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TOPICS IN AUTOMOTIVE NETWORKING
Modeling Urban Traffic:
A Cellular Automata Approach
Ozan K. Tonguz and Wantanee Viriyasitavat, Carnegie Mellon University
Fan Bai, General Motors Corporation
ABSTRACT
In this article we introduce a new cellular
automata approach to construct an urban traffic
mobility model. Based on the developed model,
characteristics of global traffic patterns in urban
areas are studied. Our results show that different
control mechanisms used at intersections such as
cycle duration, green split, and coordination of
traffic lights have a significant effect on intervehicle spacing distribution and traffic dynamics.
These findings provide important insights into
the network connectivity behavior of urban traffic, which are essential for designing appropriate
routing protocols for vehicular ad hoc networks
in urban scenarios.
INTRODUCTION
It is clear that vehicular traffic in an urban
area exhibits a different pattern than that
observed in a highway scenario. While a vehicle on a highway can only go straight, due to
the specific topology and geometry of city
roads, a vehicle in a network of roads (e.g.,
streets and avenues in New York City) might
go straight, make a turn, or stop at an intersection. Car motion is no longer restricted to a
one-dimensional pattern; rather, the road network allows two-dimensional motion where the
direction of motion of a vehicle may change at
an intersection. Due to the crossing of different directional flows, the intersections are
equipped with either unsignalized or signalized
traffic controls. Thus, traffic lights as well as
the synchronization effect of traffic lights at
the intersections have a significant impact on
traffic behavior in urban areas. In other words,
allowing traffic to flow in one direction at an
intersection implies the blockage of traffic flow
in the crossing direction. As a result, car
queues may form before an intersection while
the road after the intersection corresponding
to the turning direction is free [1]. The traffic
pattern therefore exhibits great spatial diversity, making car distribution far from uniform.
Thus, modeling global traffic patterns in a
complex road network that comprises a large
number of intersections is a challenging task.
Since there are no realistic and extensive traces
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0163-6804/09/$25.00 © 2009 IEEE
for urban vehicular traffic, in this article we
attempt to develop a new mobility model based
on the cellular automata (CA) concept to study
traffic in urban areas.
The remainder of this article is organized as
follows. In the next section we discuss related
work. We then present an overview of the CA
concept and several fundamental cellular
automata used for modeling vehicular traffic.
The new CA-based mobility model for urban
traffic is proposed and described in the following
section. The details of the simulation setup used
to obtain numerical results are then presented.
Next, we study how intersections and their control mechanisms affect global traffic patterns and
report the main results of the article. The key
implications of the results are discussed in the
following section, and the final section concludes
the article.
RELATED WORK
Existing traffic mobility models can be classified
into two categories based on the modeling
approach: car following and CA. Examples of
mobility models based on car following include
the Manhattan model [2] and street random
waypoint (STRAW) [3]. Models using car following (e.g., the Manhattan model) either do not
support any intersection control mechanisms
such as traffic lights or stop signs, or (e.g.,
STRAW) require real street maps and support
only two intersection control operations: traffic
lights and stop signs. However, current models
cannot support scenarios with more than two
streets per traffic light in a collision-free environment.
The second modeling approach employs the
CA concept. Despite its ease of implementation and simplicity, CA is a powerful tool that
can generate realistic mobility traces. This concept has been used in many traffic engineering
software packages including Simulation of
Urban Mobility (SUMO) [4], TRANSIM [5],
MMTS [6], and RoadSim [7]. SUMO is an
open source microscopic multimodal traffic
simulation package. Unlike the fundamental
CA model, this tool simulates vehicle movement based on space-continuous cellular
automata in which only time is discrete. Other
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CA-based traffic simulators are TRANSIM
and the multi-agent traffic simulator MMTS.
They are widely used proprietary traffic simulator software developed at ETH Zurich.
These simulators have been used to simulate
public and private transportation and human
behavior in Switzerland, and mainly used for
traffic planning strategies. However, due to
their proprietary nature, the implementation
details of both TRANSIM and MMTS are
not publicly available. RoadSim is the most
recent CA-based model developed by Artimy
et al. It uses the basic CA concept with a
Nagel-Schreckenberg (NaSch) model to
determine the movement of each vehicle.
