Intervehicle Transmission Rate Control for Cooperative Active Safety System

IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 12, NO. 3, SEPTEMBER 2011 645

Intervehicle Transmission Rate Control forCooperative Active Safety System

Ching-Ling Huang, Yaser Pourmohammadi Fallah, Raja Sengupta, Member, IEEE, andHariharan Krishnan, Member, IEEE

Abstract—We propose an intervehicle communication frame-work for the cooperative active safety system (CASS) whoseoperation is based on the dissemination of each vehicle’s stateinformation through a wireless network. Such a CASS requireseach subject vehicle to be aware of its surroundings, particularlyof the motion and position of other vehicles in its proximity. Inthis paper, we assume that all vehicles are equipped with onboardcommunication devices. In such situations, the wireless channelis simultaneously shared by a large number of vehicles, and oneof the most difficult challenges in designing CASS is to maintainreal-time tracking accuracy of neighboring vehicles while avoidingnetwork congestion and failure. To address this issue, we analyzethe problem that multiple scalar linear time-invariant dynamicalsystems track each other over a multiaccess channel, and then, wepropose a rate adaptation algorithm to distributively control theself-information broadcast behavior of each vehicle. The proposedalgorithm uses a closed-loop control concept and accounts forthe lossy channel. Simulation results show that, if the messagegeneration rate is dynamically adjusted in an on-demand fashion,more accurate and robust tracking performance can be achievedunder various traffic conditions.

Index Terms—Active safety, dedicated short-range communica-tion, intelligent transportation systems, transmission rate control,vehicle tracking.

I. INTRODUCTION

T ECHNOLOGY has always been the centerpiece of newdevelopments for transportation systems. Advances in

passive safety systems, such as the airbag and the antilockbrake system (ABS), have contributed to a safer driving en-vironment. Aside from passive safety mechanisms that protectthe driver and passengers during a crash, active safety designsare proposed to prevent crashes from happening. For example,computer vision and associated filter designs are proposed toassist the driver in detecting the critical motion of neighboringcars [23], identifying lanes and road boundaries [25], and evenmonitoring other drivers’ attentiveness to predict their inten-

Manuscript received July 31, 2009; revised May 30, 2010; acceptedAugust 15, 2010. Date of publication October 25, 2010; date of current versionSeptember 6, 2011. This work was supported in part by the General MotorsR&D Center under Contract TCS 70709 through the University of California,Berkeley. The views expressed here are those of the authors and not of theresearch sponsors. The Associate Editor for this paper was Y. Wang.

C. L. Huang, Y. P. Fallah, and R. Sengupta are with the Systems Engineer-ing Group, Department of Civil and Environmental Engineering, Universityof California, Berkeley, Berkeley, CA 94720 USA (e-mail: [email protected]).

H. Krishnan is with the Electrical and Controls Integration Laboratory,General Motors R&D Center, Warren, MI 48092 USA.

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TITS.2010.2070873

tions [24]. However, the biggest promise yet is that of intelligenttransportation systems (ITSs) empowered by wireless technolo-gies. Based on the developed IEEE 802.11 standard, 802.11ptransceivers [27], which are known as Dedicated Short-RangeCommunications (DSRC) or Wireless Access in VehicularEnvironments (WAVE), are put on cars and make informa-tion exchange possible either in vehicle-to-vehicle (V2V) orvehicle-to-infrastructure (V2I) fashion. This kind of interve-hicle communications (IVC) and vehicular ad hoc networks(VANETs) have drawn much attention in recent years dueto their important role in hosting safety, navigation, trafficmanagement, and automation applications [6], [31].

