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934 IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 5, NO. 5, SEPTEMBER 2018
A Dynamic Road Incident Information Delivery
Strategy to Reduce Urban Traffic Congestion
Liang Qi, Member, IEEE, Mengchu Zhou, Fellow, IEEE, and Wenjing Luan, Student Member, IEEE
Abstract—Advanced information and communication technolo-
gies can be used to facilitate traffic incident management. If an
incident is detected and blocks a road link, in order to reduce the
incident-induced traffic congestion, a dynamic strategy to deliver
incident information to selected drivers and help them make
detours in urban areas is proposed by this work. Time-dependent
shortest path algorithms are used to generate a subnetwork
where vehicles should receive such information. A simulation
approach based on an extended cell transmission model is used to
describe traffic flow in urban networks where path information
and traffic flow at downstream road links are well modeled.
Simulation results reveal the influences of some major parameters
of an incident-induced congestion dissipation process such as the
ratio of route-changing vehicles to the total vehicles, operation
time interval of the proposed strategy, traffic density in the
traffic network, and the scope of the area where traffic incident
information is delivered. The results can be used to improve the
state of the art in preventing urban road traffic congestion caused
by incidents.
Index Terms—Cell transmission model (CTM), intelligent
transportation systems (ITS), traffic incident management (TIM),
urban traffic congestion.
I. INTRODUCTION
TRAFFIC incidents are any non-recurring events including
traffic crashes, disabled vehicles, roadway maintenance
and reconstruction projects, and special non-emergency events,
e.g., ball games, concerts, or any other events that significantly
affect roadway operations [1]. They can cause a significant
capacity reduction of roadways. Traffic incident management
(TIM) makes a systematic effort to detect, respond to, and
Manuscript received November 13, 2017; accepted March 7, 2018. This
work was supported by the National Natural Science Foundation of China
(61374148). Recommended by Associate Editor Yanjun Liu. (Corresponding
author: Mengchu Zhou.)
Citation: L. Qi, M. C. Zhou, and W. J. Luan, “A dynamic road incident
information delivery strategy to reduce urban traffic congestion,” IEEE/CAA
J. of Autom. Sinica, vol. 5, no. 5, pp. 934−945, Sep. 2018.
L. Qi is with the Department of Computer Science and Technology,
Shandong University of Science and Technology, Qingdao 266590, China,
with the Department of Computer Science, Tongji University, Shanghai
201804, China, and also with the Department of Electrical and Computer
Engineering, New Jersey Institute of Technology, Newark NJ 07102, USA
(e-mail: qiliangsdkd@163.com).
M. C. Zhou is with the Department of Electrical and Computer Engineer-
ing, New Jersey Institute of Technology, Newark NJ 07102, USA (e-mail:
zhou@njit.edu).
W. J. Luan is with the Key Laboratory of Embedded System and Service
Computing, Ministry of Education, Shanghai Electronic Transactions and
Information Service Collaborative Innovation Center, Department of Com-
puter Science, Tongji University, Shanghai 201804, China (e-mail: wenjing-
mengjing@163.com).
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/JAS.2018.7511165
remove traffic incidents. It aims to offer the rapid recovery
of traffic safety and capacity, and leads to many measurable
benefits, such as decreases in fuel consumption, incident
duration, secondary accidents, and traffic jams [1], [2].
There are many traditional traffic control methods for TIM
in highways, such as lane control [3], variable speed limit con-
trol [4], and ramp metering control [5]. So far, incident-based
urban traffic congestion is mostly controlled and prevented
through traffic flow diversion with the help of the traffic police.
Such a strategy is unfortunately labor-intensive, inflexible,
and costly. Intelligent transportation systems [6]−[8], such
as advanced traveler information systems (ATIS), can be
employed to improve the network efficiency via direct or
indirect recommendation of alternative routes [9]. Real-time
traffic information can be sent to drivers through two main
kinds of devices: in-car [10] and road-side devices [11]. The
type, such as radio GPS-navigators and Google Maps, helps
drivers make sensible routing decisions at bifurcation nodes
of the network. However, there are some disadvantages with
these kinds of devices. On one hand, drivers who are familiar
with the traffic conditions in a network may not use such
agencies and thus optimize their individual routes based on
past experiences. On the other hand, incident information is
only useful to a finite number of selected drivers near the
incident, and useless to others. The second kind of devices
can be used to deliver information on major traffic events
(e.g., incidents and congestion) and reduce incident-based
congestion or enhancing traffic safety. However, they are
usually spatially and/or temporally limited and constrained
in the amount of information delivered. Thus, to the best
of our knowledge, we find no intelligent strategies that can
decide which drivers should be informed of a particular traffic
incident. Recently, the proliferation of mobile communication
technologies and devices such as smartphones and on-board
units of connected vehicles makes it possible to construct an
accessible and cost-effective platform for public-sector Traffic
Operation Centers to deliver location-based and personalized
traveler information in a timely fashion [12]. In this work,
we design a new strategy to deliver incident information to a
finite number of selected drivers in urban areas. The Dijkstra’s
algorithm is used to generate a subnetwork where vehicles
can receive the traffic incident information. This helps reduce
incident-induced congestion at a manageable communication
cost. Simulations are conducted to give a quantitative result
regarding traffic congestion reduction with the proposed strat-
egy.
Many simulation models are proposed to model traffic
jam formation due to incidents. Wright and Roberg propose an
QI et al.: A DYNAMIC ROAD INCIDENT INFORMATION DELIVERY STRATEGY TO REDUCE URBAN TRAFFIC CONGESTION 935
incident-based jam growth model in [13] and discuss the im-
pact of the length of the channelized part of roads and stopline
width assignment on jam formation. Roberg et al. develop
several alternative strategies in [14] to prevent gridlock of a
network and dissipate traffic jams once they have been formed.
Long et al. [15] extend a cell transmission model (CTM)
and apply it to simulate incident-based jam propagation in
two-way rectangular grid networks. They also propose control
strategies for dispersing incident-based traffic jam and evaluate
their efficiency [16]. CTM-based models can depict traffic flow
at downstream road links well. However, the aforementioned
simulation models do not contain any path-related information
when studying travelers’ detour behaviors and the incident-
induced congestion formulation. In this work we further extend
the CTM, build a model to simulate incident-based traffic jams
in urban areas and illustrate the effectiveness of our proposed
strategy.
