cellphones or mobile
sensors with cellular access have been investigated to collect
real-time traffic information for traffic forecast or reconstruc-
tion in experimental research. In [8], a traffic management sys-
tem with loop detectors for continuous traffic measurement and
monitoring along arterials is introduced. However, inevitable
drawbacks cast a shadow on the application of cellular systems
and loop detectors. For cellular systems, as they are not ded-
icated for traffic data collection, the collection services can be
highly costly, and the high volume of traffic data may also cause
congestion for other cellular services. For the loop detectors,
the deployment expense can also be very high. Moreover, the
inaccuracy of position measurement becomes a problem for
short-distance transmissions particularly in dense networks,
which will degrade the performance of path planning [22], [23].
Due to VANETs, V2V and V2R communications can make
real-time message delivery much quicker, cheaper, and more
efficient than the existing systems, even for short-distance
transmissions in dense networks [24], [25]. More importantly,
RSUs in VANETs can greatly enhance the timeliness of data
collection and dissemination [26], which makes it possible to
perform coordinated path planning for a group of vehicles. To
improve the quality of experience (QoE), a point-to-point-based
vehicular network can be utilized to support the application
of multimedia delivery [27], [28], which however may still
experience large transmission delay. Hence, in this paper, to
reduce the end-to-end transmission delay, taxis or buses are
considered as super relays to help in delivering the information
through the cellular network of public transportation system.
On the other hand, in [27] and [28], media service applica-
tions, introducing heavy load to the involved cellular networks,
are studied; however, in this paper, the delivered information
composes limited small-size packets, leading to a different
transmission scenario with smaller data traffic load.
Many works have studied real-time vehicle path planning
with the assist of VANETs. A distributed path planning method
to avoid congestion is put forward in [11] using real-time traffic
data collected from VANETs, with the increased traffic flow.
Aiming to save gasoline for individual vehicle, a navigation
system is designed in [12] to avoid congestion. However, the
individual-user-optimal schemes may introduce additional traf-
fic congestion due to human uncoordinated selfish behaviors.
Thus, the paths of different vehicles should be jointly planned
to balance the network traffic. The works in [13] and [14]
consider multivehicle path planning, but the average travel cost
or the drivers’ preference is not considered. Moreover, how
communications in VANETs can impact on the path-planning
algorithm is still not clear.
Therefore, in this paper, a globally optimal path-planning
algorithm is proposed for vehicles to avoid traffic congestion

TABLE I
SUMMARY OF THE IMPORTANT MATHEMATICAL NOTATIONS
(including those caused by accidents) in a suburban scenario.
With the real-time traffic information collection and decision
delivery enabled by a hybrid-VANET-enhanced network, the
road network resources are fully utilized, and the average
travel cost of vehicles is significantly reduced. In addition, the
impacts of VANETs on the path-planning algorithm are further
discussed.
III. SYSTEM MODEL
Aiming at providing real-time planned paths for vehicles
from a global perspective, we first introduce the following
network architecture. The traffic flow model is then elaborated
upon, followed by the vehicle categorization and mobility
model. A summary of the important mathematical notations
used in this paper is given in Table I.
A. Hybrid-VANET-Enhanced Transportation System
Fig. 1 shows the architecture of the considered hybrid-
VANET-enhanced transportation system, consisting of vehicles,
RSUs, cellular base stations (BSs), and a vehicle-traffic server.
Vehicles are equipped with the onboard units that enable
multihop V2V communication used in delivering the peri-
odic vehicle information (e.g., vehicle velocity, density, and
location). When vehicles sense accident-related congestion,
the warning message can be generated to alert the emergent
accident information and then be shared not only among ve-
hicles but with the nearest RSU via V2R communications as
well. Moreover, pure VANETs, cellular communications, e.g.,
a GSM system which is set up for the functions such as mobile
telemonitoring and management systems for intercity public
transportation [29], are also involved. Hence, the taxis or buses
can directly upload the received warning message to the nearest
cellular BS, and the BS will deliver the message to the vehicle-
traffic server.
RSUs deployed along the roads are assumed able to obtain
vehicle-traffic statistical information (e.g., the vehicle arrival/
departure rate on each road). We consider that taxis and buses
are perfectly connected to the cellular system, and RSUs are
well connected with each other through wireline. If RSUs are
deployed at intersections, the traffic information can be detected
by the equipped cameras or traffic flowmeters connected to
RSUs directly [30]. Otherwise, the traffic flow can be predicted
by the nearest RSUs based on the obtained vehicle information
(e.g., periodically obtained vehicle density and velocity) from
the VANETs [31]. An RSU can share its own collected infor-
mation with other RSUs and the vehicle-traffic server. When an
accident happens, based on all the collected information, the
vehicle-traffic server is capable of performing real-time path
planning to provide globally optimized travel paths for vehicles
of interest.
We further define a road network into four main compo-
nents (i.e., intersections, roads, vehicles, and RSUs) as ς =
(I, Γ, V, R). The set of all intersections is denoted as I. Let Γ
be the set of all the roads in the network. Each road between two
adjacent intersections is assumed bidirectional, possibly with
multiple lanes in one direction. We refer to each of those lanes
with the same direction in a road as a road segment, i.e., one
normal bidirectional road between two adjacent intersections i
and j has two different road segments with opposite directions,
i.e., road segment (i, j) and road segment (j, i). The set of
vehicles and that of RSUs are defined as V and R, respectively.
B. Traffic Flow Model
To understand a vehicle-traffic flow more clearly, we model
vehicle traffic as an “inflow/outflow” system [32]. Each vehicle
is expected to follow a planned path from its starting point
toward its destination. Here, the planned path can be referred to
as a path preset in a GPS, according to the driver’s preferences
and based on the locations of the starting and ending points.
The driver will keep following the preset path until the vehicle
receives any information on congestion or accident. When an
accident or congestion occurs, by running the path-planning
algorithm, the vehicle-traffic server will be in charge of finding
an optimal alternative path or routing for the vehicles of inter-
est. Specifically, in this paper, we refer to the road segments in
which one vehicle’s starting point and destination are located as
s (∈ Γ) and d (∈ Γ), respectively.
Let Ji denote the set of neighboring crossings of intersec-
tion i. Define the inflow rate of road segment (i, j), λij(t),
as the upstream-vehicle arrival rate from neighboring road seg-
ments in time slot t, where j ∈ Ji, as shown in Fig. 2. Let λd
ij(t)
(j ∈ Ji) denote the traffic flow rate on road segment (i, j) with
the same destination d in time slot t, and λij(t) = d∈Γ λd
ij(t).

Fig. 1. Real-time path planning in VANET-enhanced hybrid networks. (a) Hybrid-VANET-enhanced network architecture. (b) Path planning in a VANET-
enhanced ITS.
Fig. 2. Traffic flow model.