RoadSim currently supports a limited set of
scenarios: highway, racetrack, and urban
streets with one intersection; the network
connectivity exhibited in such scenarios is
studied in [7].
Among several CA-based mobility models
for urban traffic, the work done by Esser and
Schreckenberg [8] is the most similar to our
work. In contrast to [8], however, our work
implements a realistic intersection control
mechanism with traffic signal coordination and
provides rules for realistic motion of turning
vehicles. In addition, traffic patterns in urban
areas are extensively analyzed, whereas such
analyses do not exist in [8]. While the CA
model is a low-fidelity model (compared to the
car following model), extensive investigations
conducted in [9, 10] have shown that despite its
simplicity, the CA model is capable of capturing and reproducing realistic features of traffic
flow. In addition, due to its discrete nature, the
CA model allows very fast implementation and
can simulate a very large network microscopically in real time [8]. In this article we propose
and use a new CA-based mobility model as a
framework to study characteristics of urban
traffic.
CELLULAR AUTOMATA MODEL
CELLULAR AUTOMATA CONCEPT
A cellular automaton (CA) is a discrete computing model which provides a simple yet flexible
platform for simulating complicated systems and
performing complex computation. Generally, it
is an idealization of physical systems in which
both space and time are assumed to be discrete.
Each cellular automaton consists of two components: a set of cells and a set of rules. The problem space of a CA is divided into cells; each cell
can be in one of some finite states. The CA rules
define transitions between the states of these
cells. At each discrete time step, the rules are
applied to each CA generation repeatedly, causing the system to evolve with time. Note that
based on how a cell and rules are defined, CA
can be used to simulate a simple or very complex system.
The simplest cellular automaton for vehicular
traffic simulates traffic on a one-way single-lane
road; hence, a one-dimensional two-state cellular
automaton is used. In this model the problem
space (i.e., road) is represented by a line of cells.
Each cell can be in either state 1 or 0 depending
on the occupancy of the cell. In other words, the
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v Ÿ current vehicle speed
/* Acceleration step */
if v is less than maximum speed then
increase v by one cell/step
end if
/* Deceleration step */
if a vehicle will collide with vehicle in front with v then
decrease v by one cell/step so that the vehicle stops behind the vehicle in front
end if
/* Randomization step */
if v is greater than 0 then
Decrease v with probability pslow.
end if
/* Movement step */
Update the vehicle speed with v
Vehicle moves forward v cells
Algorithm 1. Vehicle position update algorithm (NaSch model).
cell is in state 1 if it is occupied by a vehicle;
otherwise, it is in state 0. The rules of this cellular automaton define the motion of vehicles. At
each time step, a vehicle can either be at rest or
move forward by one cell if the next cell is
empty. Clearly, the state of each cell entirely
depends on the occupancy of the cell itself and
its two neighboring cells, and the rule can be
formulated as [1]
(t)
(t)
xi(t+1) = (1 – xi(t)) x(t)
i–1 + xi (1 – x i+1),
where xi(t) is the state of cell i at time t, and x(t)
i–1
and x (t)
i+1 are the states of the upstream and
downstream cells at time t, respectively.
ONE-DIMENSIONAL
NAGEL-SCHRECKENBERG MODEL
A more realistic CA rule for one-dimensional
vehicular traffic is the NaSch model proposed by
Nagel and Schreckenberg [11]. In order to take
into account acceleration, random braking, and
individual driving behavior, motion rules used in
the NaSch model are described in Algorithm 1.
Note that for each time step, each vehicle
computes its speed and position based on the
above steps.
TWO-DIMENSIONAL STREET MODEL
Based on NaSch model, Chopard develops a
traffic model for a network of two-dimensional
streets [1]. In this model the motion rules
imposed on vehicles are similar to those used in
the NaSch model with the exception of rules for
vehicles near intersections. To simplify vehicle
movement at a road crossing, Chopard assumes
that a rotary is located at each crossing. In other
words, all vehicles at the road junction (i.e.,
inside the rotary) always move counterclockwise,
and the rotary vehicles have priority over any
entering vehicle. The motion rules of this twodimensional motion model can be found in [1].
