modeling urban traffic: a cellular automata...

IEEE Communications Magazine • May 2009142 0163-6804/09/$25.00 © 2009 IEEE

INTRODUCTION

It is clear that vehicular traffic in an urbanarea exhibits a different pattern than thatobserved in a highway scenario. While a vehi-cle on a highway can only go straight, due tothe specific topology and geometry of cityroads, a vehicle in a network of roads (e.g.,streets and avenues in New York City) mightgo straight, make a turn, or stop at an intersec-tion. Car motion is no longer restricted to aone-dimensional pattern; rather, the road net-work allows two-dimensional motion where thedirection of motion of a vehicle may change atan intersection. Due to the crossing of differ-ent directional flows, the intersections areequipped with either unsignalized or signalizedtraffic controls. Thus, traffic lights as well asthe synchronization effect of traffic lights atthe intersections have a significant impact ontraffic behavior in urban areas. In other words,allowing traffic to flow in one direction at anintersection implies the blockage of traffic flowin the crossing direction. As a result, carqueues may form before an intersection whilethe road after the intersection correspondingto the turning direction is free [1]. The trafficpattern therefore exhibits great spatial diversi-ty, making car distribution far from uniform.Thus, modeling global traffic patterns in acomplex road network that comprises a largenumber of intersections is a challenging task.Since there are no realistic and extensive traces

for urban vehicular traffic, in this article weattempt to develop a new mobility model basedon the cellular automata (CA) concept to studytraffic in urban areas.

The remainder of this article is organized asfollows. In the next section we discuss relatedwork. We then present an overview of the CAconcept and several fundamental cellularautomata used for modeling vehicular traffic.The new CA-based mobility model for urbantraffic is proposed and described in the followingsection. The details of the simulation setup usedto obtain numerical results are then presented.Next, we study how intersections and their con-trol mechanisms affect global traffic patterns andreport the main results of the article. The keyimplications of the results are discussed in thefollowing section, and the final section concludesthe article.

RELATED WORKExisting traffic mobility models can be classifiedinto two categories based on the modelingapproach: car following and CA. Examples ofmobility models based on car following includethe Manhattan model [2] and street randomwaypoint (STRAW) [3]. Models using car fol-lowing (e.g., the Manhattan model) either do notsupport any intersection control mechanismssuch as traffic lights or stop signs, or (e.g.,STRAW) require real street maps and supportonly two intersection control operations: trafficlights and stop signs. However, current modelscannot support scenarios with more than twostreets per traffic light in a collision-free envi-ronment.

The second modeling approach employs theCA concept. Despite its ease of implementa-tion and simplicity, CA is a powerful tool thatcan generate realistic mobility traces. This con-cept has been used in many traffic engineeringsoftware packages including Simulation ofUrban Mobility (SUMO) [4], TRANSIM [5],MMTS [6], and RoadSim [7]. SUMO is anopen source microscopic multimodal trafficsimulation package. Unlike the fundamentalCA model, this tool simulates vehicle move-ment based on space-continuous cellularautomata in which only time is discrete. Other

ABSTRACTIn this article we introduce a new cellular

automata approach to construct an urban trafficmobility model. Based on the developed model,characteristics of global traffic patterns in urbanareas are studied. Our results show that differentcontrol mechanisms used at intersections such ascycle duration, green split, and coordination oftraffic lights have a significant effect on interve-hicle spacing distribution and traffic dynamics.These findings provide important insights intothe network connectivity behavior of urban traf-fic, which are essential for designing appropriaterouting protocols for vehicular ad hoc networksin urban scenarios.

TOPICS IN AUTOMOTIVE NETWORKING

Ozan K. Tonguz and Wantanee Viriyasitavat, Carnegie Mellon University

Fan Bai, General Motors Corporation

Modeling Urban Traffic:A Cellular Automata Approach

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IEEE Communications Magazine • May 2009 143

CA-based traffic simulators are TRANSIMand the multi-agent traffic simulator MMTS.They are widely used proprietary traffic simu-lator software developed at ETH Zurich.These simulators have been used to simulatepublic and private transportation and humanbehavior in Switzerland, and mainly used fortraffic planning strategies. However, due totheir proprietary nature, the implementationdetails of both TRANSIM and MMTS arenot publicly available. RoadSim is the mostrecent CA-based model developed by Artimyet al . It uses the basic CA concept with aNagel-Schreckenberg (NaSch) model todetermine the movement of each vehicle.RoadSim currently supports a limited set ofscenarios: highway, racetrack, and urbanstreets with one intersection; the networkconnectivity exhibited in such scenarios isstudied in [7].