In this paper, we consider each sample time duration (denoted
as Δ and including a series of time slots) as a time unit, which
is defined by sampling theorem to avoid information loss in
the compressive sensing for traffic estimation in [33]. Within
the Tth sample time duration, based on the traffic flow rates
of the involved time slots collected by RSUs, the average inflow
rate of road segment (i, j) of the Tth sample time duration is
denoted as λij(T) and expressed as
λij(T) =
1
Δ
T Δ
t=(T −1)Δ
λij(t). (1)
Similarly, the outflow rate μij(T) of road segment (i, j) is the
average departure rate of vehicles moving to neighboring road
segments in the Tth sample time. Note that all variables for the
opposite directed road segment of (i, j), namely road segment
(j, i), can be defined correspondingly, e.g., λji(T) and μji(T).
Let cij(T) denote the maximum number of outflow vehicles
of road segment (i, j) in Tth sample time, i.e., road capacity,
which is determined by the road conditions, the number of
lanes, the length of the road, and traffic congestion, etc. Due to
fluctuating road conditions and traffic flow conditions, the road
capacity can fluctuate with time but is considered to remain
constant within one sample time unit.
There are two kinds of traffic congestion: recurrent conges-
tion and nonrecurrent congestion [34]. The recurrent congestion
is due to the tension between the current traffic flow situation
(e.g., the traffic inflow λij(T)) and the road conditions (e.g., the
road capacity cij(T)), which is nonincident related. The nonre-
current congestion is caused by an accident or incident, which
can reduce the road capacity (to be introduced in Section V). We
define a congestion indicator of a warning message, δ(Iij)(∈
[0, 1]), to represent how the congestion type I happening
on road segment (i, j) impacts on the road capacity, where
δ(Iij) = 1 means recurrent congestion and δ(Iij) ∈ [0, 1) im-
plies nonrecurrent congestion.
Each vehicle traveling from one intersection to the next
is called routing in this paper. For each intersection (e.g.,
intersection i), consider that the RSU nearest to the intersection
maintains a virtual queue of length Qd
i (T), representing the
number of the buffered vehicles at this intersection specifically
destined to destination d (∈ Γ) in sample time T. Then, the total
length of all virtual queues of intersection i for all destinations
is Qi(T) = d∈Γ Qd
i (T), where
Qd
i (T) = max
⎧
⎨
⎩
Qd
i (T − 1) −
j∈Ji
μd
ij(T − 1), 0
⎫
⎬
⎭
+
u∈Ji
λd
ui(T − 1) (2)
with μd
ij(T − 1) being the outflow rate of road segment (i, j)
with destination d in the (T − 1)th sample time, satisfying
μij(T − 1) = d∈Γ μd
ij(T − 1). Similarly, for road segment
(i, j), we define the leftover number of vehicles in sample time
T as Qij(T)=max{Qij(T −1)−μij(T −1), 0}+λij(T −1).
C. Vehicle Categorization and Mobility Model
Three types of vehicles are considered in this paper, namely
private cars, taxis, and buses. GPS devices are supposed to be
deployed on all vehicles, and GPS devices have ordered the

service of providing shortest paths. Compared with changeable
paths of taxis or private cars, scheduled paths of buses are
usually fixed. Let wm ∈ {0, 1}(m ∈ V) denote the capability of
flexible turning for the vehicle m when the vehicle receives any
information about congestion or accident, and take the value 1
if vehicle m is a taxi or a private car and 0, otherwise, since
taxis or private cars can change their paths whereas buses have
to wait until the traffic trap is cleaned up.
Furthermore, we refer to taxis and buses as super nodes,
connected to a control center through GSM systems. With
a specially designed message transmission mechanism (to be
introduced in Section IV), warning messages can be delivered
to the vehicle-traffic server as efficiently as possible to facilitate
real-time path planning.
The mobility of each vehicle can be characterized by two
random variables (V, D) [35]. Here, V represents the vehicle
velocity that takes two possible values (i.e., a lower velocity vL
and a higher velocity vH). The velocity transition is modeled as
a two-state continuous-time Markov chain with state transition
rate 1/D. Under this model, a vehicle initially chooses vL (or
vH), and after an exponentially distributed time interval with
the mean of D, the velocity changes to vH (or vL). The model
can be exploited to describe the realistic driving behaviors, i.e.,
a driver usually drives at a constant velocity for a period and
then changes to a higher/lower velocity based on his/her will
and/or road conditions. Moreover, when the vehicle density
is low or medium (e.g., no larger than 30 vehicle/km/lane),
vehicles can be considered to move independently [36] and
the headway distance2
follows the exponential distribution with
rate ζ [37].
IV. TRANSMISSION MECHANISM AND
PERFORMANCE ANALYSIS
Since the incident-related warning message is pivotal to the
viability of a real-time path-planning algorithm, we propose
the following rapid message transmission mechanism and give
corresponding analytical results on the end-to-end transmission
performance.
A. Outline of Transmission Mechanism
After sensing the congestion, vehicles in the vicinity of the
congestion will generate and forward the warning message
to other vehicles via multihop V2V relaying. If a supernode
receives a warning message, it will upload the message to
the nearest cellular BS through cellular communication of
the public transportation system; otherwise, the message will
be transmitted all the way to one RSU via V2V and V2R
transmissions. To reduce the redundancy of multihop relaying,
the following relay node selection is adopted. If there is one
bus/taxi within the transmission range of a vehicle, the bus/taxi
will be the next-hop receiver; otherwise, the farthest vehicle
ahead in the same lane within the transmission range will be
2In this paper, the headway distance is defined as the distance between two
neighboring vehicles in the same lane.
selected as the next relay [35]. Moreover, we assume that a ve-
hicle deletes the warning message once it has been transmitted.
On the other hand, a global message lifetime TL is preset for
each warning message, at the end of which all the transmis-
sions of the corresponding message will be terminated, thus to
further control the redundancy in message delivery. Once an
RSU or cellular BS receives a warning message, it forwards
the message to the vehicle-traffic server via wireline. Upon
receiving the warning message, the traffic server will operate
the path-planning algorithm based on the collected timely road-
traffic information. By leveraging this transmission mechanism,
emergent messages (e.g., congestion indicators) are promising
to be disseminated more efficiently as compared with only
utilizing VANETs or the cellular communication capabilities
of the public transportation system. Finally, after the vehicle-
traffic server finished path planning, replanned paths are fed
back to vehicles, demanding path planning via a downlink
transmission (i.e., traffic server–RSU/vehicle relay–vehicle in
need of path planning).
As shown in Fig. 1, the overall communications in the
proposed VANET-enhanced ITS can be divided into three
layers: V2V and V2R communications in VANETs, wireless
communication between super nodes, and BSs via a cellular
system, and wired communication between RSUs (or BSs) and
the vehicle-traffic server. Thus, the main issues affecting the
efficiency of the end-to-end message transmission comes to
transmission delay in VANETs. By considering the following
ideal medium access control (MAC) for V2V and V2R commu-
nications, we will analyze the transmission delay in VANETs in
the following. Specifically, for analytical simplicity, we assume
that once a vehicle moves into the coverage range of an RSU
or another vehicle, time slots can be scheduled with neglectable
delay for the corresponding V2R or V2V transmissions. More-
over, the link rate of a V2V or V2R transmission is assumed
constant, and the contact duration between each transmission
pair is considered long enough to accomplish at least one packet
delivery, which can be achieved by appropriately setting the
packet size [38].