This model, however, does not capture the real
traffic behavior as the model gives a higher pri-
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In the case of
non-turning vehicle,
the update
ority to turning traffic than to through traffic. In
the next section we propose a modified CA
model that addresses this issue in order to simulate and analyze more realistic traffic in urban
scenarios.
mechanism is similar
to the one used by
the NaSch model
except the
deceleration step.
In this model, vehicle
may slow down due
to not only the
vehicle in front, but
also the intersection.
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CA-BASED MOBILITY MODEL FOR
URBAN TRAFFIC
The fundamental model for two-dimensional
traffic is the Biham-Middleton-Levine (BML)
model introduced in 1992. In the BML model
each street allows only single-lane one-way traffic, and intersections where two streets intersect
are represented by lattice sites. The states of
horizontal and vertical traffic are updated in
parallel at odd and even discrete time steps,
respectively. In this model vehicles are not
allowed to turn; thus, the number of cars on
each street is entirely determined by the initial
condition. Due to these assumptions, a rotary is
not needed, and the motion rules used to update
the states are similar to those of the one-dimensional NaSch model [11] whose algorithm is
explicitly described in the previous section.
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tion ensures that turning vehicles do not make a
turn at high speed and stop at the intersection
before making a turn. In addition, the second
condition assigns priority to a right-turning vehicle (over a left-turning vehicle) in the case of a
two-way street.
Note that even though horizontal and vertical
traffic are updated at odd and even time steps,
the same motion rules are applied. As opposed
to the NaSch model where cells are updated in
parallel, the state of each cell in our model is
updated sequentially. In other words, the location
of a vehicle in each street is updated only after
the vehicle in front of it (in the same street) is
updated. This feature is incorporated into our
model for incorporating more realistic traffic
behavior, especially in the scenario where traffic
lights are coordinated (usually known as greenwave synchronization). Note that in addition to
the rules defined in our model, there are several
other ways one can specify the motion rules for
two-dimensional urban traffic. However, the
model we develop in this article is a generic
framework that can be tailored to satisfy other
specific requirements; the study presented here
is an illustrative example.
MOTION RULES
INTERSECTION CONTROL MECHANISM
In our model D cells are inserted between each
pair of adjacent lattices (i.e., successive crossings) to construct a segment of the streets. Thus,
each street segment between intersections can
be modeled in the same way as in the NaSch
model. However, due to traffic signals at intersections, additional rules are required for vehicles entering road junctions. Depending on the
turning decision of the vehicle, its position is
updated based on Algorithm 2.
In the case of a non-turning vehicle, the
update mechanism is similar to the one used by
the NaSch model except for the deceleration
step. In this model a vehicle may slow down due
to not only the vehicle in front, but also the
intersection. Note that in the randomization
step, the speed of the vehicle decreases by one
cell/step with a slowdown probability p slow to
take into account the different behavior patterns
of individual drivers. This step is crucial as it
captures the non-deterministic acceleration due
to random external factors and the overreaction
of drivers while slowing down, and its value
depends on the overall driving behavior of people, which may vary with traffic density and time
of the day. High slowdown probability corresponds to drivers who overreact while slowing
down and maintain a larger than required safety
distance to the car in front. This cautious driving
pattern is usually observed in midnight traffic
where the traffic volume is low and cars travel at
a high speed. As a result, these individuals traveling at high speeds tend to decelerate well
ahead of time. On the other hand, a small slowdown probability corresponds to a less cautious
driving pattern, which is usually observed in rush
hour traffic. During this time period, vehicles
travel at low speeds and move closely together;
the intervehicle spacing is small. Hence, the
drivers put on the brakes exactly when they need
to.
In the case of turning vehicles, the first condi-
In addition to the modifications above, we incorporate into the mobility model one of the intersection control operations used in today’s traffic.
Among many types of intersection control, the
three signal operations that have been most used
are pre-timed, actuated, and computer controlled signals. A pre-timed traffic signal is the
most fundamental signaling mechanism, where
the time durations of red and green lights in
each direction are predetermined. Similar to
pre-timed signals, actuated signals have a predetermined green/red light duration. However, an
actuated signal can change its phase (from red
to green, or green to red) before its scheduled
time if the traffic volume is low. Actuated signals
are usually used in rural areas or at night when
the traffic density is very low [12]. Lastly, a computer-controlled signal, unlike the first two signaling modes, does not have predetermined light
intervals. The red/green durations are intelligently computed and dynamically adjusted based
on the current traffic condition. Computer-controlled signals have been implemented in areas
with highly congested traffic such as some parts
of the city of Los Angeles and Washington, DC.