The rest of this paper is organized as follows. Section II
reviews the related work. Section III presents some definitions
about the traffic network. Section IV gives traffic incident
information delivery strategies. In this section, given some as-
sumptions regarding traffic flow routing choices, a traffic flow
sub-network is generated based on Dijkstra’s algorithm, and
traffic flow in the network is modeled by an extended CTM.
Section V gives a case study and evaluates the effectiveness
of the proposed detour strategies via simulation. Section VI
concludes this paper.
II. RE LATE D WOR K
A. Traffic Incident Management (TIM)
There are many traditional traffic control methods for TIM.
For example, lane control systems [3] deploy lane control
signals in the context of lane closure. They are used to manage
traffic at a lane level to facilitate a smooth lane change by in-
forming drivers about an impending bottleneck. Variable speed
limit control [4] in highways is verified to be able to increase
work-zone throughputs and decrease total vehicle delays.
Traffic signals at on-ramps of freeway [5] can help manage the
traffic inflow rate and reduce lane-blocking incident-induced
traffic congestion. These methods are suitable for TIM in
highways. So far incident-based urban traffic congestion is
mostly controlled and prevented through traffic flow diversion
with the help of traffic police, which is unfortunately labor-
intensive, inflexible, and costly. Traffic light control [6] at road
intersections is regarded as a major strategy to guarantee the
safe crossing of conflicting streams of vehicles and pedestrians
and lead to efficient network operations. They are suitable for
non-saturated and stable traffic conditions. However, changing
conditions in a non-predictable way such as an incident may
lead to the invalidation of the aforementioned traffic light
control strategies, and causes unexpected congestion. Some
intelligent systems have recently been designed for preventing
incident-induced traffic congestion [17], [18]. In such systems,
ban signals are used to notify road users of a ban situation that
might not be readily apparent [19]−[21].
B. Dynamic Traffic Assignment (DTA)
DTA is used to assign time-varying traffic flow to different
highways given the vehicular demand and certain behavioral
rules [22]. It consists of two components: a travel choice
principle and a traffic-flow component. The former models
how travelers decide whether to travel or not [22], and
if so, how they select their routes, departure time, modes,
and destinations. The latter depicts how traffic propagates
inside a transport network. DTA is an important research
area because of its a wide range of applications in real-time
traffic control and management [23]. In fact, DTA models
are key components in developing sophisticated intelligent
transportation systems (ITS) technologies such as advanced
traveler information systems (ATIS) [24] and advanced traffic
management systems (ATMS) [25]. In ATIS, DTA models
can determine the best route and departure time and provide
some anticipatory traffic information for travelers based on a
forecasted traffic pattern.
DTA models can be developed by either an analytical [26]
or simulation-based approach [27]. DTA problems can be
formulated analytically in terms of mathematical problems
[23], [28], such as mathematical programming [29], optimal
control [30], and variational inequality problems [31]. Most
prior studies focus on determining in advance the solution
properties of the models, such as solution existence and
uniqueness. The simulation approach focuses on enabling
practical deployment of the DTA models for realistic highway
networks, their applicability to real-life highway networks,
and their ability to adequately capture traffic dynamics and
microscopic driver behavior such as lane changing. However,
a simulation-based approach cannot guarantee the solution
properties of the model in general [23].
DTA problems are formulated as both path-based [31],
[32] and link-based models [28]. An important feature of
the former is that the path set has to be explicitly defined
and can range from medium to large-sized networks. Hence,
for large-scale network applications, path enumeration has not
been used to obtain the path set. Link-based models can avoid
path enumeration in the solution procedure, and hence can be
applied to large-scale networks. However, they do not contain
path-related information and cannot capture certain realistic
traffic dynamics such as dynamic traffic intersections across
multiple links.
The commonly adopted travel choice principle in DTA
is the dynamic extension of Wardrop’s Principle called the
Dynamic User Optimal (DUO) principle [23], [31]. This
principle assumes that travelers select their routes and/or
departure times to minimize their travel costs such as travel
time. Most existing planning and management procedures are
developed with this notion. Virtually all network planning
models adhering to Wardrop’s principle require the following
strong assumptions: 1) travelers know the travel time on all
routes, and 2) travelers are able to select the paths costing
the shortest travel time. While these assumptions may be
reasonable in a static network, they are questionable for
real-world networks because they are dynamic and can be
highly stochastic. The current research is not presented as an
936 IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 5, NO. 5, SEPTEMBER 2018
operational model for actual applications. For example, we can
deliver the incident information to the corresponding traveler
if we know the path of each vehicle. However, we do not
know such path information, and in this case we should design
incident delivery strategy to travelers to deal with the cases in
which an incident takes place.
C. Advanced Traveler Information Systems (ATIS)
ATIS are any systems that acquire, analyze, and present
information to assist surface transportation travelers in moving
from their starting location (origin) to their desired destination.
Relevant information may include locations of incidents, if
any, weather and road conditions, optimal routes, recom-
mended speeds, and lane restrictions [24]. ATIS are considered
a powerful tool to enhance travelers’ experience [33]. ATIS are
also claimed to be useful under recurrent network congestion
as they reduce the uncertainty of travelers with respect to travel
time [33]. Moreover, they are useful for travelers who are
unfamiliar with the network (e.g., tourists), as well as for all
travelers when the network is temporarily affected by some
significant disruptions and/or by unexpected or non-recurrent
traffic conditions [34]. Recently, the proliferation of mobile
communication technologies and devices such as smartphones
and on-board units of connected vehicles makes it possible to
construct an accessible and cost-effective platform for public-
sector Traffic Operation Centers to deliver location-based and
personalized traveler information in a timely fashion [12]. Our
work lies in the scope of the ATIS when it selectively delivers
incident information to a finite number of selected drivers
but not all vehicles. The effectiveness is verified through a
simulation approach.