Among several CA-based mobility modelsfor urban traffic, the work done by Esser andSchreckenberg [8] is the most similar to ourwork. In contrast to [8], however, our workimplements a realistic intersection controlmechanism with traffic signal coordination andprovides rules for realistic motion of turningvehicles. In addition, traffic patterns in urbanareas are extensively analyzed, whereas suchanalyses do not exist in [8]. While the CAmodel is a low-fidelity model (compared to thecar following model), extensive investigationsconducted in [9, 10] have shown that despite itssimplicity, the CA model is capable of captur-ing and reproducing realistic features of trafficflow. In addition, due to its discrete nature, theCA model allows very fast implementation andcan simulate a very large network microscopi-cally in real time [8]. In this article we proposeand use a new CA-based mobility model as aframework to study characteristics of urbantraffic.

CELLULAR AUTOMATA MODEL

CELLULAR AUTOMATA CONCEPTA cellular automaton (CA) is a discrete comput-ing model which provides a simple yet flexibleplatform for simulating complicated systems andperforming complex computation. Generally, itis an idealization of physical systems in whichboth space and time are assumed to be discrete.Each cellular automaton consists of two compo-nents: a set of cells and a set of rules. The prob-lem space of a CA is divided into cells; each cellcan be in one of some finite states. The CA rulesdefine transitions between the states of thesecells. At each discrete time step, the rules areapplied to each CA generation repeatedly, caus-ing the system to evolve with time. Note thatbased on how a cell and rules are defined, CAcan be used to simulate a simple or very com-plex system.

The simplest cellular automaton for vehiculartraffic simulates traffic on a one-way single-laneroad; hence, a one-dimensional two-state cellularautomaton is used. In this model the problemspace (i.e., road) is represented by a line of cells.Each cell can be in either state 1 or 0 dependingon the occupancy of the cell. In other words, the

cell is in state 1 if it is occupied by a vehicle;otherwise, it is in state 0. The rules of this cellu-lar automaton define the motion of vehicles. Ateach time step, a vehicle can either be at rest ormove forward by one cell if the next cell isempty. Clearly, the state of each cell entirelydepends on the occupancy of the cell itself andits two neighboring cells, and the rule can beformulated as [1]

xi(t+1) = (1 – xi

(t)) x(t)i–1 + xi

(t)(1 – x(t)i+1),

where xi(t) is the state of cell i at time t, and x(t)

i–1and x(t)

i+1 are the states of the upstream anddownstream cells at time t, respectively.

ONE-DIMENSIONALNAGEL-SCHRECKENBERG MODEL

A more realistic CA rule for one-dimensionalvehicular traffic is the NaSch model proposed byNagel and Schreckenberg [11]. In order to takeinto account acceleration, random braking, andindividual driving behavior, motion rules used inthe NaSch model are described in Algorithm 1.

Note that for each time step, each vehiclecomputes its speed and position based on theabove steps.

TWO-DIMENSIONAL STREET MODELBased on NaSch model, Chopard develops atraffic model for a network of two-dimensionalstreets [1]. In this model the motion rulesimposed on vehicles are similar to those used inthe NaSch model with the exception of rules forvehicles near intersections. To simplify vehiclemovement at a road crossing, Chopard assumesthat a rotary is located at each crossing. In otherwords, all vehicles at the road junction (i.e.,inside the rotary) always move counterclockwise,and the rotary vehicles have priority over anyentering vehicle. The motion rules of this two-dimensional motion model can be found in [1].This model, however, does not capture the realtraffic behavior as the model gives a higher pri-

� Algorithm 1. Vehicle position update algorithm (NaSch model).

v current vehicle speed

/* Acceleration step */if v is less than maximum speed then

increase v by one cell/stepend 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 frontend if

/* Randomization step */if v is greater than 0 then

Decrease v with probability pslow.end if

/* Movement step */Update the vehicle speed with vVehicle moves forward v cells


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IEEE Communications Magazine • May 2009144

ority to turning traffic than to through traffic. Inthe next section we propose a modified CAmodel that addresses this issue in order to simu-late and analyze more realistic traffic in urbanscenarios.

CA-BASED MOBILITY MODEL FORURBAN TRAFFIC

The fundamental model for two-dimensionaltraffic is the Biham-Middleton-Levine (BML)model introduced in 1992. In the BML modeleach street allows only single-lane one-way traf-fic, and intersections where two streets intersectare represented by lattice sites. The states ofhorizontal and vertical traffic are updated inparallel at odd and even discrete time steps,respectively. In this model vehicles are notallowed to turn; thus, the number of cars oneach street is entirely determined by the initialcondition. Due to these assumptions, a rotary isnot needed, and the motion rules used to updatethe states are similar to those of the one-dimen-sional NaSch model [11] whose algorithm isexplicitly described in the previous section.