Nevertheless, pre-timed operated signals are the
most commonly used intersection control mechanism in most urban cities. In this article we
therefore assume that the signalized intersections are equipped with pre-timed signals.
In order to realistically simulate the operation of pre-timed signals, there are three necessary parameters that have to be carefully
configured: cycle duration, green split, and traffic signal coordination. Cycle duration (or traffic
light duration) is defined as the amount of time
taken to complete one signal timing cycle; that
is, the amount of time the signal turns green,
changes to yellow, then red, and then green
again. Note that in one cycle duration there is
lost time which takes into account the time an
intersection is unused during the beginning and
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if the vehicle goes straight at the next intersection then
go to Non-turning vehicle
else
go to Turning vehicle
end if
Non-turning vehicle
v Ÿ current vehicle speed
/* Acceleration step */
if v is less than maximum speed then
increase v by one cell/step
end if
/* Deceleration step */
if Red or yellow light at the intersection then
if a vehicle will collide with vehicle in front or pass the intersection with speed v then
decrease v so that the vehicle stops behind the vehicle in front or at intersection (whichever comes first)
end if
else
if a vehicle will collide with vehicle in front with speed v then
decrease v so that the vehicle stops behind the vehicle in front
end if
end if
/* Randomization step */
if v is greater than 0 then
Decrease v by one cell/step with probability pslow.
end if
/* Movement step */
Update the vehicle speed with v
Vehicle moves forward v cells
Turning vehicle
if The vehicle is not yet at the intersection then
go to Non-turning vehicle and assume red light at the intersection
else
if Red light at the intersection or the destination street is congested then
The vehicle does not move
else
if The vehicle wants to make a right turn, or (it makes a left turn and no upcoming traffic from the opposite direction)
then
The vehicle moves to the destination street
else
The vehicle does not move
end if
end if
end if
Algorithm 2. New vehicle position update algorithm (Tonguz-Viriyasitavat-Bai algorithm).
end of a phase (i.e., when the right of way
changes and light indications of all directions are
red). Green split is the fraction of time in a cycle
duration in which specific movements have the
right of way (green indications). In our model,
since we assume an equal amount of traffic in
each direction, the green split value is fixed at
50/50 (i.e., each traffic direction has an equal
amount of green time at any intersection). The
other important operational parameter is the
traffic signal coordination, which is a method of
establishing relationships between adjacent traffic control signals. This coordination is controlled by the value of signal offset defined as the
time from which the signal turns green until the
signal on the succeeding intersection turns green.
If offset is zero (referred to as simple coordination), all the lights will turn green at the same
time. Thus, with an appropriate offset value, a
series of traffic lights are coordinated in such a
way that they allow continuous traffic flow over
several intersections. In the developed model
these three important parameters are calculated
based on traffic volume, traffic speed, and distance between intersections, as shown in Table
1. Figure 1 shows a snapshot of a traffic pattern
generated by our model.
SIMULATION SETTING
NETWORK TOPOLOGY
In the simulations we assume a 2 km × 2 km network topology with 16 evenly spaced horizontal
and vertical streets; thus, two consecutive intersections are separated by 125 m. Each street is
represented by a line of 5 m cells, and two-way
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Parameters
Values
Fixed parameters
Network density (vehicles/km2)
Turning probability for transit traffic
pslow
Speed limit (km/h)
Signal offset (s)
Lost time (s)
80, 160, 240, 320
0.25 (left), 0.25 (right)
0.5
36
10
2
Variable parameters
Signal cycle duration (s)
Signal coordination
45, 90, 120
Simple, green-wave
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Table 1. Values of parameters used in the simulations.
traffic is assumed on each street. All road junctions are equipped with pre-timed signals whose
parameters are given in Table 1. In addition, the
network topology is assumed to be a torus: when
a vehicle reaches the network boundary, it reappears on the same street on the opposite side of
the network boundary.