In general, the transmission delay in VANETs can be dis-
cussed under two cases. First, when the vehicle density is very
high (e.g., more than 56 vehicles/mi), the connections among
vehicles can be found with high probability, considering that the
transmission range of a vehicle (e.g., more than 100 m as shown
in dedicated short-range communications) is way more than the
average headway distance. In this case, for a given connection
path, for example, from a vehicle to an RSU, we consider
neglectable transmission delay because of the assumption of
the ideal MAC and small-size packet delivery. Second, for the
medium or sparse vehicle density case, due to the intermittency
of vehicle communications caused by high-speed mobility
and/or node sparsity, the intercontact time, namely, the waiting
time of each hop for the receiver (vehicle or RSU) to fall into
the transmission range of the transmitter, dominates the end-to-
end transmission delay. Notice that congestion may cause an
unbalanced vehicle distribution on neighboring roads, and the
traffic information report on a road of low node density can be
the bottleneck of the VANET-assisted information collection.
As such, in the following, we analyze the impact of vehicle

density on the intercontact time of one-hop V2V or V2R
transmission and further on the end-to-end transmission delay
along the transmission path.
B. End-to-End Delay Analysis
In the following, we analyze the intercontact time for the
aforementioned transmission mechanism. The end-to-end delay
analysis begins from the transmissions in pure VANETs, and
then involves the public transportation system.
1) End-to-End Delay in Pure VANETs: First, consider an
uplink with no taxis or buses, i.e., all the hops are based on V2V
and V2R communications. We evaluate the transmission delay
for the last hop of the V2R transmission. The transmission
delay here is mainly due to the intercontact time between a
vehicle and an RSU. Similar to [35], we define the last hop
as an ON–OFF model, where a vehicle either directly connects
to an RSU (i.e., during the ON-state) or is the only vehicle
approaching the RSU and there is no other vehicle in the
transmission range of the RSU (i.e., during the OFF-state).
According to the transmission model, the transmission delay
of a packet during the ON-state should be way smaller than that
during the OFF-state. Therefore, the transmission delay of the
last V2R hop is mainly due to the OFF-state period.
Denote the ON-state period and the OFF-state period of a
vehicle as Ton and Toff , respectively. Accordingly, the travel
distances within the two periods are defined as Uon and Uoff ,
respectively, with Ton = Uon/V and Toff = Uoff /V , where V
is the average velocity for a vehicle based on the ON–OFF
mobility model (see Section III-C). Similar to [35], the event
that a vehicle moves a distance of at least u during Ton before
being scheduled to communicate with an RSU should satisfy
the following: 1) There is no other vehicle within the distance u
from the end of the RSU coverage ahead of the vehicle; and
2) there is at least one vehicle within the distance 2R − u,
which results in this vehicle moving at least u distance to avoid
the collision, with R representing the transmission range of an
RSU or a vehicle. Then, we have
Pr(Uon > u) =
(e−ζ·u
)
bγ−1
1 − e−ζ·(2R−u) bγ−1
1 − (e−ζ·2R)
bγ
(3)
where b is the summation of all road lengths, and γ is the
average vehicle density on the roads. Since the vehicle headway
distance follows an exponential distribution, as mentioned in
Section III-C, the probability that a headway distance is larger
than u is e−ζ·u
. Based on (3), we can obtain
E[Uon] =
2R
0
Pr(Uon > u) du. (4)
Similarly, the event that a vehicle moves a distance of at least
u during Toff should satisfy the following: 1) There is no vehicle
within a distance of 2R + u from the end of the coverage range
of the nearest RSU ahead of the vehicle; and 2) there is at least
one vehicle within the distance L − (u + 2R), where L is the
distance between the adjacent RSUs. Then, we have
Pr(Uoff>u)=
e−ζ·(2R+u) bγ−1
1− e−ζ·(L−(2R+u)) bγ−1
(e−ζ·2R)
bγ
1− e−ζ·(L−2R) bγ
(5)
E[Uoff ]=
L−2R
0
Pr(Uoff > u) du. (6)
In addition, the previous hops between vehicles within a
transmission path, except the last hop, can be characterized
with the vehicle mobility model. The process of the relative
velocity between two vehicles can be represented by a CTMC
with a state space H = {h0, h1, h2}. Here, h0 represents a
negative relative velocity when the vehicle in front moves with
vL, whereas the vehicle behind moves with vH; h1 models a
zero relative velocity (i.e., both vehicles move with the same
velocity); h2 represents a positive relative velocity. If each
vehicle keeps the same velocity for an exponential time with
an average of D, the transition rate between any two states
of the Markov process is equal to 2/D. Thus, from [35], the
average number of hops M of an end-to-end transmission path
from a message source to an RSU in pure VANETs can be
approximated as
M =
6 (L − E[Uon] − E[Uoff ])
D(vL + vH)
. (7)
Then, based on the average number of hops, the transmission
delay of such a transmission path can be shown as
ψ = (M − 1)E[TV 2V ] + E[Toff ] (8)
where E[TV 2V ] = 1/(1 − e−ζR
) is the average transmission
delay for a V2V hop since the headway distance follows an
exponential distribution. E[Toff ] is the average duration of
the OFF-state period, as defined earlier. If we consider the
downloading as a similar process with uploading, the total
transmission delay can be approximated by 2ψ.3
Note that
this transmission delay is related to the parameters, including
vehicle mobility parameters (V and D), vehicle density (γ),
and RSU-related parameters (the transmission range R and the
average distance between RSUs L). Then, the probability of an
M-hop transmission path with all V2V and V2R communica-
tions equals the probability that there is neither taxi nor bus in
any hop within the M-hop transmission path, i.e., (1 − PT −
PB)M
, where PT (PB) is the percentage of taxis (buses) in the
traffic stream.
2) End-to-End Delay in Hybrid-VANET-Enhanced Network:
If the public transportation system is involved in delivering
messages as aforementioned, the probability of a given number
of hops from a private car to the nearest bus/taxi follows a
3The approximation is valid if the end-to-end transmission delay can be well
controlled to a small value in which the network topology changes little or the
source vehicle only moves a relatively short distance.

geometric distribution. The average number of hops in the
hybrid-VANET-enhanced ITS, i.e., M , is
M = M · (1 − PB − PT )M
+
M
i=1
(i − 1) · (1 − PB − PT )i−1
· (PB + PT ). (9)
Then, if we consider that the public transportation system are
perfectly connected with no delay, the average transmission
delay is dominated by the transmission delay in VANETs.
Based on the probability of a given number of hops from a
private car to the nearest bus/taxi, the transmission delay in a
multihop message transmission path is rewritten as
ψ = ψ · (1 − PB − PT )M
+
M
i=1
(i − 1) · (1 − PB − PT )i−1
· (PB + PT ) · E[TV 2V ]. (10)
From (10), the end-to-end transmission delay in hybrid ITS
is related to 1) vehicle mobility parameters (i.e., V and D),
2) vehicle density and super-node percentage (i.e., γ, PB, and
PT ), and 3) RSU deployment in the network (e.g., the transmis-
sion range R and the average distance between RSUs L).