One of the most challenging mechanisms planned for de-ployment over IVC is the cooperative active safety system(CASS). See an illustration of the proposed CASS in Fig. 1(a similar framework also appears in [37]). Each vehicle con-tains communication control logic, a bank of estimators fortracking other vehicles, a plant (vehicle dynamics), a GlobalPositioning System (GPS) receiver, and other onboard sensors(producing vehicle-state measurements). In this CASS concept,each vehicle broadcasts self-information (e.g., GPS position,speed, and heading) in the form of safety messages to neigh-boring vehicles through the DSRC channel. These V2V safetymessages are transmitted as WAVE short messages (WSMs),which are defined in IEEE 1609.3, for rapid and efficientinformation exchange [28]. The receiving vehicle can then useincoming messages to track the sending vehicle in real time.The estimated states of all neighboring vehicles (e.g., in a radiusof 150 m), called Vehicle Neighborhood Mapping in Fig. 1, willbe fed into active safety applications, e.g., cooperative collisionwarning (CCW), electronic emergency brake light (EEBL), andslow/stopped-vehicle alert (SVA) [6]. These safety applicationsthen provide warnings to the driver or take emergency controlof the vehicle in case of an imminent danger. Note that ourproposed rate control algorithm (illustrated in the upper rightcorner in Fig. 1) works on top of the 802.11p transceiver andwill later be specified in Section V.

In this paper, we first propose a mathematical frameworkwhere multiple scalar linear time-invariant (LTI) dynamicalsystems can track each other over a multiaccess channel andanalyze different communication policies for self-informationdissemination. This specific type of tracking problem is in-teresting, because it is real time and over a shared channeljust like our CASS problem setting. Tracking performanceis studied for three uncontrolled communication policies:1) probabilistic (random access); 2) deterministic (round-robinscheduling); and 3) combined (grouped channel access). In

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646 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 12, NO. 3, SEPTEMBER 2011

Fig. 1. Functional blocks of the proposed CASS IVC unit.

addition, two controlled communication policies are analyzed,and their performances are compared using preliminary Matlabsimulations. This theoretical exercise gives us insights into howwe can design CASS communication logic (i.e., the dashedbox) in Fig. 1.

Based on the analysis, we propose a decentralized trans-mission control algorithm to decide how the state informationof a vehicle should be broadcast to neighboring vehicles forsafety/tracking purposes. This algorithm has an on-demand na-ture, because of two reasons: 1) It increases the communicationrate when a vehicle suspects that the estimation error of neigh-boring vehicles toward itself has increased, and 2) it throttlesthe rate during channel congestion to avoid further collisions(efficiency degradation and message losses). This simple yetintuitive design allows all vehicles to properly share availablechannel resource. Our proposed algorithm is shown to achievetracking accuracy and robustness for different traffic scenarios.Its performance has been evaluated through realistic simula-tions, involving vehicle trajectories generated by the SHIFT[29] traffic simulator and large-scale wireless network simula-tions using OPtimized Network Engineering Tools (OPNET)[30] with the best-known DSRC channel model reported in [5].Our algorithm outperforms the standard solution suggested bythe Vehicle Safety Communications Consortium (VSCC) [31].

This paper is organized as follows. Section II provides anoverview of related work on IVC. Section III states the problemformulation for multiple scalar LTI dynamic systems to trackeach other over a multiaccess channel and the performanceanalysis for different transmission policies. Section IV presents

preliminary Matlab simulation results and provides insightsinto how we can design a proper rate control in a sharedchannel. Section V describes our proposed transmission ratecontrol algorithm. Section VI states large-scale traffic/networksimulation settings, implemented algorithms, and simulationresults. Section VII concludes this paper.

II. RELATED WORK

In [7] and [8], IVC is used to relay downstream trafficinformation to upstream drivers to expand their perceptionhorizon. This kind of early-warning system gives the drivermore time to react to a hazardous situation and thus reducesinjury/casualty rates. In [26], IVC is used to improve lane-levelpositioning based on Markov localization. In [9], an adaptivespace-division multiplexing protocol is proposed for vehicles toshare a DSRC channel without control messages and to mitigatedenial-of-service (DoS) attacks. A feasibility examination ofV2V collision warning based on Differential GPS (DGPS) isprovided in [11]. In this paper, we assume that such modestlyaccurate positioning information (e.g., submeter accuracy) isavailable on board, and we focus on the design of CASScommunication logic.