TRAFFIC PATTERN
Based on the commuting pattern in highly populated cities such as New York City (NYC), we
observe that there are two types of traffic: nontransit and transit traffic. A non-transit traffic
(NTT) vehicle is defined as a vehicle that may or
may not originate within the urban area but has
a destination site within the urban area. On the
other hand, transit traffic (TT) represents vehicles that only pass through the urban area; both
their source and destination locations are outside the region of interest. Consider the Manhattan business area in NYC; the traffic pattern can
be grouped into four categories:
1 Morning rush hour traffic (8 am–10 am):
During this time period, people commute
from their homes in the uptown area to
their workplaces downtown. Hence, the
traffic in this period is characterized by a
low volume of TT and a high volume of
southbound NTT; the overall traffic volume
is high and traffic speed is low.
2 Lunch time traffic (11 am–1 pm): During
this time period, we observe a moderate
volume of TT and a low volume of NTT in
random directions. Thus, overall we observe
moderate traffic volume with moderate
speed.
3 Evening rush hour traffic (4 pm–6 pm):
The traffic in this time period is similar to
that observed during the morning rush hour
as people commute back to their homes in
the uptown area. Hence, we expect to see a
high volume of northbound NTT and a low
volume of TT.
4 Midnight traffic (1 am–3 am): The traffic in
this period has very low volume but travels
at a high speed.
In this article the developed mobility model
assumes a lunch time traffic pattern where an
NTT vehicle randomly chooses its start and end
locations. Based on the chosen locations, the
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Figure 1. Snapshot of traffic pattern generated
by the CA-based model.
vehicle chooses the shortest path to traverse.
Once it arrives at its destination, the vehicle is
removed from the simulation. On the other
hand, since a transit vehicle does not have a destination within the simulation area, only the start
location is randomly chosen; thus, the number of
transit vehicles is constant throughout the simulations. Because there is no specific path between
source and destination, when a transit vehicle
arrives at an intersection, it makes a turning
decision based on a fixed turning probability. In
our simulations the transit traffic turns left,
right, and goes straight with probability 0.25,
0.25, and 0.5, respectively. In addition, due to
very low NTT volume observed during lunch
time, we assume that 80 percent of total traffic is
TT. Detailed investigation of other scenarios is
an interesting subject for future work.
PARAMETER SETTING
All parameters and their values used in the simulations are summarized in Table 1.
RESULTS
THE EFFECT OF SIGNAL CONTROL OPERATION
Due to the presence of intersections and their
control mechanisms, the movement of traffic in
urban areas is completely different from that
observed on highways. Based on the CA-based
mobility model developed, below we analyze in
detail and qualitatively discuss how intersections
and their control parameters affect the overall
traffic pattern and mobility.
Flow Rate — In this section we study traffic
flow rates that measure the rates at which vehicles pass through an intersection as a function of
time in relation to other traffic parameters. Our
simulations were performed at different traffic
light durations whose values are given in Table
1. Figure 2 shows the average flow rate (the
average is taken over all intersections and simulation runs). The results in Fig. 2 indicate that
the average flow rate depends on the cycle duration. In general, we observe that the average
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flow rate decreases as the cycle duration increases: as the signal cycle increases, the time an
intersection is unused increases, thus resulting in
more wasted time.
Consider a scenario with low traffic density
(80 vehicles/km 2 ) and cycle duration of 120 s
(dotted line in Fig. 2). From the simulations we
observe that the intersections are utilized heavily
(i.e., vehicles pass through the intersection) during the first part of the green light period; during this interval, vehicles that have accumulated
during the previous red light periods will pass
through the intersections. To illustrate , let us
assume that this heavily utilized period lasts for
20 s. Thus, the next 40 s of green time (assuming
a green split value of 50/50) is a “dead” period
in which the intersections are not efficiently utilized. This implies roughly 2/3 of green time
duration is wasted. Therefore, in order to obtain
a more efficient intersection control mechanism,
one might resort to reducing the cycle duration.
On the other extreme, however, when the signal
cycle is too short, the green time duration per
phase is proportionally decreased. Thus, the
minimum time for a cycle duration of 45 s [12] is
usually set to limit the time lost starting and
stopping traffic. Since the cycle duration heavily
influences the traffic characteristics, it is important to use realistic values for it to reflect the
behavior of realistic urban traffic.