V. PROBLEM FORMULATION
Here, based on the traffic flow model defined in Section III-B,
the traffic flow balance constraint of each intersection is first
identified. The road capacity and congestion indicator are then
discussed under different traffic conditions. Subsequently, con-
sidering the drivers’ travel-cost preferences in the path plan-
ning, the cost metric of path planning for individual vehicle is
defined. In addition, the network stability constraint is shown.
Finally, the real-time path planning problem is formulated to
not only avoid the congestion but reduce the average travel cost
caused by path planning as well.
A. Intersection Flow Balance Constraint
For an intersection i (∈ I), the following flow balance equa-
tion should be satisfied to guarantee that the aggregate vehicle
arrival rate is equal to the aggregate vehicle departure rate:
j∈Ji
μji(T) =
u∈Ji
λiu(T) ∀ i ∈ I (11)
where the left and right sides of the equation are, respectively,
referred to as the aggregate vehicle arrival and departure rates.
B. Road Capacity and Congestion Indicator
For road segment (i, j), the vehicle inflow rate for sample
time T is λij(T). The average outflow rate changes with the
inflow rate, but with some time delay (denoted as Λ seconds,
which is the travel time for a vehicle moving from intersection i
to intersection j), i.e., μij(T) = λij(T − Λ), until reaching
the outflow rate limit, i.e., road capacity cij(T). Here, Λ is
decided by the tension between the traffic inflow and road
capacity. Once an incident/accident occurs, the outflow rate
drops dramatically on one road segment. To illustrate the road
capacity under different traffic conditions, we discuss the road
capacity in two cases: 1) no incident-related congestion (i.e.,
recurrent congestion) and 2) the incident-related congestion
(i.e., nonrecurrent congestion). The road capacities under two
cases will be illustrated respectively as follows.
1) When there is no incident-related congestion on (i, j),
according to [34], we have
cij(T) = cN
ij = Nij · cp
ij · FPH ·
1
(1 + EB · PB) · A
(12)
where cN
ij is the road capacity under no incident-related
congestion case. Nij is denoted as the number of lanes in
road segment (i, j). The ideal capacity per lane is cp
ij.
FPH is the peak-hour factor, i.e., the ratio of the peak
15-min flow rate in vehicles per hour (vph) to the average
hourly flow rate (vph). EB is the bus equivalent4
to pri-
vate cars or taxis. PB is the percentage of buses in the traf-
fic stream. A is an adjustment factor to account for other
factors with impact on road capacity. Under this case
μij(T) = min {λij(T − Λr
), cij(T)} (13)
with Λr
called recurrent delay [34] and satisfying
Λr
= T0
ij + Dq
ij + 0.25T
λij(T)
cij(T)
− 1
+
λij(T)
cij(T)
− 1
2
+
16Jij · L2
ij · λij(T)
N2
ij · T2 · cij(T)
. (14)
Here, T0
ij = Lij/V0 is the segment travel time measured
at free flow speed V0, with Lij being the length of road
segment (i, j). Jij = (Tc
ij − T0
ij)
2
/L2
ij is a calibration
parameter, with Tc
ij being the segment travel time
measured when the traffic demand equals road capacity.
Dq
ij is the delay due to leftover queue from the prior
sample time, i.e.,
Dq
ij =
Qij(T)
2 · cij(T) · T
· min
⎧
⎨
⎩
T,
Qij(T)
cij(T)· 1−min 1,
λij (T )
cij (T )
⎫
⎬
⎭
.
2) When there is an incident Iij on road segment (i, j), we
still hold
μij(T) = min {λij(T − Λnr
), cij(T)} (15)
where Λnr
is called nonrecurrent delay and can also be
calculated based on (14). However, in this case
cij(T) = cI
ij = cN
ij · δ(Iij) ∀ δ(Iij) ∈ [0, 1) (16)
where δ(Iij) is the percentage of remaining road capac-
ity during incident type I on road segment (i, j), i.e.,
congestion indicator. The value of δ(Iij) depends on
the incident type I and is considered to be sensed by
witness/victim vehicles and delivered to the nearest RSU
or BS. cI
ij is thus the road capacity under the incident I.
Take the case that a road segment has one lane in each
4The bus equivalent is the number of buses displaced by a single taxi or a
private car in a suburb area [39].

direction as an example. When an accident I happens, we
may consider that δ(Iij) = 0 and μij(T) = cI
ij = 0 since
no vehicle-traffic flow will pass. On the other hand, in
the case that a road segment has multiple lanes in each
direction, the traffic flow will not be zero but might still
drop dramatically.
Furthermore, if there is no incident-related congestion on
road (i, j), δ(Iij) = 1. Then, we can extend the following
relationship between the indicator and road capacity:
cij(T) = cN
ij · δ(Iij) ∀ δ(Iij) ∈ [0, 1] (17)
which implies that the road capacity drops once an accident
happens on a certain segment until the accident is cleaned up.
The outflow rate should be always no more than that according
to the road capacity, i.e.,
μij(T) ≤ cij(T). (18)
C. Path-Planning Cost Metric
The path-planning algorithm is to avoid the congestion on
the road, with considering the preference of drivers, e.g., the
shortest path or the most familiar path. Here, we consider
the path length as the driver’s first-order preference. Let Lmd
rij
denote the changed path for vehicle m (with destination d) at
intersection i, where rij means that, according to the newly
planned path, vehicle m changes its path by going through
road segment (i, j) toward destination d, satisfying j ∈ Ji.
Compared with current path length Lmd
Si
, the increased path
length is |Lmd
rij
| − |Lmd
Si
|, where Si is the path choice before
being replanned. Obviously, it is possible that the changed path
leads to more travel time and more consumed fuel energy. Let
pmd
rij
denote the cost of vehicle m for a certain turning decision
rij toward destination d, given Si = rij. If intersection i is not
in the current path of md, pmd
rij
is zero; otherwise, it is modeled
with respect to the increased path length as follows:
pmd
rij
= ρ Lmd
rij
− Lmd
Si
(19)
where ρ(·) is a nonnegative increasing function to measure the
impacts of the increase in path length, i.e., (|Lmd
rij
| − |Lmd
Si
|)
[40]. Then, the average cost of vehicles taking turning rij on
road segment (i, j) can be calculated as
pij(T)=
⎧
⎨
⎩
1
m∈V
wm
m∈V,d∈D
wm · pmd
rij
, if
m∈V
wm =0
∞, otherwise.
(20)
For an intersection (e.g., intersection i), since there may be
several neighboring intersections as the candidates of the com-
ing intersections, the average cost of vehicles belonging to
intersection i is defined as
piJi
(T)=
⎧
⎨
⎩
1
j∈Ji
αij (T )
j∈Ji
αij(T)pij(T), if
j∈Ji
αij(T)=0
0, otherwise
(21)
where αij(T) is set as 1 in the first case of (20) (i.e., when
m∈V wm = 0); otherwise, it is 0.