D. Cell Transmission Model (CTM)
Daganzo [35] proposes a CTM to simplify the solution
scheme of the Lighthill-Whitham-Richards (LWR) model [36],
[37] such that it can be used to depict the road link traffic
which is consistent with the kinematic property of traffic
flow. The CTM has been used to accurately describe real-
istic highway traffic. Daganzo’s original development of the
CTM is mainly intended to provide transportation planners
with another way of predicting traffic behavior for a given
roadway section. Researchers have employed the CTM in
many real-world transportation applications such as dynamic
traffic assignment [38], [23], signal control [39]−[41], ramp
metering [42], [43], and traffic prediction. The advantage of
this approach is that traffic dynamics such as queue spill-
back and traffic interaction across links can be captured.
The CTM has been used in the estimation of traffic flow
density [44]−[46] and other traffic state variables such as
flows and space-mean speeds [47]. Long et al. [15] extend
the CTM and apply it to simulate incident-based jam prop-
agation in two-way rectangular grid networks. The interface
of vehicles conducting different turns at urban road links can
be well described [15]. They also propose control strategies
for dispersing incident-based traffic jams and evaluating their
efficiency [16]. The above cell-based simulation models do not
contain any path-related information when studying incident-
induced congestion formulation. In this work we further extend
CTM [15] to simulate travelers’ detour and incident-based
traffic jams in urban areas and illustrate the effectiveness of
our proposed incident information delivery strategy.
III. BASI C NOTATIO NS
First, some basic notations are presented: Ris a real number
set, R+is the set of positive real numbers, N={0,1,2, . . .}
is a natural number set, N+=N/{0}is the positive integer
set, Nm={0,1,2, . . . , m}and N+
m={1,2, . . . , m}where m
∈N+. We consider a multi-destination network as a directed
and connected graph G(N, A), where N={1,2, . . . , m}
denotes the set of nodes and Adenotes the set of links. Link
a= (la,ha)∈Ais a link with a tail node laand a head
node ha.A(j)and B(j)are the set of links leaving node j
and heading to node j, respectively. We give some definitions
regarding a multi-destination traffic network G(N, A). Usually
a path is composed of a sequence of links. We assume that
there is at most one link from a node to another. Thus, a path
can be expressed by a sequence of nodes. We give the formal
definition of a path as follows.
Definition 1: A path σ1,m = (1,2, . . . , m)is defined as a
sequence of nodes labeled from 1 to m, where (j, j + 1) ∈A,
∀j∈N+
m−1, 1 is its origin and mis its destination. The set of
all paths in Gis denoted as Γ. The set of all paths from node
1 to node mis denoted as Γ1,m. If (j, j + 1) is a link in path
σ1,m, we denote that (j, j + 1) ∈σ1,m, else (j, j + 1) /∈σ1,m;
if jis a node in path σ1,m, we denote that j∈σ1,m , else j
/∈σ1,m ; and σjdenotes a path with node jas its origin. We
define a connection between two paths as σ1,m =σ1,j +σj,m,
where j∈σ1,m.
All concepts in Definition 1 can be found in the graph theory
in [48].
Definition 2: l:A→R+is a link length function, where l(j,
j+1) is the length of the link (j, j +1); and lj,j+1 denotes the
length between two nodes jand j+1 where lj,j+1 =l(j, j +1)
if (j, j + 1) ∈A, and lj,j+1 = +∞if (j, j + 1) /∈A.
Definition 3: L:Γ→R+is a path length function, where
L(σ) =
m−1
X
j=1
lj,j+1 (1)
where σ= (1,2, . . . , m)∈Γ.
Definition 4: τ:(A, t)→R+is a link travel-time function,
where τ(a, t)denotes the travel time for a vehicle to pass link
awhen it stays at the tail of aat time t.τi,j denotes the time
needed from nodes ito j.
Definition 5: T:Γ→R+is a path travel-time function,
where
T(σ) =
m−1
X
j=1
τ(lj,j+1 , tj,j+1)(2)
denotes the travel time that a vehicle needs to pass path σ∈Γ.
Definition 6: f:Γ→N+is a node-count function, where
f(σ) = |σ| − 1denotes node count in path σ∈Γ.
Definition 7: σ∗
1,m denotes a time-dependent shortest path
with the fewest nodes from node 1 to node m, if
QI et al.: A DYNAMIC ROAD INCIDENT INFORMATION DELIVERY STRATEGY TO REDUCE URBAN TRAFFIC CONGESTION 937
∀σ∈Γ1,m :T(σ∗
1,m)≤T(σ)and f(σ∗
1,m)≤f(σ)(3)
T1,m =T(σ∗
1,m)denotes the travel time to pass the time-
dependent shortest path with the fewest nodes from node 1
to node m; and Γ∗
1,m is the set of all time-dependent shortest
path with the fewest nodes from 1 to m.Γ∗denotes the set
of all time-dependent shortest path with the fewest nodes.
IV. INCIDENT INF OR MATION DELI VE RY STR ATEGY
This section presents a dynamic strategy to deliver incident
information to a finite number of selected drivers in urban
areas in order to help them make detours. According to [13],
[14], and [16], the boundary of incident-induced traffic jams
has an approximate diamond shape in grid networks with the
first blocked junction as the center. We need to provide traffic
incident information to drivers heading towards the blocked
link. First, we make some assumptions regarding the traffic
flow evolution. Based on them, we can simplify the network
and focus on only those links where traffic flow is affected by
the incident.
A. Drivers’ Path Selection Assumptions
In urban areas, for a traveler going from an origin to a
destination, there are usually several paths. Regarding the path
which is most selected by drivers, we make the following
assumptions.
Assumption 1: Time-dependent Shortest Path Selection: We
assume that given two paths from an origin to destination,
without any information regarding the traffic condition such
as incident, drivers select the one requiring the least time. If
two paths cost the same travel time, drivers will choose the
one with the shortest path. Formally given two paths σ1,σ2∈
Γ1,m with T(σ1)< T (σ2), or T(σ1) = T(σ2)and L(σ1)<
L(σ2), then drivers select path σ1from origin 1 to destination
m.
Assumption 2: Fewest-node Path Selection: We assume that
given two same-travel-time and same-length paths from the
origin to destination, drivers usually select a path with fewer
road intersections to prevent extra traffic delay induced by
traffic signals. Formally given two paths σ1,σ2∈Γ1,m with
T(σ1) = T(σ2),L(σ1) = L(σ2)and f(σ1)< f(σ2), drivers
select path σ1from origin 1 to destination m.