Number of Congested Intersections — In
this section an intersection is considered “congested” if at least one vehicle is waiting there for
a green light. Thus, the number of congested
intersections is the number of times the traffic
flows are impeded by intersections. Since the
average flow rate decreases as the cycle duration
increases, the average number of congested
intersections is expected to increase with the signal cycle duration. This intuition is confirmed by
the simulation results shown in Fig. 3. When
traffic signals are coordinated, the average number of congested intersections changes only
slightly during the entire simulation. When the
signals are not coordinated, however, we observe
a large fluctuation in this statistic because the
uncoordinated signals disrupt the traffic flow at
almost all intersections. Vehicles are unlikely to
encounter more than two consecutive green
lights and thus have to stop at almost all intersections. Note that perfect coordinated signals
are difficult to achieve due to different driving
patterns of individuals. Nevertheless, these findings emphasize the importance of choosing realistic values for traffic light duration and signal
coordination in simulations of vehicular traffic in
urban areas.
ANALYSIS OF TRAFFIC PATTERN
Intervehicle Spacing — Figure 4 shows intervehicle spacing distributions for different network
densities. Observe that despite the intersections,
the intervehicle spacing distributions are still well
approximated by theoretical exponential distributions. The best fit Q parameters (i.e., average
intervehicle spacing) for all traffic densities are
computed using the maximum likelihood test
(ML). To determine how well the simulation
results fit the theoretical distributions, we resort
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4s
10 s
45 s
90 s
120 s
600
500
400
300
200
100
0
0
500
1000
1500
Time (s)
Figure 2. The average flow rate over all intersections as a function of time for
different cycle durations. Note that there is an optimal cycle duration that
maximizes the flow rate.
to the Kolmogorov-Smirnov test, and the goodness of fit is measured in terms of (D + , D – )
defined as (D+, D–) = max {F*(x) – F(x), F(x) –
F*(x)}, where F*(n) and F(n) denote the hypothesized exponential distribution and the distribution obtained from simulations, respectively. The
corresponding parameters for the fitted exponential distribution and goodness-of-fit measure for
each traffic density are given in Table 2. We
observe several peaks in the probability mass
function (PMF) plot at integer multiples of the
length of a road segment (125 m) and at 0 m in
Fig. 4 (left). This is because several vehicles are
queued waiting for green lights at intersections.
This result agrees with [13], which also reports
very high vehicle density near intersections
despite using a different vehicle mobility model.
Our results indicate that the observed peaks in
the PMF become less pronounced as the vehicle
density gets smaller and vice versa. Despite the
peaks in the PMF plot, however, the exponential
PDF is a good approximation of the intervehicle
spacing distribution (Fig. 4, right) obtained with
our CA model. Note that for all traffic densities,
the exponential distribution accurately estimates
the intervehicle spacing distribution, especially
for spacings larger than 50 m. This somewhat
counterintuitive finding is consistent with that
observed in highway scenarios where the empirical distribution is well estimated by an exponential distribution [14].
Nonuniformity of Traffic Pattern — In order
to gain insights into the traffic distribution in
urban areas, we analyze spatial traffic distribution from two different perspectives:
• Local viewpoint, where we analyze the patterns formed by vehicles within one road
block
• Global viewpoint, where we investigate the
traffic distribution over an entire network
(across different road blocks)
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Average flow rate at an intersection (vehicles/h)
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Coordinated traffic signals
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Uncoordinated traffic signals
30
30
45s
90s
120s
25
Number of congested intersections
Number of congested intersections
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20
15
10
5
0
45s
90s
120s
25
20
15
10
5
0
0
300
600
900
0
300
Time (s)
600
900
Time (s)
Figure 3. The average number of congested intersections are plotted against different signal cycle durations. These simulation results
are obtained from a scenario with 80 vehicles/km2 traffic density.