D. Network Stability
The definition of Queue and Network Stability [41] is used
to represent traffic congestion avoidance in our path-planning
optimization problem.5
For intersection i, Qi(T) is strongly
stable if and only if
lim
T0→∞
sup
1
T0
T0
T =0
E [Qi(T)] < ∞. (22)
The information on Qi(T) is required to identify whether an
intersection is stable or not. If the traffic inflow and outflow
information is detected by the cameras or traffic flowmeters
connected to RSUs; Qi(T) is expected to be calculated directly.
If the traffic information is relayed in VANETs as there is
no RSU at the intersection, the relayed information is utilized
in the vehicle-traffic server to predict the traffic flow infor-
mation with a certain transmission delay. According to (10),
this uploading transmission delay can be estimated as ψ /Δ,
which here is mainly caused by the intermittent connections in
VANETs. With this transmission delay, the proposed algorithm
can utilize a more accurate virtual queue information for path
planning in each sample time, i.e., Qi(T − ψ /Δ ). Note that,
if and only if all queues in the network are strongly stable,
vehicle traffic in the whole road network is strongly stable.
E. Utilization-Minus-Cost Maximization Problem
Taking account of both the traffic flows of the network
and the path-planning cost of vehicles, the objective of the
path-planning algorithm is considered to maximize the overall
spatial utilization minus planning cost at the same time with
the network congestion avoidance. This objective indicates that
the total traffic flow improvement and the path-planning cost
reduction should be jointly considered and carefully balanced.
Specifically, once the traffic server receives the traffic flow
and accident warning messages collected from both RSUs and
vehicles via VANETs (or cellular networks), a path-planning
algorithm is calculated to update and determine λij(T) accord-
ing to the optimization problem, i.e., the number of vehicles
dispatched over road segment (i, j) in the Tth sample time
max
i∈I j∈Ji
λij(T) −
i∈I
piJi
(T)
s.t. (11), (18), and (22). (23)
This objective is to maximize the spatial utility while mini-
mizing travel cost, under the following constraints: 1) the flow
balance of each intersection; 2) the limitation of outflow rate
on each road segment; and 3) the congestion avoidance of each
intersection. We exploit Lyapunov optimization process [41] to
5The definition of queue and network stability is also used, for example, in
[42] and [43] for the stability and utility optimization to make online control
decisions.

solve this problem (to be introduced in Section VI). Then, in the
sample time T, based on the path-planning algorithm, a vehicle
with destination d can be dispatched from one intersection
to another (e.g., from intersection i to intersection j with
contribution λij(T)), in order to improve the spatial utility
and to reduce travel cost. This updated path will deliver to the
GPS device to navigate the required vehicle. In other words, a
turning decision, rij, for a taxi or a private car at intersection i,
can be decided based on the corresponding λij(T) and piJi
(T),
and furthermore, the replanned path can be calculated based on
this turning decision. Note that, if the traffic flow information is
collected by VANETs (or cellular networks), the transmission
delay in VANETs, i.e., ψ /Δ, should be considered in the third
constraint as discussed in Section V-D.
VI. REAL-TIME OPTIMAL PATH PLANNING
Here, the path-planning algorithm is first proposed to help
vehicles to bypass congestion and balance traffic evenly in the
whole network. Then, the convergence and the computation
complexity of the proposed algorithm are discussed.
A. Path-Planning Algorithm Design
The optimization problem (23) can be solved by applying
the drift-plus-penalty framework in the Lyapunov optimization
process [41]. By following dynamic algorithm at each sample
time, we derive vehicles’ turning decisions for maximizing
the lower bound of network throughput. According to the
Lyapunov optimization process, let WiJi
(T) denote the weight
of intersection i in sample time T
WiJi
(T)=
j∈Ji
αij(T) min cij(T),
d∈D
Qd
i (T)−Qd
j (T)
− KpiJi
(T) (24)
where K is a nonnegative constant defined by vehicle traffic
server used for all vehicles, with the same order of the recip-
rocal of travel cost (i.e., piJi
(T)) [41]. Equation (24) implies
that the weight of an intersection (e.g., intersection i) is related
to: 1) the differential queue backlog between intersection i
and its neighboring intersections and 2) average intersection
travel cost. Vehicles at intersection with the largest weight are
replanned first. Vehicles with destination d stored at intersection
i should be dispatched to queue Qd
j∗
d
(T) of intersection j∗
d,
where j∗
d = arg maxj∈Ji
{Qd
i (T) − Qd
j (T)}, according to the
largest differential queue backlog. The number of the vehicles
with destination d replanned to intersection j∗
d is min{Qd
i (T) −
Qd
j∗
d
(T), cij∗
d
(T)}. Then, queues at all the remaining intersec-
tions are updated correspondingly. The same process continues
until all intersections related are processed. The sketch of the
proposed dynamic algorithm is summarized in Algorithm 1.
The implication of path planning is to prioritize those vehicles
in such an intersection with larger differential queue backlogs
and shorter increased path lengths under new turning decisions
(i.e., lower average travel cost).
1: procedure PATH PLANNING (Algorithm 1)
2: /∗
Initialization ∗
/
3: A candidate set of intersections Ic = ∅;
4: for each intersection i ∈ I do
5: Calculate the weight WiJi
(T) for each intersection;
6: if WiJi
(T) = 0 then
7: update the set Ic ← Ic ∪ {i}.
8: end if
9: end for
10: /∗
Path planning ∗
/
11: while intersection Ic = ∅ do
12: Schedule intersection i = arg max
u∈Ic
{WuJu
(T)}.
13: /∗
Path planning ∗
/
14: for each destination d do
15: Find j∗
d = arg max
j∈Ji
{Qd
i (T) − Qd
j (T)}.
16: qd
j∗
d
(T) ← min{Qd
i (T) − Qd
j∗
d
(T), cij∗
d
(T)}.
17: /∗
Update queues Qd
i (T) and Qd
j∗
d
(T) ∗
/
18: Qd
i (T) ← Qd
i (T) − qd
j∗
d
(T);
19: Qd
j∗
d
(T) ← Qd
j∗
d
(T) + qd
j∗
d
(T);
20: end for
21: Ic ← Ic {i}.
22: end while
23: end procedure
B. Analysis of Algorithm Performance
For the network stability of the proposed path-planning algo-
rithm, we have the following lemma.
Lemma 1: With the proposed path-planning algorithm, net-
work stability can be guaranteed.