Assumption 3: Equal Probability Selection:) If there are
Nsame-travel-time, same-length and same-number-of-node
paths from the origin to destination, the probability of each
path to be selected is equal, i.e., a driver has the probability
of 1/N to select each path.
B. Sub-network Construction
Given a network G(N, A)and a link s= (ls, hs)where an
incident happens and blocks the link, we adopt the Dijkstra’s
algorithm to generate a sub-network G(N0, A0)which contains
all paths with each satisfying the following conditions: it is a
time-dependent shortest path from the origin to its destination
hs; it has fewer nodes than other paths from the origin to
hs; and it contains link s. The traffic flow in the sub-network
could be affected by the incident on sunder Assumptions 1−3,
because some vehicles are being driven to the blocked link.
The detailed steps to obtain G(N0, A0)are shown as follows.
Algorithm 1 Generate a Sub-network G(N0, A0)
Input: A network G(N, A) and a link s= (ls, hs) where an
incident occurs.
Output: A sub-network G(N0, A0).
Step 1. Initialization
Set S:= {hs, ls}; //Scontains the nodes whose time-
dependent shortest paths to hshave been obtained
Set R:= N−S,N0:= {hs, ls},A0:= {(ls, hs)}and
σls:= s;
Set Tj,hs:= + ∝and fls,hs:= 0;
Set Γ∗
1,m := Γ∗:= {s}and Γ∗
j,hs:= ∅;
Step 2. Calculation and update
Select a node j∈Rsuch that the paths from jto ls
and then hsare the time-dependent shortest paths of
those from a node in Rto lsand then hs, i.e.,
∃σk= (k,...,ls, hs)∈Γ∗and (j, k)∈A
such that ∀σk0= (k0,...,ls, hs)∈Γ∗,j0∈Tand
(j0, k0)∈A:T(σk) + τj,k ≤T(σk0) + τj0,k0,L(σk)
+lj,k ≤L(σk0) + lj0,k0;
For each path σj
f(σj) := f(σk)+1if σj= (j, k) + σk.
If σjis a time-dependent shortest path with the
fewest nodes from jto hs, then
Γ∗
j,hs:= Γ∗
j,hs∪ {σj};
Take node jout of R, i.e., R:= R− {j};
Put node jinto S, i.e., S:= S+{j};
End If
End For
If there exists no node j0such that (j0, j)∈A, then
Put all nodes in each path σj∈Γ∗
j,hsinto N0, i.e.,
N0:= N0+{r|r∈σj};
Put all links in each path σj∈Γ∗
j,hsinto A0, i.e.,
A0:= A0+{(r,k)|(r,k)∈σj};
End If
Step 3. Iteration
Repeat Step 2 until S=N;
Return
Assume that the number of nodes in Nis n. For each node
in N, all paths with the shortest distance from it to hsshould
be computed. Therefore, the complexity of the algorithm of
generating such a sub-network is O(n2).
C. Traffic Network Model Based on CTM
Daganzo [35] proposes a CTM to simplify the solution
scheme of the Lighthill-Whitham-Richards (LWR) model [36],
[37] such that it can be used to depict the road link traffic
which is consistent with the kinematic property of traffic flow.
This work extends CTM to model urban network traffic flow.
The path-related information will be contained in the model
when studying the incident-induced congestion formulation.
We use a time-step method based on the extended CTM
to simulate the formation and dissipation of incident-based
938 IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 5, NO. 5, SEPTEMBER 2018
traffic jams and evaluate the efficiency of the proposed control
strategies.
As shown in Fig. 1, each link ain the networks is divided
into two distinct zones: downstream queue storage areas L,
Sand Rwhere vehicles are organized into separate turning
movements (left in L, straight in S, and right in R), and an
upstream reservoir where the turning movements are mixed.
Notice that there may be less than three storage areas, e.g.,
the queue storage areas are composed of Sand Rwhere there
is no left turn for the traffic outflow of link a. We assume that
the upstream reservoir is composed of λcells indexed from 1
to λ, and the channelized queue area occupies a cell indexed
λ+ 1. We adopt φL,φS, and φRto denote the proportions
of vehicles travelling in the left turning, straight, and right
turning directions, respectively. Stopline width assignment
variables αL,αS,αR, respectively, denote the proportions of
the segregated queue areas devoted to the left turning queue
storage area, to the straight queue storage area and to the right
turning queue storage area. According to the definition, we
have φL+φS+φR= 1 and αL+αS+αR= 1. We adopt a
“balanced” layout of stop line assignment [13] such that the
stop line widths devoted to the straight and turning directions
are in exactly the same ratio as the demands, i.e., φL=αL,
φS=αS, and φR=αR.
Fig. 1. Link ain networks.
Note that traffic rules will not be changed and the vehicles in
the downstream queue areas will not change lanes. Using the
network model, we design a network traffic simulation model
based on the time-step method. Traffic flow formulation can
be classified into the following categories: inflow of upstream
reservoir of the origin and the other nodes (i= 1), inflow of
upstream cells (1 < i ≤λ−1), and inflow and outflow of
channelized downstream queue area (i=λ). In the following
equations, v(miles per hour) is the free flow speed and w
(miles per hour) is the speed of all backward moving waves.
yi(t)is the number of vehicles that enter cell iduring time
interval t,ni(t)is the number of vehicles in cell ibefore
t,Ni(t)denotes the maximum number of vehicles that can
be contained in cell iduring t, and Qi(t)denotes the inflow
capacity in cell iduring t. More details regarding CTM can be
referred to [35]. The inflow formulation under normal traffic
conditions, i.e., without incidents, is presented as follows:
1) Inflow of Upstream Reservoir From an Origin: Let da(t)
denote traffic demand rate from an origin node lato link ain
time interval t,ds
a(t)traffic demand rate from node lathrough
link ato link sat time t,φs
a(t)and the proportion of vehicles
entering link aat time twith the destination to s. The inflow
of upstream reservoir of the origin can be calculated as
y1
a(t) = min (da(t), Q1
a(t),w¡N1
a(t)−n1
a(t)¢
v).(4)
The number of vehicles that enter the first cell of link ain
time interval tand choose bas the next link is calculated as
y1
ab(t) = φab (t)y1
a(t).(5)
The proportion of vehicles that enter the first cell of link a
and head to link sin time interval tis computed as
φ1s
a(t) = ds
a(t)
da(t).(6)
The number of vehicles that enter the first cell of link ain
time interval twith the destination to sis calculated as
y1s
a(t) = φ1s
a(t)y1
a(t).(7)
The number of vehicles that enter the first cell of link a
in time interval t, choose bas the next link and head to sis
calculated as
y1s
ab(t) = φ1s
ab(t)y1
a(t)(8)
where φ1s
ab(t)is determined according Assumptions 1−3.