0.1
1
80 vehicles/km2
160 vehicles/km2
240 vehicles/km2
320 vehicles/km2
0.08
0.8
80 vehicles/km2
0.6
160 vehicles/km2
CDF
PMF
0.06
240 vehicles/km2
0.04
0.4
0.02
0.2
0
0
0
500
1000
1500
2000
320 vehicles/km2
Simulations
Exponential CDF
0
Intervehicle spacing (m)
500
1000
1500
2000
Intervehicle spacing (m)
Figure 4. Comparison between simulation results and the theoretical exponential distribution. The dotted and solid lines in the CDF
plot represent perfect exponential distributions and our simulation results, respectively. The traffic signal has 45 s cycle duration and
50/50 green split, and all signals are coordinated.
In the global viewpoint the density of each
road block is computed, and the result shown in
Fig. 5 (left) illustrates how the density of different road blocks in the network varies. Observe
that in a dense network (density of 320 vehicles/km2), while there are some road blocks that
have high traffic density (i.e., eight vehicles within one road block), there is a large portion of
road blocks (i.e., 35 percent) that have no vehicles. Similar behavior is observed across different traffic densities. In a sparse network with
traffic density of 80 vehicles/km 2 , while most
road blocks have low traffic density, we observe
high traffic density in some road segments.
These results further corroborate the previous
snapshot of traffic generated by the CA model
(Fig. 1).
In addition to the global viewpoint, we also
take the local viewpoint where we analyze how
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vehicles are formed within a single road segment. Figure 5 (right) shows that the local traffic
also exhibits a nonuniform distribution. Observe
that over 50 percent of vehicles are within 20 m
of the intersections. This suggests that the region
near intersections can be very dense, while the
middle section of the road block may have very
low traffic density.
DISCUSSION
It is clear that CA is a powerful tool that can be
used to simulate and analyze urban vehicular
traffic. Based on the results of the previous section, several key observations can be made:
•Using the new CA model proposed, the distribution of intervehicle spacing (both the PMF
and CDF) can be computed. The computed
PMF reveals the presence of several peaks at 0
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1
1
80 vehicles/km2
160 vehicles/km2
240 vehicles/km2
320 vehicles/km2
0.8
0.9
Fraction of vehicles that are less
than x meters from intersections (CDF)
Fraction of road blocks that
contains less than x vehicles (CDF)
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0.6
0.4
0.2
0
0.8
0.7
0.6
0.5
0.4
0.3
0.2
80 vehicles/km2
160 vehicles/km2
240 vehicles/km2
320 vehicles/km2
0.1
0
0
2
4
6
8
10
0
10
Number of vehicles in one road block
20
30
40
50
60
Distance from intersection (m)
Figure 5. Traffic density in each road segment and the distribution of vehicles around an intersection. The traffic signal has 45 s cycle
duration, 50/50 green split, and all signals are coordinated.
m, 125 ms, 250 m, and so on, of which the most
prominent one is, as expected, the peak at 0 m.
It is interesting to note that, especially for low
traffic density and/or low penetration ratio of
DSRC technology, exponential distribution is an
excellent approximation to the actual intervehicle spacing distribution.
•In a two-dimensional scenario, clearly the
number of high rises, buildings, and other obstacles determine the transmission coverage area of
a vehicle. If this is known, this information coupled with the exponential distribution of intervehicle spacing can be used to exactly predict the
number of neighbors to a vehicle. This, in turn,
is a very useful piece of information in determining the connectivity pattern of vehicles. Specifically, based on the observation in the previous
section, the exponential distribution is an accurate approximation when the intervehicle spacing is larger than 50 m. Since the network
connectivity of a vehicle mainly depends on the
number of its immediate neighbors, and a vehicle’s radio transmission range usually extends
beyond 50 m, this exponential finding allows us
to determine the connectivity of a vehicle and
analyze the network connectivity of the entire
network. While the exponential distribution is an
approximation, it can facilitate an accurate and
simple analytical framework capable of modeling
network connectivity in urban vehicular ad hoc
networks (VANETs). Such insights are very
important in designing an efficient routing protocol for urban traffic.