MOTION RULESIn our model D cells are inserted between eachpair of adjacent lattices (i.e., successive cross-ings) to construct a segment of the streets. Thus,each street segment between intersections canbe modeled in the same way as in the NaSchmodel. However, due to traffic signals at inter-sections, additional rules are required for vehi-cles entering road junctions. Depending on theturning decision of the vehicle, its position isupdated based on Algorithm 2.

In the case of a non-turning vehicle, theupdate mechanism is similar to the one used bythe NaSch model except for the decelerationstep. In this model a vehicle may slow down dueto not only the vehicle in front, but also theintersection. Note that in the randomizationstep, the speed of the vehicle decreases by onecell/step with a slowdown probability pslow totake into account the different behavior patternsof individual drivers. This step is crucial as itcaptures the non-deterministic acceleration dueto random external factors and the overreactionof drivers while slowing down, and its valuedepends on the overall driving behavior of peo-ple, which may vary with traffic density and timeof the day. High slowdown probability corre-sponds to drivers who overreact while slowingdown and maintain a larger than required safetydistance to the car in front. This cautious drivingpattern is usually observed in midnight trafficwhere the traffic volume is low and cars travel ata high speed. As a result, these individuals trav-eling at high speeds tend to decelerate wellahead of time. On the other hand, a small slow-down probability corresponds to a less cautiousdriving pattern, which is usually observed in rushhour traffic. During this time period, vehiclestravel at low speeds and move closely together;the intervehicle spacing is small. Hence, thedrivers put on the brakes exactly when they needto.

In the case of turning vehicles, the first condi-

tion ensures that turning vehicles do not make aturn at high speed and stop at the intersectionbefore making a turn. In addition, the secondcondition assigns priority to a right-turning vehi-cle (over a left-turning vehicle) in the case of atwo-way street.

Note that even though horizontal and verticaltraffic are updated at odd and even time steps,the same motion rules are applied. As opposedto the NaSch model where cells are updated inparallel, the state of each cell in our model isupdated sequentially. In other words, the locationof a vehicle in each street is updated only afterthe vehicle in front of it (in the same street) isupdated. This feature is incorporated into ourmodel for incorporating more realistic trafficbehavior, especially in the scenario where trafficlights are coordinated (usually known as green-wave synchronization). Note that in addition tothe rules defined in our model, there are severalother ways one can specify the motion rules fortwo-dimensional urban traffic. However, themodel we develop in this article is a genericframework that can be tailored to satisfy otherspecific requirements; the study presented hereis an illustrative example.

INTERSECTION CONTROL MECHANISMIn addition to the modifications above, we incor-porate into the mobility model one of the inter-section control operations used in today’s traffic.Among many types of intersection control, thethree signal operations that have been most usedare pre-timed, actuated, and computer con-trolled signals. A pre-timed traffic signal is themost fundamental signaling mechanism, wherethe time durations of red and green lights ineach direction are predetermined. Similar topre-timed signals, actuated signals have a prede-termined green/red light duration. However, anactuated signal can change its phase (from redto green, or green to red) before its scheduledtime if the traffic volume is low. Actuated signalsare usually used in rural areas or at night whenthe traffic density is very low [12]. Lastly, a com-puter-controlled signal, unlike the first two sig-naling modes, does not have predetermined lightintervals. The red/green durations are intelli-gently computed and dynamically adjusted basedon the current traffic condition. Computer-con-trolled signals have been implemented in areaswith highly congested traffic such as some partsof the city of Los Angeles and Washington, DC.Nevertheless, pre-timed operated signals are themost commonly used intersection control mecha-nism in most urban cities. In this article wetherefore assume that the signalized intersec-tions are equipped with pre-timed signals.