For information propagation in wireless ad hoc networks,the analysis in [4] gives a fundamental bound on the productof rate and distance. The implication of such a capacity notionis that, when the network becomes denser, one needs to eitherthrottle the data rate or reduce the transmission power sothat a limited channel resource can be properly shared by all

HUANG et al.: INTERVEHICLE TRANSMISSION RATE CONTROL FOR COOPERATIVE ACTIVE SAFETY SYSTEM 647

nodes. Therefore, most existing designs for broadcasting safetymessages focus on either rate or power adaption for differentvehicular traffic conditions.

One such design trend is on transmission range (power)control for safety messages. For example, [12] proposes tofairly allocate transmission power across all cars in a max–minfashion, which helps reduce the beacon load at every point ofa formulated 1-D highway and thus reserves bandwidth foremergency messages with higher priorities. This method as-sumes a predefined maximum load as the target. By utilizing thewater-filling concept, [12] proves a centralized algorithm thatachieves this fairness goal and gives a decentralized algorithmthat approximates the operations of the centralized algorithm.Another work on transmission range adaptation is [13], inwhich estimated local vehicle density and traffic engineeringintuitions are used as algorithm input. The goal in [13], how-ever, is to reduce DSRC channel interference while maintainingnetwork connectivity among vehicles.

Another design trend for safety messages is on rate control.Because many applications require the same data elementsfrom neighboring vehicles, the message dispatcher in [14] isproposed to reduce the required data rate by removing duplicateelements. The message dispatcher at the sender side will groupdata elements from the application layer (i.e., the informationsource) and decides how frequently each data element shouldbe broadcast. At the receiver side, the message dispatcherpushes received data elements to designated applications (i.e.,the sink). This design is similar to compression ideas in sourcecoding [3].

For IVC-based CASS, which heavily relies on tracking ac-curacy, our approach is to correlate communication behaviorswith the tracking error magnitude, which is fundamentallydifferent from any previous designs. In [15] and [16], errorthreshold crossing is used as the transmission trigger; commu-nication of the state information happens only when thresholdis violated. However, this threshold crossing policy only worksfor a very reliable (lossless) channel and, thus, is not feasiblefor VANETs when the market penetration of onboard wirelessdevices is high (i.e., more contentions and packet collisionsin the shared channel). Our on-demand design in this paperfollows the same rationale but adopts a stochastic rate controlpolicy that considers both real-time tracking error and potentialmessage losses. Unlike previous designs, our proposed algo-rithm is easy to implement; it also works in a decentralizedfashion, which makes it more suitable for CASS.

This paper is an extension of our preliminary works in[20]–[22], where multiple scalar LTI dynamical systems trackeach other over a shared channel; our works were, in turn,inspired by the error-driven communication design in [17].In the existing control literature, the remote tracking problemis usually formulated as the sender–receiver pair with one-to-one channel scenario. Channel losses are usually assumedto follow an independent and identically distributed (i.i.d.)distribution and be independent of the transmission behavior atthe sender side. In [18], the sender keeps track of successfullytransmitted state information and performs estimation for itslocal process, which is assumed to reach the same estimationresults by the receiver. The optimal controlled communication

policy is derived with the cost function, which is defined asthe weighted summation of the mean-square estimation errorand the packet rate. In [19], the authors suggest that each nodeshould process raw measurements with a Kalman filter (KF)before sending them out. The minimum packet rate for stabiliz-ing the estimation error to the stochastic moments is given foruncontrolled communication. Controlled communication logicis also proposed based on the doubly stochastic Poisson process(DSPP). At each moment, the jump intensity of the DSPP isdecided by the current estimation error.

Stability constraints for lossy observations are investigatedin [32]. In the formulation in [32], raw measurements aretransmitted to remote estimators, and the channel drops packetsin an i.i.d. Bernoulli fashion. On the receiver, intermittent ob-servations are processed with a time-varying KF. The stabilitythreshold of channel loss probability is also derived. In [34], atype of network source coding is designed to compensate forthe communication delay for the KF. Inspired by the structureof a special KF, an encoding strategy is proposed in [35] bytransferring the information set and is shown to be optimal forall possible network topologies and data dropping sequences.Due to space limitations, see [36] for a summary of rate controlfor networked control systems.