•Even though the intervehicle spacing of
both highway and urban traffic can be approximated by the exponential distribution, the connectivity pattern of a vehicle is very different in
these two scenarios. Unlike one-dimensional
traffic as in a highway scenario, a vehicle in
urban areas may be connected to vehicles traveling on the same or different roads. In other
words, a vehicle on a highway is disconnected
from the network if it has no front or back neighbors in the same or opposite direction. However,
a vehicle in an urban area might not be disconnected in such a situation; it is disconnected only
Traffic density
(vehicle/km2)
Average
intervehicle
spacing (m)
(D–, D+)
80
160
240
320
405.4
207.2
140.0
106.3
(2.4, 4.2)
(2.3, 8.2)
(2.7, 11.5)
(3.1, 14.2)
Table 2. K-S test results for intervehicle distributions against the exponential distributions with
different network densities.
when it does not have neighbors in the intersecting directions. Thus, the disconnected network
problem is less pronounced in an urban scenario
than in a highway scenarios.
•Because of richer network connectivity
observed in urban areas, any two vehicles can
communicate through multiple routes (as
opposed to a single path in a highway scenario).
This, in turn, may add flexibility to the design of
a routing protocol whereby the routing in urban
scenarios can be done via multipath routing as
opposed to only the single-path routing used in a
highway scenario.
•Cellular automata-based mobility modeling
of urban vehicular traffic reveals that while some
parts of the region of interest will be very dense,
other parts will be quite sparse (Fig. 1). This
suggests that a broadcast protocol designed for
urban areas will have to be able to deal with
both the broadcast storm problem [15] and disconnected network problem simultaneously.
•It would be interesting to see if a sensor
network that receives real-time traffic data from
all traffic lights could improve flow rate and ease
congestion in urban areas with a centralized
decision and control system. Ultimately, this
approach seems synergistic to dynamic load balancing [16].
•While the simulation and analysis conducted
in this article were based on a regular Manhattan grid topology, we believe that the methodol-
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Based on a new CA
model, we have
investigated how
urban traffic is
affected by intersections and their
control mechanisms.
Our results show
that control mechanisms such as cycle
duration, green split,
and coordination of
traffic lights have a
significant bearing
on traffic dynamics
and inter-vehicle
spacing distribution.
ogy and techniques developed can be used to
study other urban topologies as well (even irregular ones).
•It would be interesting to compare the predictions of the new CA model proposed in this
article with empirical urban traffic traces. This,
in turn, can verify the validity of the mobility
model used in this article or provide valuable
feedback on how to further refine it.
CONCLUSION
Based on a new CA model, we have investigated
how urban traffic is affected by intersections and
their control mechanisms. Our results show that
control mechanisms such as cycle duration,
green split, and coordination of traffic lights
have a significant bearing on traffic dynamics
and intervehicle spacing distribution. Our findings on urban mobility also provide important
insights into the network connectivity pattern
and how a VANET routing protocol should be
designed in urban settings.
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BIOGRAPHIES
O ZAN K. T ONGUZ ([email protected])
____________ is a tenured full
professor in the Electrical and Computer Engineering
Department of Carnegie Mellon University (CMU). He currently leads substantial research efforts at CMU in the
broad areas of telecommunications and networking. He
has published about 300 papers in IEEE journals and conference proceedings in the areas of wireless networking,
optical communications, and computer networks. He is the
author (with G. Ferrari) of the book Ad Hoc Wireless Networks: A Communication-Theoretic Perspective (Wiley,
2006). His current research interests include vehicular ad
hoc networks, wireless ad hoc and sensor networks, selforganizing networks, bioinformatics, and security. He currently serves or has served as a consultant or expert for
several companies, major law firms, and government agencies in the United States, Europe, and Asia.
WANTANEE VIRIYASITAVAT ([email protected])
____________ is a Ph.D.
candidate in electrical and computer engineering at CMU.
She received her B.S. and M.S. degrees, both from CMU, in
2006. During 2006–2007 she worked as a lecturer in the
Computer Science Department of Mahidol University, Thailand. Her main research interests include traffic mobility
modeling and network protocol design for vehicular ad
hoc networks.
FAN BAI ([email protected])
_________ has been a senior researcher in
the Electrical and Control Integration Laboratory, General
Motors Corporation, since Sept. 2005. Before joining General Motors, he received a B.S. degree in automation engineering from Tsinghua University, Beijing, China, in 1999,
and M.S.E.E. and Ph.D. degrees in electrical engineering
from the University of Southern California, Los Angeles, in
2005. His current research is focused on the discovery of
fundamental principles, and the analysis and design of protocols/systems for next-generation vehicular ad hoc networks.
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