Proof: To prove network stability, according to [41], we
need to show that the summation of the average square of
queue sizes of those intersections’ virtual queues does not
increase with time. Consider the interflow exchange between
any two intersections (e.g., i and j). Let Qi(T) (Qi(T + 1))
and Qj(T) (Qj(T + 1)), respectively, denote the queue lengths
of intersections i and j in sample time T (T + 1). In specific,
based on our path-planning algorithm, between two neigh-
boring intersections, vehicles are always dispatched from a
long queue to a short queue. Assume that the change of the
queue length of the two intersection is because qd
j (T) vehicles,
where d ∈ Γ, are dispatched from intersection i to intersec-
tion j, i.e., Qd
i (T + 1) = Qd
i (T) − qd
j (T) and Qd
j (T + 1) =
Qd
j (T) + qd
j (T). Then, the consequence of qd
j (T) dispatched
vehicles is
E [Qi(T +1)]2
+[Qj(T +1)]2
− [Qi(T)]2
+ [Qj(T)]2
= 2E
d
qd
j (T) − Qi(T) + Qj(T) ·
d
qd
j (T)
(25)
where d qd
j (T) is the total number of vehicles, which are
dispatched from intersection i to intersection j at time T. As we

have qd
j (T)=min{Qd
i (T)−Qd
j (T), cij(T)},Qi(T)= d Qd
i (T),
and Qj(T) = d Qd
j (T), the following inequality holds:
d
qd
j (T) + Qj(T) − Qi(T) ≤ 0. (26)
Thus, the right side of (25) is no more than zero. Then, the
summation of average squares of queue size is satisfied as
E [Qi(T + 1)]2
+ E [Qj(T + 1)]2
≤ E [Qi(T)]2
+ E [Qj(T)]2
. (27)
That is, the summation of average square of queue size of
those intersections’ virtual queues does not increase with time.
Under the cases with all destinations and multiple intersections,
the similar results still hold, which implies the stability of
network and the avoidance of traffic congestion in a network,
as discussed in [41].
Furthermore, the computational complexity of the proposed
algorithm is given as the following lemma.
Lemma 2: The total computational complexity is propor-
tional to the square of the number of intersections in the
map times the upper bound of the number of neighboring
intersections.
Proof: We first calculate the weight of each intersection;
thus, the complexity of this step is O(|I|). Second, we schedule
each intersection in Ic. For each intersection to be scheduled,
we need to find the right neighboring intersection j∗
d for each
destination d. Therefore, the complexity of the second step is
O(|Ic|((1 + |Ic|)/2 + |Γ|U)), where U is the upper bound of
the number of neighboring intersections of one intersection. As
the |Ic| and |I| are in the same order, the overall complexity is
given by
O (|I|) + O
|I| + |I|2
2
+ |I||Γ|U . (28)
Furthermore, as the number of roads |Γ| and that of intersec-
tions |I| have the relationship 2Γ/U ≤ |I|, the complexity can
be further simplified as
O (|I|) + O
|I| + |I|2
2
+
|I|2
U2
2
= O |I|2
U2
. (29)
Thus, the total computational complexity is proportional to the
square of the number of intersections in the map times the upper
bound of the number of neighboring intersections.
The proposed path-planning algorithm can perform better
than the conventional path planning because of the following
reasons. First, the proposed path-planning algorithm is up-
dated based on real-time and accurate messages received from
V2V/V2R communication, by which, for instance, a warning
message of traffic jam can be delivered and impact timely on de-
cisions of path planning. Second, in hybrid-VANET-enhanced
networks, public transportation system can help to deliver the
messages, leading to the reduced transmission delay for delay-
sensitive real-time path planning. Third, the proposed path
planning is designed to reduce traveling cost in a coordinated
manner to avoid particular parts of the road network over-
loaded. Finally, the relatively low computational complexity
Fig. 3. Simulation scenario of University of Waterloo region in VISSIM.
of the proposed algorithm makes the path-planning algorithm
achieve better performance in a reasonable and realistic way.
VII. PERFORMANCE EVALUATION
Here, we consider a realistic suburb scenario, as shown in
Fig. 3, which is the region around the campus of University
of Waterloo, Waterloo, ON, Canada. To emulate the timeliness
of the proposed communication framework, a highly realistic
microscopic vehicle traffic simulator, known as VISSIM [44],
is employed to generate vehicle trace files for recording the
vehicle mobility characteristics, based on which the effective-
ness of the hybrid communication in supporting real-time path
planning is studied. However, since the paths of vehicles cannot
be changed or controlled by the external algorithm in VISSIM,
we further develop a Java-based platform to investigate the
performance of the proposed path-planning algorithm. Specif-
ically, average moving delay (AMD), defined as the average
travel time per trip, is used as a metric in the evaluation.
A. Simulation Setup
1) Simulation Settings in VISSIM: To simulate a VANET
with VISSIM in Kitchener–Waterloo (K–W) downtown region,
vehicles are pushed into the region of 6000 m ∗ 2800 m, as
shown in Fig. 3. At the beginning of the simulation, vehicles are
set to enter the region from the preset entries (e.g., nine entries
at the ends of main roads), following a Poisson process at a rate
of 2500 vehicle/h/entry. The proportion of a bus or a taxi in the
traffic flow is set as 5%. After the duration of the first 240 s,
the vehicle pushing in stops to reach an equivalent average den-
sity of 30 vehicle/km/lane, which represents a medium-density
scenario. Similarly, if the first duration is set to be 480 s, the
scenario becomes a high-density one. In the VISSIM, vehicle
information (e.g., location and velocity, etc.) is recorded every
0.2 s. The total simulation time lasts for 3600 s. In addition, the
velocity distribution for all vehicles follows the velocity model
described in Section III-C with parameters vL = 30 km/h,
vH = 60 km/h, and D = 600 s. The reduced speed areas can
be set at any time during the simulation in VISSIM, to simulate
different kinds of incidents/accidents in the suburb scenarios.
2) Simulation Settings in Java: To evaluate the performance
of the path-planning algorithm in Java, with the same region,
500 vehicular nodes with transmission radius of 150 m are
first randomly deployed to cover the K–W downtown region,
as shown in Fig. 3. In addition, 12 intersections are chosen
as candidates for RSU deployment in the region. Further, each

Fig. 4. Performance evaluation of the proposed transmission mechanism in a medium-vehicle-density scenario. (a) Transmission performances in a high-vehicle-
density scenario. (b) PDF of V2V distance. (c) PDF of the last hop V2R distance. (d) Transmission delay of a vehicle to an RSU given the transmission range.
vehicle moves to its destination with a velocity of 60 km/h (or
30 km/h). The path planning can be performed at the beginning
of a sample time, e.g., 10 s. The lifetime of a warning message,
i.e., TL, is set as 300 s. The duration for each simulation is set to
be 3 h, and the results are averaged over 100 runs. To illustrate
the effect of different kinds of accidents on path planning, big
accidents are set to last for 20 min, whereas small accidents are
set to last for only 10 min.
B. Evaluation of Transmissions in VISSIM
We first evaluate the transmission performance of VANETs
in a high-density scenario. The evaluated metrics are the con-
nection probability of a vehicle to an RSU and the end-to-end
transmission delay. As shown in Fig. 4(a), in a high-density
scenario, the connection probability is high even without the
support of a cellular network. For instance, when the vehicle
transmission range is 120 m (which is very easy to be reached
as discussed in [45] and way larger than the average headway
distance), the connection probability can be 80%. As the trans-
mission range of vehicle increases, the connection probability
increases; since the increased, the transmission range supplies
more chances to connect with other vehicles or RSUs. Fur-
thermore, as shown in Fig. 4(a), in the high-density case, the
transmission delay is only around 5.5 s, which is less than a
sample time of 10 s. Notice that a short end-to-end transmission
delay facilitates the implementation of real-time path planning,
which needs traffic information update as timely and accurate
as possible.