III. TRACKING OVER A MULTIACCESS CHANNEL

In this section, we consider a simple scenario where multiplescalar LTI dynamical systems track each other over a sharedchannel; then, we describe its mathematical framework andcompare the tracking performance of different communicationpolicies to understand our CASS tracking problem. For a decen-tralized communication policy, we show that the tracking errorand channel collisions need to be taken into account to achievea robust tracking performance.

A. Tracking Problem Formulation

Classically, the remote estimation problem has been for-mulated as a sender–receiver pair with one-to-one channelsetting (e.g., in [17]). Channel losses are usually assumedto follow a stationary distribution and be independent of thetransmission behavior at the sender. This assumption makesanalysis tractable. However, this classical setting is not suitablefor multiaccess channels, because the performance of suchchannels heavily depends on the transmission behavior of allnodes. For example, an increase in transmission attempts doesnot always translate to an increase in the amount of informationsuccessfully delivered.

Consider a real-time tracking problem with finite n scalardynamical systems n = 2, 3, . . ., where their dynamics areassumed to be decoupled. In analogy to the CASS problemsetting, these nodes represent all vehicles in proximity. To easeour discussion, for each node index j ∈ 1, 2, . . . , n, let itsstate transition be represented by a simple LTI model. We have

xj(t) = aj × xj(t − 1) + εj(t − 1) (1)

where xj(t) is the scalar state of node j, εj(t) is the stationaryzero-mean noise process with bounded variance σ2

j > 0, and


Fig. 2. Node internal structure in the analyzed real-time tracking problem.

t is the time index t ∈ N. The amplification factor aj decideshow fast the state xj(t) evolves. In analogy to our CASSproblem setting, by extending the dimensions of parameters inthe LTI model (1), aj can be used to model physical laws thatgovern that vehicle’s movement, and εj(t) can be used to modelmechanical disturbance. This LTI approximation has been usedin the control literature (e.g., see [32] and [33]).

As shown in Fig. 2, those n nodes share the same wirelesschannel, and each node contains a discrete-time LTI scalarprocess (1), a communication logic, and a bank of synchronizedmodel-based estimators. Similar to the minimum packet rateformulation in [17], the true state (a real number with anacceptable distortion) of the sender j will be broadcast to theshared channel by its communication logic. The wireless chan-nel access is assumed to be slotted as in slotted ALOHA [1]. Tosimplify our analysis in Sections III and IV, one discrete step ofthe process (1) is assumed to be the same as the required packettransmission time through a channel (i.e., one time slot). Basedon the received information, each node tries to estimate stateson other nodes. Let xij(t) be the estimated state of sender j byreceiver i. This xij(t) is the expectation conditioned on all pre-vious received information xij(t) ≡ E[xj |Y 1

i , Y 2i , . . . , Y t−1

i ],where Y t

i is the received information by receiver i at time t.When the channel is idle or has a collision at t, Y t

i = ∅.Otherwise, Y t

i = xs(t) from a certain successful sender s ∈1, 2, . . . , n. In this formulation, channel loss is only due tocollisions. Each node can instantaneously detect collisions, butthere is no retransmission for lost packets. Neither a fade effectnor a hidden terminal problem is modeled for simplicity (welater consider these effects in our large-scale simulations inSection VI). Therefore, each node is assumed to get the samecopy of information from the channel. The real-time estimatorat receiver i switches between the following two operations.

• If no information of node j is received at t − 1, i.e.,Y t−1

i = xj(t − 1), the estimator uses xij(t − 1) and theknown model (1) to carry on, i.e., xij(t)=aj×xij(t−1).

• Otherwise, if the state information of node j is received att − 1, i.e., Y t−1

i = xj(t − 1), the estimator uses the latestinformation to reset the tracking error, i.e., xij(t) = aj ×xj(t − 1).