2) Inflow of Upstream Cells: nis
a(t)denotes the number of
vehicles contained in cell iof aand head to sat the start
of time interval t;φi
ab(t)denotes the proportion of vehicles
contained in cell iof link aand choose bas the next link;
φis
a(t)denotes the proportion of vehicles that enter cell iof
link aand head to link sin time interval t;yis
a(t)denotes the
number of vehicles that enter cell iof link a, choose bas the
next link and head to sin time interval t;φis
ab(t)and yis
ab(t)
respectively denote the proportion and number of vehicles that
enter cell iof link a, where link bis the next link, and the
time to link sis time interval t. The inflow of upstream cells
can be calculated as
yi
a(t) = min (ni−1
a(t), Qi
a(t),w¡Ni
a(t)−ni
a(t)¢
v),
1< i ≤λ−1(9)
φi
ab(t) =
ni−1
ab (t)
ni−1
a(t),if ni−1
a(t)6= 0
0,else
(10)
yi
ab(t) = φi
ab(t)yi
a(t)(11)
φis
a(t) =
ni−1,s
a(t)
ni−1
a(t),if ni−1
a(t)6= 0
0,else
(12)
yis
a(t) = φis
a(t)yi
a(t)(13)
φis
ab(t) =
ni−1,s
ab (t)
ni−1
a(t),if ni−1
a(t)6= 0
0,else
(14)
yis
ab(t) = φis
ab(t)yi
a(t).(15)
QI et al.: A DYNAMIC ROAD INCIDENT INFORMATION DELIVERY STRATEGY TO REDUCE URBAN TRAFFIC CONGESTION 939
3) Inflow of Channelized Downstream Queue Area: The
upper bound of inflow of the downstream queue area for
vehicles travelling from link ato link bis computed as follows:
y0
ab(t) = min ½αab Qλ
a(t),w(αabNλ
a(t)−nλ
ab(t))
v¾.(16)
Because of interference between turning vehicles and
straight vehicles [30], the total inflow of the channelized
queues area can be formulated as follows:
yλ
a(t) = min
b∈B(ha)½y0
ab(t)
αab ¾.(17)
The inflow of each direction can be calculated as follows:
φλ−1
ab (t) =
nλ−1
ab (t)
nλ−1
a(t),if nλ−1
a(t)6= 0
0,else
(18)
yλ
ab(t) = min ©φλ−1
ab (t)yλ
a(t), φλ−1
ab (t)nλ−1
a(t)ª.(19)
The proportion of vehicles that enter cell λof link a, choose
link bas the next link, and head to link sin time interval tis
computed as
φλs
ab (t) =
nλ−1,s
a(t)
knλ−1
a(t),if nλ−1
a(t)6= 0 and b∈A(ha)∩A0
0,if nλ−1
a(t) = 0
(20)
where k=|A(ha)∩A0|.
The number of vehicles that enter cell λof link a, choose
link bas the next link, and head to link sin time interval tis
computed as
yλs
ab (t) =
φλs
ab (t)yλ
a(t),if b∈A(ha)∩A0
0,else.
(21)
4) Outflow of Channelized Downstream Queue Area: yλ+1
is defined as the outflow of the terminal cell λ. The outflow
of the channelized downstream queue area can be calculated
as follows:
yλ+1
ab (t) = min ½nλ
ab(t), αab Qλ
a(t),γabw(N1
b(t)−n1
b(t))
v¾
(22)
where γab =αλ
ab(t)/Pa∈B(lb)∩Aαλ
ab(t).
φλ+1,s
ab (t) = nλs
ab (t)
nλ
ab(t)(23)
yλ+1,s
ab (t) = φλ+1,s
ab (t)yλ+1
ab (t)(24)
yλ+1
a(t) = X
b∈B(ha)
yλ+1
ab (t).(25)
5) Inflow of Upstream Reservoir From a No-Origin Node:
y1
a(t) = X
b∈A(la)∩A0
yλ+1
ba (t) + ua(t)(26)
where ua(t)denotes the inflow rate from node lathrough link
aat time t.
y1,s
a(t) = X
b∈A(la)∩A0
yλ+1,s
ba (t)(27)
y1
ab(t) =
max ½φab(t)y1
a(t),y1,s
a(t)
k¾,if b∈A(ha)∩A0
k1µy1
a(t)−X
c∈A(ha)∩A0
max ½φac(t)y1
a(t),y1,s
a(t)
k¾¶,
if b∈A(ha)/A0
(28)
where k=|A(ha)∩A0|and k1=φab(t)/Pb∈A(ha)/A0φab(t).
As a result from the above formulae, the updated number of
vehicles contained in each cell is formulated as follows. For
1≤i≤λ, we have
ni
a(t+ 1) = ni
a(t) + yi
a(t)−yi+1
a(t)(29)
ni
ab(t+ 1) = ni
ab(t) + yi
ab(t)−yi+1
ab (t)(30)
nis
a(t+ 1) = nis
a(t) + yis
a(t)−yi+1,s
a(t)(31)
nis
ab(t+ 1) = nis
ab(t) + yis
ab(t)−yi+1,s
ab (t).(32)
Traffic incidents are modeled by modifying the value of the
corresponding flow capacity of the affected cells. Qi
a(t) = 0
if tbelongs to the period with an obstruction on cell i. We
assume that Qi
a(t)and Ni
a(t)are independent of time and
cells’ indices. Hence, they are constants denoted as Qi
a(t) = Q
and Ni
a(t) = N, where N,Q∈R+.
Traffic jam size is used to describe the effect of congestion.
A cell is jammed if its density in the cells of upstream reservoir
or in any direction of the downstream channelized areas is
greater than 0.9N[16], where Nis the maximal number of
vehicles that a cell in the upstream reservoir or an area in
the downstream channelized areas can contain. The size of
the traffic jam is described in terms of the total number of
jammed cells.