The intercontact time is evaluated through the vehicle head-
way distance (i.e., V2V distance) and the last-hop V2R dis-
tance. Based on the trace files from VISSIM, Fig. 4(b) shows
the probability density function (pdf) of vehicle headway
distance. It is shown that the pdf of the headway distance
matches well with an exponential distribution, as shown in
Fig. 4(b), which validates the premise in Section III-C. Based
on the resultant headway-distance distribution, the average
V2V intercontact time E[Tv2v] can be obtained, as shown in
Section IV-B,
Moreover, the pdf of the distance from the last-hop vehicle
to the nearest RSU for one delivery is given in Fig. 4(c). The
simulated pdf matches well with the theoretical pdf, which is
calculated with the parameters in the simulation setup based
on (5). According to Fig. 4(c), the average distance from a
last-hop vehicle to its neatest RSU can be further calculated
to be around 180 m. Then, the transmission delay incurred
by the intercontact time of the last-hop V2R transmission can
be calculated as discussed in Section IV-B, i.e., E[Toff ] =
E[Uoff ]/V = E[Last − hop V 2R distance − R]/V .
We then investigate the end-to-end transmission performance
in terms of the connection probability and transmission delay
in the medium-density scenario. Based on the proposed trans-
mission mechanism, a hybrid VANET is utilized to reduce the
transmission delay, making the path planning more efficient and

timely. As shown in Fig. 4(d), via pure VANETs, the average
end-to-end transmission delay decreases as the transmission
range increases since the increased transmission range gives
higher possibilities for a transmitting vehicle to find an end-to-
end path to an RSU (given neglectable transmission delay when
two vehicles are within the transmission range of each other).
Moreover, in hybrid VANETs, when the public transportation
system is utilized, the increased transmission range can signifi-
cantly create more chances to meet a bus or a taxi, thus leading
to a smaller transmission delay. Notice that, once any bus or taxi
nodes receive the messages, they can help deliver the messages
to the vehicle-traffic server directly via the cellular network,
and the intermittent connections of the multihop VANET can
be efficiently reduced. In particular, as the transmission range
of vehicles becomes smaller (i.e., the problem of intermittent
connections in VANETs is more severe), the delay reduction
comes to be bigger if the hybrid-VANET-enhanced transporta-
tion system is involved. The reason is that, with a smaller
transmission range, an end-to-end transmission path is more
difficult to be guaranteed by pure VANETs, leading to a larger
delay gap compared with the one that utilizes the hybrid-
VANET-enhanced transportation system. In addition, the simu-
lated results of transmission delay match well to the theoretical
ones shown in (10). Hence, based on the proposed transmission
mechanism, an efficient and timely message transmission for
path planning can be achieved, which makes it possible to
perform global real-time path planning.
C. Simulation of the Proposed Path Planning in Java
Fig. 5(a) shows the AMD with and without implementing
the proposed path-planning algorithm. We can observe that the
AMD with the proposed path planning is much lower than that
without path planning. For example, when accident number
is two, AMD is reduced by 35%. Furthermore, with more
accidents, AMD becomes longer; however, the ones utilizing
the proposed path-planning algorithm increase more slowly.
The cost of path planning in terms of the increased path length
is also shown in Fig. 5(a). When a vehicle wants to change its
previous shortest path due to a sensed accident ahead, a novel
smooth path is generated with less AMD at the cost of the
increased path length. It shows that the average cost for users
is still admissible when traffic environments are experiencing
terrible conditions.
In addition, Fig. 5(b) shows the AMD comparison between
our proposed path-planning algorithm and a distributed path-
planning algorithm proposed in [46]. In the distributed path
planning, each individual vehicle researches a new path based
on the known information of accidents when it receives any in-
formation on congestion or accidents but neither with coordina-
tion among vehicles nor considering the individual cost of path
planning. As shown in Fig. 5(b), AMD under our proposed path
planning is reduced on average by 27%, as compared with that
of the distributed algorithm. Because each individual vehicle
plans path only on its own interest, it is very possible that a
number of vehicles swarm into the same road segment based
on the same warning message information. Then, new traffic
jam can happen with high probability and result in the increased
Fig. 5. AMD reduction by path planning. (a) Comparison of AMD between
the proposed path planning and the traditional one. (b) Comparison of AMD
between the proposed path planning and one distributed algorithm.
AMD. Fig. 5(b) shows a good adaptability of the proposed path-
planning algorithm to avoid introducing other traffic jam.
Fig. 6(a) shows the effect of different kinds of accidents
on AMD. It is shown that, when a big accident continues for
long duration (i.e., 20 min), AMD increases, compared with a
small accident (i.e., lasting 10 min only). This is because, as
some vehicles have no capabilities to change their current paths
(e.g., buses), AMD increases due to their longer trapped time in
congestion. Similarly, when the number of accidents increases,
AMD becomes longer, but not much. Thus, it implies that our
proposed path-planning algorithm is with a good adaptability
to different accident duration. Moreover, if the number of
slow-speed vehicles increases, more vehicles slowed down to
30 km/h will introduce larger AMD, as shown in Fig. 6(b).
Since more slow vehicles on one road can result in high vehicle
density, Fig. 6(b) shows good adaptability to vehicle densi-
ties. Furthermore, comparing this performance with the one in
Fig. 5(a), AMD is a little longer than the case under few slow
vehicles since network vehicle-traffic throughput is diminished
due to more vehicles with slow speed stranded on one road.
The sensitivity analyses in terms of both the vehicle number
and the number of accidents on AMD are discussed in Fig. 7.
Here, we considered that the accidents are big, lasting for
20 min. First, we can see that the AMD increases with the
increased number of vehicles under our algorithm in Fig. 7.

Fig. 6. AMD versus specified accidents. (a) AMD comparison between dif-
ferent accident time duration. (b) AMD comparison between different numbers
of slow vehicles.
Fig. 7. AMD versus both the number of vehicles and specified accidents.
The reason for this AMD increment is that more vehicles may
result in a higher probability of introducing another traffic jam
at crossings. However, taking the case with three accidents as
an example, even when the number of vehicles increases to 800,
AMD is relatively small, around 375 s, as shown in Fig. 7. This
result shows a good adaptability of the proposed path-planning
algorithm to the total vehicle number. In addition, Fig. 7 shows
that the AMD increases with the increased number of accidents
with the similar trend as stated previously.
VIII. CONCLUSION
In this paper, we have developed a hybrid-VANET-enhanced
real-time path planning for vehicles to avoid congestion in an
ITS. We first propose a hybrid-VANET-enhanced ITS frame-
work with functionalities of real-time traffic information collec-
tion, involving both V2V and V2R communications in VANETs
and cellular communications in public transportation system.
Then, a globally optimal real-time path-planning algorithm
is designed to improve overall spatial utilization and reduce
average vehicle travel cost by means of Lyapunov optimization.
Extensive simulations have been conducted to demonstrate
that the proposed path-planning algorithm can achieve better
performance than that without real-time path planning in terms
of AMD and the adaptability to different accident duration and
traffic densities. In future work, we intend to find large-scale
real-world vehicle traffic traces to further validate benefits of
the proposed algorithm in practical scenarios.