Note that xij(t) in the aforementioned calculations is theminimum mean square error (MMSE) optimal estimate, be-cause the noise process εj has zero mean. The tracking erroreij(t), the ith node’s estimation error for node j, is definedas eij(t) ≡ xj(t) − xij(t). Thus, the mean square error (MSE)

at time t, which is denoted as ϕij(t), is given by ϕij(t) ≡E[eij(t)2].

Based on the operations of this real-time estimator, if anupdate is only received k steps before k = 1, 2, . . . t − 1, theestimate of xj at receiver i is given by

xij(t) = akj × xj(t − k). (2)

Assuming that the latest measurement arrives at the receiverside at the t − k moment, conditioned on elapsed time steps kafter receiving an update from the jth node, (2) becomes

ϕij(t) = E[E

[(xj(t) − ak

j xj(t − k))2 |k < t

]](3)

where its inner part can be expressed as

xj(t) − akj xj(t − k) =

k∑l=1

ak−lj εj (t − (k − l + 1))

where εj(t) is the noise process at moment t for node j. In (3),the inner expectation is taken with respect to the randomnessof the process noise, where the outer expectation is taken withrespect to the randomness of the interarrival time. Because thenoise process εj(t) are assumed to be i.i.d. zero mean with finitevariance σ2

j , (3) can be organized as

ϕij(t) = E

[k∑

l=1

a2(k−l)j |k < t

]× σ2

j (4)

where E[∑k

l=1 a2(k−l)j |k < t] can further be specified once the

communication design and the probability distribution of theinterarrival time k are known. To compare different commu-nication policies, which may have nonstationary distributionsfor ϕij , we choose an asymptotic time-averaged MSE, which isdenoted as Φij , as the performance metric, i.e.,

Φij ≡ limT→∞

∑Tt=1 E

[eij(t)2

]T

= limT→∞

∑Tt=1 ϕij(t)

T. (5)

If we further assume that the process on each node is iden-tical, i.e., aj = a and σ2

j = σ2 for all j = 1, 2, . . . , n, we candenote Φj instead of Φij for all i, because we assume that allnodes can get the same copy of information from the channel.Note that this performance measure (5) is only used for thetheoretical discussions in Sections III and IV. Due to practicalreasons concerning our CASS tracking problem, another per-formance measure for evaluating large-scale simulations willbe used in Section VI.

B. Uncontrolled Transmission Policies

In this section, three common types of uncontrolled channelaccess schemes for a multiaccess channel are analyzed. Thatis, the dissemination of state information follows a predefinedprotocol instead of being dynamically adjusted. Our analysis in[20] first derives ϕij(t) in (4) based on the interarrival delaydistribution of each policy and then incorporates it into Φij(t)in (5). Here, we focus on the interpretation of these resultsin [20].


Probabilistic (Random Access): Each node broadcasts itsown state information with a fixed probability p at each timestep. We denote its tracking MSE as ΦP

j for (5). With boundednoise variance σ2 > 0, the stability condition to have ΦP

j < ∞is given by

0 < |a| <

(1 − 1

n

(1 − 1

n

)n−1)− 1

2

. (6)

Based on (6), when n is large enough, the channel can only sup-port stable tracking of scalar dynamical systems with |a| ≤ 1if this policy is used. Under (6), the optimal broadcast proba-bility is proven to be p∗ = 1/n for all nodes. Otherwise, thereis no bounded tracking MSE for this scheme. The minimumachievable ΦP

j by this policy, which is denoted as ΦP∗j , almost

surely exists ∀j = 1, . . . , n, i.e.,

ΦP∗

j =

(1 − a2 +

1n

(1 − 1

n

)n−1

× a2

)−1

× σ2 (7)

if |a| satisfies the stability requirement in (6).Deterministic (Round Robin): Deterministic design refers to

the round-robin scheduling to fairly serve each node. All nnodes are assumed to have this time-division multiple access(TDMA) scheduling knowledge and to be perfectly synchro-nized. At each moment, there will be only one node scheduledto broadcast its own state information, and thus, there is nocollision (message loss) in the channel. Because each node willdefinitely get a chance to broadcast its own state informationafter waiting a finite time (i.e., n slots), no finite |a| will maketracking error grow unbounded between measurement arrivals.Therefore, there is no such upper bound for |a| as that in (6).We denote its tracking MSE as ΦD

j for (5). Its asymptotic time-averaged MSE almost surely exists ∀j = 1, . . . , n, for |a| = 1.We have