D. Drivers’ Detour Model
When drivers heading towards the incident-blocked link
obtains information regarding the incident, they may detour at
the following intersections along the path. In this section, we
consider three detour strategies where the detour rates could
be related to certain traffic conditions. Let sbe a road link
blocked by an incident. In the following discussion, αdenotes
the proportion of vehicles heading to link sthat will change
their direction and release from a node along its path; βa
represents the proportion of flows that change their direction
to the incident-blocked link and release link a’s head node.
There are assumptions that we will adopt to define the detour
rate:
940 IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 5, NO. 5, SEPTEMBER 2018
Assumption 4: Equal Detour Rate: If a vehicle in link a
heading to the incident-blocked link sreceives the incident
information and decides to detour, it has equal probability to
detour at each of the following nodes on its path to link s.
Formally, let σhabe the path of vehicles from the head node
of link ato s, and let the proportion of vehicles that detour
at a’s head node be βa= 1/f(σha).
Assumption 5: Distance-related Detour Rate: If a vehicle
heading to the incident-blocked link sreceives the incident
information and decides to detour, its probability to detour
is related with the distance to s, i.e., the detour probability
is bigger when the distance is shorter. Formally, let σhabe
the path of vehicles from the head node of link ato s; the
proportion of vehicles detour at node athen equals
βa=
1
L(σha)
X
j∈σhaµ1
L(σj)¶.(33)
Assumption 6: 100 % Detour: The proportion of vehicles
that detour at a’s head node is equal to 100 % when there
is another equal-length time-dependent path containing no
incidental link from the a’s head node to s’s head node.
In the CTM model, given αand βa, we first modify the
number of vehicles in each cell as follows:
ni
ab(t) =
ni
ab(t)−αβanis
a(t)
k1
, b ∈A(ha)∩A0
ni
ab(t) + αβanis
a(t)
k2
, b ∈A(ha)/A0
(34)
where k1=|A(ha)∩A0| 6= 0, k2=|A(ha)/A0| 6= 0, and 1≤
i < λ,
nis
a(t) = (1 −αβa)nis
a(t),1≤i < λ. (35)
At downstream queue channel areas, the number of vehicles
is changed as follows:
nλ,s
ab (t) = (1 −αβa)nλ,s
ab (t).(36)
We also need to change inflow of the upstream reservoir
from an origin for the next time interval. If y1s
a(t)enters the
1st cell, then αproportion of flows leading to link swill
change their direction immediately. Thus, we have
y1s
a(t) = (1 −αβa)y1s
a(t)(37)
yi
ab(t) =
yi
ab(t)−αβayis
a(t)
k1
, b ∈A(ha)∩A0
yi
ab(t) + αβayis
a(t)
k2
, b ∈A(ha)/A0
(38)
where k1=|A(ha)∩A0| 6= 0, k2=|A(ha)/A0| 6= 0, and 1≤
i < λ.
We also need to change inflow of the upstream reservoir
of links that are not the origin for the next time interval.
Suppose that yλ+1,s
ba (t)vehicles enter the 1 st cell from b.
Then αportion of flows change their direction immediately.
Suppose the outflow from link b∈A(la)∩A0to swithout
any traffic incident information from equals y0. Then, after
receiving the incident information, the amount of y0αvehicles
will change their directions while y0αβbvehicles change their
directions and leave from link b, and y0α(1 −βb)vehicles
change directions at upcoming nodes in the path. In the next
link a, the number of vehicles that change their directions is
y0α(1−βb)βa. We use ¯yλ+1,s
ba (t)to denote the outflows of the
terminal cell λof link athat choose link bas the next link and
head to link sin time interval t. Thus, we have the following
equations:
¯yλ+1,s
ba (t) = yλ+1,s
ba (t)−y0α×(1 −βb)βa.(39)
Given that
yλ+1,s
ba (t) = y0×(1 −αβb)
we have that
y0=yλ+1,s
ba (t)
1−αβb
.
Replacing y0in (39), we have
¯yλ+1,s
ba (t) = yλ+1,s
ba (t)×1−α(βb+βa−βbβa)
1−αβb
.(40)
As a result, we change the inflow of the upstream reservoir
of link aduring each next time interval as follows:
y1,s
a(t) = X
b∈A(la)∩A0
yλ+1,s
ba (t)×1−α(βb+βa−βbβa)
1−αβb
.
(41)
Also, we change the following inflow value:
y1
ac(t) =
y1
ac(t)−X
b∈A(la)∩A0
yλ+1,s
ba (t)×α(1 −βb)βa
k1(1 −αβb),
c∈A(ha)∩A0
y1
ac(t) + X
b∈A(la)∩A0
yλ+1,s
ba (t)×α(1 −βb)βa
k2(1 −αβb),
c∈A(ha)/A0
(42)
where k1=|A(ha)∩A0|,k2=|A(ha)/A0|,k2×k26= 0, and
1≤i < λ.
V. C AS E STU DY
A. An Example to Construct a Sub-Network
We give a one-way grid network as an example as shown
in Fig. 2 (a) where it is composed of one-way road links with
adjacent rows or columns having opposite directions. Note that
this kind of road networks is very common in major cities,
for example, New York City. We install a single incident in
the network: a single incident occurs on link (33, 34) in the
network as shown in the figure. Note that in the grid network,
the shortest paths are the time-dependent shortest paths.
According to Algorithm 1, for each node in G, we compute
all the shortest paths leading to node 34 with (33, 34) as the
last link. After that, we obtain the following paths to generate
the sub-network.
Path 1: (3, 23, 28, 33, 34);
Path 2: (18, 31, 32, 33, 34);
QI et al.: A DYNAMIC ROAD INCIDENT INFORMATION DELIVERY STRATEGY TO REDUCE URBAN TRAFFIC CONGESTION 941
Fig. 2. A traffic network with an incident in (a) and the generated sub-
network in (b).
Path 3: (7, 30, 29, 28, 33, 34);
Path 4: (14, 42, 37, 32, 33, 34);
Path 5: (1, 21, 22, 23, 28, 33, 34);
Path 6: (20, 21, 22, 23, 28, 33, 34);
Path 7: (5, 25, 30, 29, 28, 33, 34);
Path 8: (1, 21, 26, 31, 32, 33, 34);
Path 9: (20, 21, 26, 31, 32, 33, 34);
Path 10: (16, 41, 42, 37, 32, 33, 34).