In order to realistically simulate the opera-tion of pre-timed signals, there are three neces-sary parameters that have to be carefullyconfigured: cycle duration, green split, and traf-fic signal coordination. Cycle duration (or trafficlight duration) is defined as the amount of timetaken to complete one signal timing cycle; thatis, the amount of time the signal turns green,changes to yellow, then red, and then greenagain. Note that in one cycle duration there islost time which takes into account the time anintersection is unused during the beginning and

In the case of

non-turning vehicle,

the update

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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end of a phase (i.e., when the right of waychanges and light indications of all directions arered). Green split is the fraction of time in a cycleduration in which specific movements have theright of way (green indications). In our model,since we assume an equal amount of traffic ineach direction, the green split value is fixed at50/50 (i.e., each traffic direction has an equalamount of green time at any intersection). Theother important operational parameter is thetraffic signal coordination, which is a method ofestablishing relationships between adjacent traf-fic control signals. This coordination is con-trolled by the value of signal offset defined as thetime from which the signal turns green until thesignal on the succeeding intersection turns green.If offset is zero (referred to as simple coordina-tion), all the lights will turn green at the same

time. Thus, with an appropriate offset value, aseries of traffic lights are coordinated in such away that they allow continuous traffic flow overseveral intersections. In the developed modelthese three important parameters are calculatedbased on traffic volume, traffic speed, and dis-tance between intersections, as shown in Table1. Figure 1 shows a snapshot of a traffic patterngenerated by our model.

SIMULATION SETTING

NETWORK TOPOLOGYIn the simulations we assume a 2 km × 2 km net-work topology with 16 evenly spaced horizontaland vertical streets; thus, two consecutive inter-sections are separated by 125 m. Each street isrepresented by a line of 5 m cells, and two-way

� Algorithm 2. New vehicle position update algorithm (Tonguz-Viriyasitavat-Bai algorithm).

if the vehicle goes straight at the next intersection thengo to Non-turning vehicle

elsego to Turning vehicle

end if

Non-turning vehiclev current vehicle speed

/* Acceleration step */if v is less than maximum speed then

increase v by one cell/stepend 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 thendecrease v so that the vehicle stops behind the vehicle in front or at intersection (whichever comes first)

end ifelse

if a vehicle will collide with vehicle in front with speed v thendecrease v so that the vehicle stops behind the vehicle in front

end ifend 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 vVehicle moves forward v cells

Turning vehicleif The vehicle is not yet at the intersection then

go to Non-turning vehicle and assume red light at the intersectionelse

if Red light at the intersection or the destination street is congested thenThe vehicle does not move

elseif 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 streetelse

The vehicle does not moveend if

end ifend if


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traffic is assumed on each street. All road junc-tions are equipped with pre-timed signals whoseparameters are given in Table 1. In addition, thenetwork topology is assumed to be a torus: whena vehicle reaches the network boundary, it reap-pears on the same street on the opposite side ofthe network boundary.

TRAFFIC PATTERNBased on the commuting pattern in highly popu-lated cities such as New York City (NYC), weobserve that there are two types of traffic: non-transit and transit traffic. A non-transit traffic(NTT) vehicle is defined as a vehicle that may ormay not originate within the urban area but hasa destination site within the urban area. On theother hand, transit traffic (TT) represents vehi-cles that only pass through the urban area; boththeir source and destination locations are out-side the region of interest. Consider the Manhat-tan business area in NYC; the traffic pattern canbe grouped into four categories:1 Morning rush hour traffic (8 am–10 am):

During this time period, people commutefrom their homes in the uptown area totheir workplaces downtown. Hence, thetraffic in this period is characterized by alow volume of TT and a high volume ofsouthbound NTT; the overall traffic volumeis high and traffic speed is low.

2 Lunch time traffic (11 am–1 pm): Duringthis time period, we observe a moderatevolume of TT and a low volume of NTT inrandom directions. Thus, overall we observemoderate traffic volume with moderatespeed.

3 Evening rush hour traffic (4 pm–6 pm):The traffic in this time period is similar tothat observed during the morning rush houras people commute back to their homes inthe uptown area. Hence, we expect to see ahigh volume of northbound NTT and a lowvolume of TT.

4 Midnight traffic (1 am–3 am): The traffic inthis period has very low volume but travelsat a high speed.In this article the developed mobility model

assumes a lunch time traffic pattern where anNTT vehicle randomly chooses its start and endlocations. Based on the chosen locations, the

vehicle chooses the shortest path to traverse.Once it arrives at its destination, the vehicle isremoved from the simulation. On the otherhand, since a transit vehicle does not have a des-tination within the simulation area, only the startlocation is randomly chosen; thus, the number oftransit vehicles is constant throughout the simu-lations. Because there is no specific path betweensource and destination, when a transit vehiclearrives at an intersection, it makes a turningdecision based on a fixed turning probability. Inour simulations the transit traffic turns left,right, and goes straight with probability 0.25,0.25, and 0.5, respectively. In addition, due tovery low NTT volume observed during lunchtime, we assume that 80 percent of total traffic isTT. Detailed investigation of other scenarios isan interesting subject for future work.