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Miao Wang received the B.Sc. degree from
Beijing University of Posts and Telecommunica-
tions, Beijing, China, in 2007 and the M.Sc. degree
from Beihang University, Beijing, in 2010. She is
currently working toward the Ph.D. degree with the
Department of Electrical and Computer Engineering,
University of Waterloo, Waterloo, ON, Canada.
Her current research interests include traffic con-
trol, capacity and delay analysis, and routing proto-
col design for vehicular networks.
Hangguan Shan (M’10) received the B.Sc. degree
in electrical engineering from Zhejiang University,
Hangzhou, China, in 2004 and the Ph.D. degree
in electrical engineering from Fudan University,
Shanghai, China, in 2009.
From 2009 to 2010, he was a Postdoctoral Re-
search Fellow with the University of Waterloo,
Waterloo, ON, Canada. Since February 2011, he has
been with the Department of Information Science
and Electronic Engineering, Zhejiang University, as
an Assistant Professor. His research interests include
resource management and quality-of-service provisioning in vehicular ad hoc
networks, wireless body area networks, and cooperative networks.
Dr. Shan coreceived the Best Industry Paper Award at the IEEE Wireless
Communications and Networking Conference, Quintana-Roo, Mexico, in 2011.
Rongxing Lu (S’09–M’11) received the Ph.D. de-
gree in computer science from Shanghai Jiao Tong
University, Shanghai, China, in 2006 and the Ph.D.
degree in electrical and computer engineering from
the University of Waterloo, Waterloo, ON, Canada,
in 2012.
From May 2012 to April 2013, he was a Post-
doctoral Fellow with the University of Waterloo,
Waterloo, ON, Canada. Since May 2013, he has been
an Assistant Professor with the School of Electrical
and Electronics Engineering, Nanyang Technolog-
ical University, Singapore. His research interests include wireless network
security, big data security and privacy, network coding security, and applied
cryptography.
Ran Zhang received the B.E. degree in electron-
ics engineering from Tsinghua University, Beijing,
China, in 2010. He is currently working toward the
Ph.D. degree with the Broadband Communication
Research Group, University of Waterloo, Waterloo,
ON, Canada.
His current research interests include resource
management in heterogeneous wireless access net-
works, carrier aggregation in Long-Term Evolution
Advanced systems, and electrical vehicle charging
control in smart grids.

Xuemin (Sherman) Shen (M’97–SM’02–F’09) re-
ceived the B.Sc. degree from Dalian Maritime Uni-
versity, Dalian, China, in 1982 and the M.Sc. and
Ph.D. degrees from Rutgers University, Piscataway,
NJ, USA, in 1987 and 1990, all in electrical
engineering.
From 2004 to 2008, he was the Associate Chair for
Graduate Studies with the Department of Electrical
and Computer Engineering, University of Waterloo,
Waterloo, ON, Canada. He is currently a Professor
and the University Research Chair with the Depart-
ment of Electrical and Computer Engineering, University of Waterloo. He is
a coauthor or editor of six books and the author of several papers and book
chapters in wireless communications and networks, control, and ﬁltering. His
research interests include resource management in interconnected wireless/
wired networks, wireless network security, wireless body area networks, and
vehicular ad hoc and sensor networks.
Dr. Shen served as the Technical Program Committee Chair for the 2010 Fall
IEEE Vehicular Technology Conference (IEEE VTC’10 Fall); the Symposia
Chair for the 2010 IEEE International Conference on Communications (IEEE
ICC’10); the Tutorial Chair for IEEE VTC’11 Spring and IEEE ICC’08;
the Technical Program Committee Chair for the 2007 IEEE Global Commu-
nications Conference; the General Cochair for the 2007 IEEE International
Conference on Communications and Networking in China and the 2006 Third
International Conference on Quality of Service in Heterogeneous Wired/
Wireless Networks; and the Chair for IEEE Communications Society Technical
Committee on Wireless Communications and Peer-to-Peer Communications
and Networking. He also serves/served as the Editor-in-Chief for IEEE NET-
WORK, Peer-to-Peer Networking and Application, and IET Communications; as
a Founding Area Editor for IEEE TRANSACTIONS ON WIRELESS COMMUNI-
CATIONS; as an Associate Editor for IEEE TRANSACTIONS ON VEHICULAR
TECHNOLOGY, Computer Networks, and ACM Wireless Networks; and as
the Guest Editor for IEEE JOURNAL ON SELECTED AREAS IN COMMUNI-
CATIONS, IEEE WIRELESS COMMUNICATIONS, IEEE COMMUNICATIONS
MAGAZINE, and ACM Mobile Networks and Applications. He is a registered
Professional Engineer of Ontario, Canada; a Fellow of the Canadian Academy
of Engineering and the Engineering Institute of Canada; and a Distinguished
Lecturer of the IEEE Vehicular Technology and Communications Societies.
Fan Bai received the B.S. degree in automation en-
gineering from Tsinghua University, Beijing, China,
in 1999 and the M.S. and Ph.D. degrees in elec-
trical engineering from the University of Southern
California, Los Angeles, CA, USA, in 2005.
Since September 2005, he has been a Senior
Researcher with the Electrical and Control Inte-
gration Laboratory, Research and Development and
Planning, General Motors Corporation, Warren, MI,
USA. He is also serving as a Ph.D. supervisory
committee member at Carnegie Mellon University,
Pittsburgh, PA, USA, and the University of Illinois at Urbana-Champaign,
Champaign, IL, USA. He is the author of about 40 book chapters and papers
presented in conference and published in prestigious journals, including the
ACM Annual International Conference on Mobile Computing and Networking,
the IEEE International Conference on Computer Communications, the ACM
International Symposium on Mobile Ad Hoc Networking and Computing,
the IEEE Communications Society Conference on Networks, the IEEE Inter-
national Conference on Communications, the IEEE Global Communications
Conference, the IEEE Wireless Communications and Networking Confer-
ence, the IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, the
IEEE WIRELESS COMMUNICATION MAGAZINE, the IEEE COMMUNICA-
TION MAGAZINE, and the Elsevier Ad Hoc Networks Journal. His current
research interests include the discovery of fundamental principles and the
analysis and design of protocols/systems for next-generation vehicular ad hoc
networks for safety, telematics, and infotainment applications.
Dr. Bai serves as a Technical Program Cochair for the 2007 IEEE Interna-
tional Symposium on Wireless Vehicular Communications and the 2008 Inter-
national Workshop on Mobile Vehicular Networks. He also currently serves
as an Associate Editor for the IEEE TRANSACTION ON VEHICULAR TECH-
NOLOGY and the IEEE TRANSACTION ON MOBILE COMPUTING. He also
serves as a Guest Editor for IEEE WIRELESS COMMUNICATION MAGAZINE,
IEEE VEHICULAR TECHNOLOGY MAGAZINE , and Elsevier Ad Hoc Networks
Journal. He received the Charles L. McCuen Special Achievement Award
from General Motors Corporation in 2006, in recognition for his extraordinary
accomplishment in the area of vehicle-to-vehicle communications for drive
assistance and safety.

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