Thus, we have N0={34, 33, 28, 23, 3, 32, 31, 18, 29, 30,
7, 37, 42, 14, 22, 21, 1, 20, 25, 5, 26, 41, 16},A0={(33,
34), (28, 33), (23, 28), (3, 23), (32, 33), (31, 32), (18, 31),
(29, 28), (30, 29), (7, 30), (37, 32), (42, 37), (14, 42), (22,
23), (21, 22), (1, 21), (20, 21), (25, 30), (5, 25), (26, 31), (21,
26), (41, 42), (16, 41)}. After the above steps, the generated
sub-network is shown in Fig. 2 (b). According to Assumptions
1−3, when a traffic incident happens, we only need to provide
the incident information to drivers in the subnetwork. Drivers
from other links of the network in Fig. 2 (a) will not head to
the blocked link, and thus the incident information is useless
for them.
B. Simulation and Results
Now we evaluate the effectiveness of the proposed strategy
by employing MATLAB software through simulation. We first
set specific values for the parameters in our simulation. We set
a single incident on the 5th cell of link (33, 34) in the network
as shown in Fig. 2 (a). The corresponding values of the sub-
network are shown in Table I. In the traffic network in Fig. 3,
according to the special structure, the flow proportions for
directions are set as: φT=αS= 0.5where φT∈ {φL, φR}.
The analysis period of interest is divided into 2000 intervals
(i.e., 2.78 h). The network is assumed to be empty initially.
Traffic starts to enter the network from origins 1−20 at the
first time interval. Several time intervals are required to allow
the system to stabilize. The incident occurs at the t1= 301st
interval. Note that here we do not consider the effect of traffic
light signal strategies regulating the traffic flow. This can be
easily realized by modifying the value of the corresponding
flow capacity of the affected cells. In the simulation, in order
to keep the balance of the traffic flow, we set all inflows as
well as all outflows of links to be equal. We have the value
of inflow and outflow of the nodes.
With the simulation of our designed model, we study the
traffic jam in the traffic network in Fig.2 (b). After the incident
messages are delivered, drivers will then detour. We identify
the influences of some important parameters, i.e., the inflow
rate, the detour rate of drivers, and the start time for providing
traffic incident information. We provide a sensitivity test of the
following parameters as shown in Table II.
Fig. 3. Congestion formulation and dissipation under no traffic control
strategy when traffic incident is from the 300th to 1000th interval, and the
proportion of traffic demand heading to the blocked link is p= 0.1.
First, let zdenote a constant traffic demand at origins, i.e.,
∀t,a,z=da(t), and pdenote the proportion of traffic flow
heading to the blocked link s at origins. We study the effect
of zon jam formation and dissipation if there is no traffic
control strategy. The incident occurs at the 301st interval and
is cleared at the 1000th interval. We set p= 0.1. Some
simulation results of congestion formation and dissipation
are shown in Fig. 3. We learn that when the traffic demand
increases, the traffic jam forms more quickly. We have a result
that if z≤1.3, the traffic jam can dissipate in 100 intervals
(8.33 minutes). In the following simulation, we set the traffic
demand z= 0.8.
Then, we study the proportion of traffic demand at origins
that head to the blocked link, with the results being shown in
Fig. 4. Under the situation where z= 0.8, with a increase of
p, the number of jammed cells grows sharply. There is little
congestion when pis below 0.01.
Fig. 4. Congestion formulation and dissipation under no traffic control
strategy and the proportion of traffic demand at origins that head to the blocked
link is p=0.01, 0.05, 0.1, 0.2, and 0.3, respectively, and z= 0.8.
We further study the end time of the traffic incident and the
results are shown in Fig. 5. Under the traffic conditions where
942 IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 5, NO. 5, SEPTEMBER 2018
TABLE I
PARA ME TERS FO R TH E CTM [16]
Parameters Meaning
The length of each time interval 5 s
Jam density 133 vehicles/km/lane (i.e., 7.5 m for every vehicle in each lane)
Free-flow speed 54 km/h (i.e., 15 m/s), and backward shock-wave speed: 21.6 km/h (i.e., 6 m/s)
Number of lanes 2
Flow capacity 1800 vehicles/h/lane (i.e., 2.5 vehicles/time interval/cell)
Cell length 75 m, and the holding capacity of each cell is 20 vehicles
The number of cells of each link 9 (i.e., the length of every link is 675 m)
TABLE II
PARA ME TE RS TO TE ST
Parameters Values
zA constant traffic demand at origins, i.e., ∀t,a,z=da(t)
αProportion of flows heading to the incident-blocked link that change their direction and release from an intersection (node) along their path
pProportion of traffic flow heading to the blocked link sat origins, i.e., p=ds
a(t)/da(t)
t2Incident clearance time
t3Start time to provide incident information to drivers
ηA constant denoting that the number of nodes from a link in A00 ⊆A0to link sis no more than fwhile the number of nodes from a link
in A0−A00 to sis greater than η
Fig. 5. Congestion formulation and dissipation under no traffic control
strategy and the incident is cleared at the 400th,500th,600th,700th, and
1000th intervals, respectively, where z= 0.8and p= 0.1.
z= 0.8and p= 0.1, if the incident is cleared and traffic
capacity of the blocked link is recovered in 200 intervals
(16.67 minutes), the number of jammed cells can be kept
below 10.
We study when to provide incident information to drivers
in the traffic network in Fig. 6. Under Assumption 4 and the
traffic conditions z= 0.8and p= 0.1, if the proportion of
flows that change their direction to link sis 0.9, there is little
congestion when we start to deliver the incident information
in less than 100 intervals (8.33 minutes). Under Assumption
5, we have similar results as shown in Fig.7.
We study the detour proportion αand have the results as
shown in Fig. 8. We can find there is little congestion formed
when α > 0.8, which means that if more than 80 % vehicles
can obtain the incident information and then detour when z≤
0.8and p≤0.1, no traffic jam occurs. Under Assumption 5,
Fig. 6. Congestion formulation and dissipation when traffic control strategy
begins from the 300th,400th,410th,420th,430th,440th, and 450th
intervals, respectively, under Assumption 4 and where z= 0.8and p= 0.1.