PARAMETER SETTINGAll parameters and their values used in the sim-ulations are summarized in Table 1.

RESULTS

THE EFFECT OF SIGNAL CONTROL OPERATIONDue to the presence of intersections and theircontrol mechanisms, the movement of traffic inurban areas is completely different from thatobserved on highways. Based on the CA-basedmobility model developed, below we analyze indetail and qualitatively discuss how intersectionsand their control parameters affect the overalltraffic pattern and mobility.

Flow Rate — In this section we study trafficflow rates that measure the rates at which vehi-cles pass through an intersection as a function oftime in relation to other traffic parameters. Oursimulations were performed at different trafficlight durations whose values are given in Table1. Figure 2 shows the average flow rate (theaverage is taken over all intersections and simu-lation runs). The results in Fig. 2 indicate thatthe average flow rate depends on the cycle dura-tion. In general, we observe that the average

� Table 1. Values of parameters used in the simulations.

Parameters Values

Fixed parametersNetwork density (vehicles/km2)Turning probability for transit trafficpslow

Speed limit (km/h)Signal offset (s)Lost time (s)

80, 160, 240, 3200.25 (left), 0.25 (right)0.536102

Variable parametersSignal cycle duration (s)Signal coordination

45, 90, 120Simple, green-wave

� Figure 1. Snapshot of traffic pattern generatedby the CA-based model.


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flow rate decreases as the cycle duration increas-es: as the signal cycle increases, the time anintersection is unused increases, thus resulting inmore wasted time.

Consider a scenario with low traffic density(80 vehicles/km2) and cycle duration of 120 s(dotted line in Fig. 2). From the simulations weobserve that the intersections are utilized heavily(i.e., vehicles pass through the intersection) dur-ing the first part of the green light period; dur-ing this interval, vehicles that have accumulatedduring the previous red light periods will passthrough the intersections. To illustrate , let usassume that this heavily utilized period lasts for20 s. Thus, the next 40 s of green time (assuminga green split value of 50/50) is a “dead” periodin which the intersections are not efficiently uti-lized. This implies roughly 2/3 of green timeduration is wasted. Therefore, in order to obtaina more efficient intersection control mechanism,one might resort to reducing the cycle duration.On the other extreme, however, when the signalcycle is too short, the green time duration perphase is proportionally decreased. Thus, theminimum time for a cycle duration of 45 s [12] isusually set to limit the time lost starting andstopping traffic. Since the cycle duration heavilyinfluences the traffic characteristics, it is impor-tant to use realistic values for it to reflect thebehavior of realistic urban traffic.

Number of Congested Intersections — Inthis section an intersection is considered “con-gested” if at least one vehicle is waiting there fora green light. Thus, the number of congestedintersections is the number of times the trafficflows are impeded by intersections. Since theaverage flow rate decreases as the cycle durationincreases, the average number of congestedintersections is expected to increase with the sig-nal cycle duration. This intuition is confirmed bythe simulation results shown in Fig. 3. Whentraffic signals are coordinated, the average num-ber of congested intersections changes onlyslightly during the entire simulation. When thesignals are not coordinated, however, we observea large fluctuation in this statistic because theuncoordinated signals disrupt the traffic flow atalmost all intersections. Vehicles are unlikely toencounter more than two consecutive greenlights and thus have to stop at almost all inter-sections. Note that perfect coordinated signalsare difficult to achieve due to different drivingpatterns of individuals. Nevertheless, these find-ings emphasize the importance of choosing real-istic values for traffic light duration and signalcoordination in simulations of vehicular traffic inurban areas.

ANALYSIS OF TRAFFIC PATTERNIntervehicle Spacing — Figure 4 shows interve-hicle spacing distributions for different networkdensities. Observe that despite the intersections,the intervehicle spacing distributions are still wellapproximated by theoretical exponential distribu-tions. The best fit parameters (i.e., averageintervehicle spacing) for all traffic densities arecomputed using the maximum likelihood test(ML). To determine how well the simulationresults fit the theoretical distributions, we resort

to the Kolmogorov-Smirnov test, and the good-ness 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 hypoth-esized exponential distribution and the distribu-tion obtained from simulations, respectively. Thecorresponding parameters for the fitted exponen-tial distribution and goodness-of-fit measure foreach traffic density are given in Table 2. Weobserve several peaks in the probability massfunction (PMF) plot at integer multiples of thelength of a road segment (125 m) and at 0 m inFig. 4 (left). This is because several vehicles arequeued waiting for green lights at intersections.This result agrees with [13], which also reportsvery high vehicle density near intersectionsdespite using a different vehicle mobility model.Our results indicate that the observed peaks inthe PMF become less pronounced as the vehicledensity gets smaller and vice versa. Despite thepeaks in the PMF plot, however, the exponentialPDF is a good approximation of the intervehiclespacing distribution (Fig. 4, right) obtained withour CA model. Note that for all traffic densities,the exponential distribution accurately estimatesthe intervehicle spacing distribution, especiallyfor spacings larger than 50 m. This somewhatcounterintuitive finding is consistent with thatobserved in highway scenarios where the empiri-cal distribution is well estimated by an exponen-tial distribution [14].

Nonuniformity of Traffic Pattern — In orderto gain insights into the traffic distribution inurban areas, we analyze spatial traffic distribu-tion from two different perspectives:• Local viewpoint, where we analyze the pat-

terns formed by vehicles within one roadblock

• Global viewpoint, where we investigate thetraffic distribution over an entire network(across different road blocks)

� Figure 2. The average flow rate over all intersections as a function of time fordifferent cycle durations. Note that there is an optimal cycle duration thatmaximizes the flow rate.

Time (s)5000

0

100Ave

rage

flo

w r

ate

at a

n in

ters

ecti

on (

vehi

cles

/h)

200

300

400

500

600

1000 1500

4 s10 s45 s90 s120 s


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In the global viewpoint the density of eachroad block is computed, and the result shown inFig. 5 (left) illustrates how the density of differ-ent road blocks in the network varies. Observethat in a dense network (density of 320 vehi-cles/km2), while there are some road blocks thathave high traffic density (i.e., eight vehicles with-in one road block), there is a large portion ofroad blocks (i.e., 35 percent) that have no vehi-cles. Similar behavior is observed across differ-ent traffic densities. In a sparse network withtraffic density of 80 vehicles/km2, while mostroad blocks have low traffic density, we observehigh traffic density in some road segments.These results further corroborate the previoussnapshot of traffic generated by the CA model(Fig. 1).

In addition to the global viewpoint, we alsotake the local viewpoint where we analyze how

vehicles are formed within a single road seg-ment. Figure 5 (right) shows that the local trafficalso exhibits a nonuniform distribution. Observethat over 50 percent of vehicles are within 20 mof the intersections. This suggests that the regionnear intersections can be very dense, while themiddle section of the road block may have verylow traffic density.

DISCUSSIONIt is clear that CA is a powerful tool that can beused to simulate and analyze urban vehiculartraffic. Based on the results of the previous sec-tion, several key observations can be made:

•Using the new CA model proposed, the dis-tribution of intervehicle spacing (both the PMFand CDF) can be computed. The computedPMF reveals the presence of several peaks at 0

� Figure 3. The average number of congested intersections are plotted against different signal cycle durations. These simulation resultsare obtained from a scenario with 80 vehicles/km2 traffic density.

Time (s)

Coordinated traffic signals

30000

5Num

ber

of c

onge

sted

inte

rsec

tion

s

10

15

20

25

30

600 900Time (s)

Uncoordinated traffic signals

30000

5Num

ber

of c

onge

sted

inte

rsec

tion

s

10

15

20

25

30

600 900

45s90s120s

45s90s120s

� Figure 4. Comparison between simulation results and the theoretical exponential distribution. The dotted and solid lines in the CDFplot represent perfect exponential distributions and our simulation results, respectively. The traffic signal has 45 s cycle duration and50/50 green split, and all signals are coordinated.

Intervehicle spacing (m)

5000

0.02

PMF

0.04

0.06

0.08

0.1

0 1000 1500 2000

Intervehicle spacing (m)

50000

0.2

CD

F

0.4

0.6

0.8

1

1000

80 vehicles/km2

160 vehicles/km2

240 vehicles/km2

320 vehicles/km2

1500 2000

80 vehicles/km2160 vehicles/km2240 vehicles/km2320 vehicles/km2

SimulationsExponential CDF


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m, 125 ms, 250 m, and so on, of which the mostprominent one is, as expected, the peak at 0 m.It is interesting to note that, especially for lowtraffic density and/or low penetration ratio ofDSRC technology, exponential distribution is anexcellent approximation to the actual intervehi-cle spacing distribution.