Fig. 7. Congestion formulation and dissipation when traffic control strategy
begins from the 300th,400th,410th,420th,430th,440th, and 450th
intervals, respectively, under Assumption 5 and where z= 0.8and p= 0.1.
we have similar results as shown in Fig.9. Lastly we study
the detour models given by Assumptions 4 and 5, respectively.
Under the traffic conditions that z= 0.8and p= 0.1, we set
QI et al.: A DYNAMIC ROAD INCIDENT INFORMATION DELIVERY STRATEGY TO REDUCE URBAN TRAFFIC CONGESTION 943
z= 2.5,p= 0.4,t3= 450. The results in Fig. 10 show that
there is more congestion under the traffic detour strategy of
Assumption 5 compared to that of Assumption 4. It means
that drivers approaching the blocked link need to leave the
path earlier to help reduce the traffic congestion induced by
the incidents.
Fig. 8. Congestion formulation and dissipation when the strategy begins from
the 300th to 1000th interval, and the detour proportion α=0.5, 0.6, 0.7, 0.8,
and 0.9, respectively, under Assumption 4 and where z= 0.8and p= 0.1.
Fig. 9. Congestion formulation and dissipation when the strategy begins from
the 300th to 1000th interval, and the detour proportion α=0.5, 0.6, 0.7, 0.8,
and 0.9, respectively, under Assumption 5 and where z= 0.8and p= 0.1.
Fig. 10. Congestion formulation and dissipation under traffic conditions z=
2.5,p= 0.4, and when the traffic control strategy begins at t3= 450, and
under the two detour strategies of Assumptions 4 and 5, respectively.
We study a link set A00 and a constant ηwhere the number
of nodes from a link in A00 ⊆A0to link sis no more than η
while the number of nodes from a link in A0−A00 to sis bigger
than η. We only deliver the incident information to drivers at
road links in A00 instead of A0. Obviously, ηrepresents the
scope of area where incident information is delivered. Some
simulation results are shown in Figs. 11 and 12: when α=
0.95, we only deliver information to drivers in link (28, 33)
and (32, 33) such that at most one cell is congested as shown in
Fig. 11. With the decrease of α, when delivering the incident
information to a larger scope of road links, we can have a
better result with fewer jammed cells.
Fig. 11. Congestion formulation and dissipation when f=1−5 under
Assumption 5, and where α= 0.95,z= 0.8and p= 0.1.
Fig. 12. Congestion formulation and dissipation when f=1−5 under
Assumption 5, and where α= 0.60,z= 0.8and p= 0.1.
VI. CONCLUSIONS
This paper presents a new strategy, which provides incident
information to drivers and helps them make detours in urban
areas. Traffic incident information is only transmitted to the
affected vehicles that head towards the blocked link created by
the incident. These vehicles are in a sub-network that can be
generated by the Dijkstra’s algorithm. Simulations are done to
test the effectiveness of the proposed strategy. The CTM-based
model is used to estimate the congestion and promote the
implementation of our strategy. Future work should consider
real world traffic conditions when different links have different
traffic density. We also need to design algorithms to accurately
944 IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 5, NO. 5, SEPTEMBER 2018
estimate the time for vehicles to pass road links, and thus,
obtain the time-dependent shortest path.
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Liang Qi (S’16−M’18) received the B.S. degree in
information and computing science and M.S. degree
in computer software and theory from Shandong
University of Science and Technology, Qingdao,
China, in 2009 and 2012, respectively. He received
the Ph.D. degree in computer software and theory
from Tongji University, Shanghai, China in 2017.
He is currently a Lecturer of computer science and
technology at Shandong University of Science and
Technology, Qingdao, China. From 2015 to 2017,
he was a visiting student in the Department of
Electrical and Computer Engineering, New Jersey Institute of Technology,
Newark, NJ, USA. He has authored over 20 technical papers in journals
and conference proceedings, including IEEE/CAA Journal of Automatica
Sinica, IEEE Transactions on System, Man, and Cybernetics: Systems, and
IEEE Transactions on Intelligent Transportation Systems. He received the
Best Student Paper Award-Finalist in the 15th IEEE International Conference
on Networking, Sensing and Control (ICNSC’2018). His current research
interests include Petri nets, discrete event systems, intelligent transportation
systems, and optimization algorithms.
Mengchu Zhou (S’88−M’90−SM’93−F’03) re-
ceived the B.S. degree in control engineering from
Nanjing University of Science and Technology, Nan-
jing, China in 1983, the M.S. degree in auto-
matic control from Beijing Institute of Technology,
Beijing, China in 1986, and the Ph.D. degree in
computer and systems engineering from Rensselaer
Polytechnic Institute, Troy, NY in 1990. He joined
New Jersey Institute of Technology (NJIT), Newark,
NJ in 1990, and is now a Distinguished Professor of
Electrical and Computer Engineering. His research
interests include Petri nets, intelligent automation, Internet of Things, big data,
web services, and intelligent transportation. He has over 700 publications
including 12 books, 400+journal papers (300+in IEEE transactions), 11
patents and 28 book-chapters. He is the founding Editor of IEEE Press Book
Series on Systems Science and Engineering and Editor-in-Chief of IEEE/CAA
Journal of Automatica Sinica. He is a recipient of Humboldt Research
Award for US Senior Scientists from Alexander von Humboldt Foundation,
Franklin V. Taylor Memorial Award and the Norbert Wiener Award from
IEEE Systems, Man and Cybernetics Society for which he serves as VP for
Conferences and Meetings. He is a life member of Chinese Association for
Science and Technology-USA and served as its President in 1999. He is a
Fellow of International Federation of Automatic Control (IFAC), American
Association for the Advancement of Science (AAAS) and Chinese Association
of Automation (CAA).
Wenjing Luan (S’16) received the B.S. and M.S.
degrees from Shandong University of Science and
Technology, Qingdao, China, in 2009 and 2012,
respectively. She is currently pursuing Ph.D. de-
gree with the Department of Computer Science
and Technology, Tongji University, Shanghai, China.
Her current research interests include location-based
social networks, recommender systems, and intelli-
gent transportation systems. She received the Best
Student Paper Award-Finalist in the 13th IEEE In-
ternational Conference on Networking, Sensing and
Control (ICNSC’2016) Conference.