•In a two-dimensional scenario, clearly thenumber of high rises, buildings, and other obsta-cles determine the transmission coverage area ofa vehicle. If this is known, this information cou-pled with the exponential distribution of interve-hicle spacing can be used to exactly predict thenumber of neighbors to a vehicle. This, in turn,is a very useful piece of information in determin-ing the connectivity pattern of vehicles. Specifi-cally, based on the observation in the previoussection, the exponential distribution is an accu-rate approximation when the intervehicle spac-ing is larger than 50 m. Since the networkconnectivity of a vehicle mainly depends on thenumber of its immediate neighbors, and a vehi-cle’s radio transmission range usually extendsbeyond 50 m, this exponential finding allows usto determine the connectivity of a vehicle andanalyze the network connectivity of the entirenetwork. While the exponential distribution is anapproximation, it can facilitate an accurate andsimple analytical framework capable of modelingnetwork connectivity in urban vehicular ad hocnetworks (VANETs). Such insights are veryimportant in designing an efficient routing pro-tocol for urban traffic.

•Even though the intervehicle spacing ofboth highway and urban traffic can be approxi-mated by the exponential distribution, the con-nectivity pattern of a vehicle is very different inthese two scenarios. Unlike one-dimensionaltraffic as in a highway scenario, a vehicle inurban areas may be connected to vehicles travel-ing on the same or different roads. In otherwords, a vehicle on a highway is disconnectedfrom the network if it has no front or back neigh-bors in the same or opposite direction. However,a vehicle in an urban area might not be discon-nected in such a situation; it is disconnected only

when it does not have neighbors in the intersect-ing directions. Thus, the disconnected networkproblem is less pronounced in an urban scenariothan in a highway scenarios.

•Because of richer network connectivityobserved in urban areas, any two vehicles cancommunicate through multiple routes (asopposed to a single path in a highway scenario).This, in turn, may add flexibility to the design ofa routing protocol whereby the routing in urbanscenarios can be done via multipath routing asopposed to only the single-path routing used in ahighway scenario.

•Cellular automata-based mobility modelingof urban vehicular traffic reveals that while someparts of the region of interest will be very dense,other parts will be quite sparse (Fig. 1). Thissuggests that a broadcast protocol designed forurban areas will have to be able to deal withboth the broadcast storm problem [15] and dis-connected network problem simultaneously.

•It would be interesting to see if a sensornetwork that receives real-time traffic data fromall traffic lights could improve flow rate and easecongestion in urban areas with a centralizeddecision and control system. Ultimately, thisapproach seems synergistic to dynamic load bal-ancing [16].

•While the simulation and analysis conductedin this article were based on a regular Manhat-tan grid topology, we believe that the methodol-

� Table 2. K-S test results for intervehicle distribu-tions against the exponential distributions withdifferent network densities.

Traffic density(vehicle/km2)

Averageintervehiclespacing (m)

(D–, D+)

80160240320

405.4207.2140.0106.3

(2.4, 4.2)(2.3, 8.2)(2.7, 11.5)(3.1, 14.2)

� Figure 5. Traffic density in each road segment and the distribution of vehicles around an intersection. The traffic signal has 45 s cycleduration, 50/50 green split, and all signals are coordinated.

Number of vehicles in one road block

200

0.2

Frac

tion

of

road

blo

cks

that

cont

ains

less

tha

nx

vehi

cles

(C

DF)

0.4

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4 6 8 10

Distance from intersection (m)

1000

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Frac

tion

of

vehi

cles

tha

t ar

e le

ssth

anx

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ers

from

inte

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tion

s (C

DF)

0.4

0.7

0.6

0.5

0.9

1

0.8

20 30 40 6050




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ogy and techniques developed can be used tostudy other urban topologies as well (even irreg-ular ones).

•It would be interesting to compare the pre-dictions of the new CA model proposed in thisarticle with empirical urban traffic traces. This,in turn, can verify the validity of the mobilitymodel used in this article or provide valuablefeedback on how to further refine it.

CONCLUSIONBased on a new CA model, we have investigatedhow urban traffic is affected by intersections andtheir control mechanisms. Our results show thatcontrol mechanisms such as cycle duration,green split, and coordination of traffic lightshave a significant bearing on traffic dynamicsand intervehicle spacing distribution. Our find-ings on urban mobility also provide importantinsights into the network connectivity patternand how a VANET routing protocol should bedesigned in urban settings.

REFERENCES[1] B. Chopard, P. O. Luthi, and P-A. Queloz, “Cellular

Automata Model of Car Traffic in a Two-DimensionalStreet Network,” J. Physics A, 1996.

[2] F. Bai, N. Sadagopan, and A. Helmy, “The IMPORTANTFramework for Analyzing the Impact of Mobility onPerformance of Routing for Ad Hoc Networks,” Ad HocNet. J., vol. 1, no. 4, Nov. 2003, pp. 383–403.

[3] D. Choffnes and F. E. Bustamante, “An IntegratedMobility and Traffic Model for Vehicular Wireless Net-works,” Proc. ACM Int’l. Wksp. Vehic. Ad Hoc Net.,Sept. 2005, pp. 69–78.

[4] D. Krajzewicz et al., “SUMO (Simulation of UrbanMObility): An Open-Source Traffic Simulation,” Proc.4th Middle East Symp. Simulation Modeling, Sept.2002, pp. 183–87.

[5] K. Nagel et al., “TRANSIMS Traffic Flow Characteristics,”Los Alamos National Lab. rep. LA-UR-97-3531, Mar.1999.

[6] Laboratory for Software Technology (ETH Zurich), “Real-istic Vehicular Traces;” http://lst.inf.ethz.ch/ad-hoc/car-traces/

[7] M. M. Artimy, W. Robertson, and W. J. Phillips, “Connectivi-ty in Inter-vehicle Ad Hoc Networks,” Proc. IEEE CanadianConf. Elec. Comp. Eng., vol. 1, 2004, pp. 293–98.

[8] J. Esser and M. Schreckenberg, “Microscopic Simulationof Urban Traffic Based on Cellular Automata,” Int’l. J.Modern Physics C, vol. 8, no. 5, 1997, pp. 1025–36.

[9] M. Rickert et al., “Two Lane Traffic Simulations UsingCellular Automata,” Physica A, vol. 231, 1996, p.534–50.

[10] P. Wagner, “Traffic Simulators Using Cellular Automata:Comparison with Reality,” Proc. World Scientific, 1996.

[11] K. Nagel and M. Schreckenberg, “A Cellular Automa-ton Model for Freeway Traffic,” J. de Physique I France,vol. 33, no. 2, 1992, pp. 2221–29.

[12] J. H. Banks, Introduction to Transportation Engineer-ing, 2nd ed., McGraw-Hill, 2002.

[13] M. Fiore and J. Härri, “The Networking Shape of VehicularMobility,” Proc. 9th ACM MobiHoc, 2008, pp. 261–72.

[14] N. Wisitpongphan et al., “Routing in Sparse VehicularAd Hoc Wireless Networks,” IEEE JSAC, Special Issue onVehicular Networks, vol. 25, no. 8, Oct. 2007, pp.1538–56.

[15] N. Wisitpongphan et al., “Broadcast Storm MitigationTechniques in Vehicular Ad Hoc Networks,” IEEE Wire-less Commun., vol. 14, no. 6, Dec. 2007, pp. 84–94,Dec. 2007.

[16] O. K. Tonguz and E. Yanmaz, “The Mathematical The-ory of Dynamic Load Balancing in Cellular Networks,”IEEE Trans. Mobile Comp., vol. 7, no. 12, Dec. 2008,pp. 1504–18.

BIOGRAPHIESOZAN K. TONGUZ ([email protected]) is a tenured fullprofessor in the Electrical and Computer EngineeringDepartment of Carnegie Mellon University (CMU). He cur-rently leads substantial research efforts at CMU in thebroad areas of telecommunications and networking. Hehas published about 300 papers in IEEE journals and con-ference proceedings in the areas of wireless networking,optical communications, and computer networks. He is theauthor (with G. Ferrari) of the book Ad Hoc Wireless Net-works: A Communication-Theoretic Perspective (Wiley,2006). His current research interests include vehicular adhoc networks, wireless ad hoc and sensor networks, self-organizing networks, bioinformatics, and security. He cur-rently serves or has served as a consultant or expert forseveral companies, major law firms, and government agen-cies 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, in2006. During 2006–2007 she worked as a lecturer in theComputer Science Department of Mahidol University, Thai-land. Her main research interests include traffic mobilitymodeling and network protocol design for vehicular adhoc networks.

FAN BAI ([email protected]) has been a senior researcher inthe Electrical and Control Integration Laboratory, GeneralMotors Corporation, since Sept. 2005. Before joining Gen-eral Motors, he received a B.S. degree in automation engi-neering from Tsinghua University, Beijing, China, in 1999,and M.S.E.E. and Ph.D. degrees in electrical engineeringfrom the University of Southern California, Los Angeles, in2005. His current research is focused on the discovery offundamental principles, and the analysis and design of pro-tocols/systems for next-generation vehicular ad hoc net-works.

Based on a new CA

model, we have

investigated how

urban traffic is

affected by intersec-

tions and their

control mechanisms.

Our results show

that control mecha-

nisms such as cycle

duration, green split,

and coordination of

traffic lights have a

significant bearing

on traffic dynamics

and inter-vehicle

spacing distribution.


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