ΦDj =

n + 12

× σ2 (8)

and for |a| = 1 and |a| < ∞, we have

ΦDj =

n −∑n

l=1 a2l

n(1 − a2)× σ2. (9)

Hybrid (Grouped Channel Access): This semicentralizeddesign bundles several nodes into one group, and scheduledcommunication instants are fairly given to each group in around-robin fashion. Channel contention only exists inside agroup. This policy is sometimes used to reduce collisions andincrease scalability when the node number is large. Assume thatthere are n nodes and θ groups and that the number of nodes inone group is given by m ≡ (n/θ). Then, n, θ, and m must bechosen to be positive integers. The communication probabilitypθ for each node in the same group is given by pθ = 1/m =θ/n when this group is scheduled to use the channel. Otherwise,pθ = 0 when other groups are using the channel.

This hybrid-θ policy can be viewed as a multiple interleavedversion of the probabilistic policy, and we denote its tracking

MSE as ΦHθj for (5). Similar to (6), the stability condition to

have ΦHθj < ∞ is given by

0 < |a| <

(1 − θ

n

(1 − θ

n

)nθ −1

)− 12θ

(10)

where 1 ≤ θ ≤ n. Here, (10) gives a relaxed condition than thelimitation of the probabilistic policy in (6), and these upperbounds all monotonically converge to 1 when n is sufficientlylarge, i.e., only stable plants can be tracked with the boundedMSE by using these randomized-access policies. The asymp-totic time-averaged MSE of this hybrid-θ policy almost surelyexists, ∀j = 1, . . . , n, for |a| = 1. We have

ΦHθj =

(n

(1 − θ

n

)1−nθ

+1 − θ

2

)× σ2 (11)

and for |a| = 1 satisfying the stability requirement in (10),we have

ΦHθj = 1 − Ω × σ2

1 − a2(12)

where

Ω ≡a2(1 − a2θ) × θ

n

(1 − θ

n

)nθ −1

θ(1 − a2)

1 − a2θ + a2θ × θn

(1 − θ

n

)nθ −1

.

Three examples of tracking MSE are plotted in Fig. 3. By ana-lyzing (7), (9), and (12), we learn that the following conditionshold: 1) When 0 < |a| < 1, three uncontrolled policies haveroughly the same tracking performance ΦD

j ≤ ΦHθj ≤ ΦP

j , and

2) when |a| ≥ 1, strictly, ΦDj < ΦHθ

j < ΦPj . One may notice

the huge performance difference between the probabilistic pol-icy and round-robin scheduling in Fig. 3. However, round-robinscheduling requires perfect coordination by either consensusamong nodes or out-of-band signaling and, thus, might not befeasible in some distributed systems, e.g., our CASS problemsetting. In the next section, we will show that it is possible for adecentralized policy, which utilizes a feedback control concept(inspired by [17]) to dynamically adapt its communication ratebased on a perceived tracking error to achieve much bettertracking performance than the probabilistic policy.

C. Controlled Decentralized Transmission Policies

In this section, two controlled communication policies,which correlate transmission behavior with real-time trackingerror, are analyzed. Their transmission controls are distribu-tively done on each node. In essence, a node uses a higherinformation rate to eliminate a potentially larger estimationerror on other nodes. Details of our derivations are given in [21].

Error Dependent: At the beginning of each time step, thecommunication probability from each node is calculated asfollows. First, the communication intensity λj(t) for node j atstep t is a function of the current estimation error ej(t) by othernodes, i.e.,

λj(t) = α × ej(t)2 (13)


Fig. 3. Performance comparison of three uncontrolled policies for |a| = 0.8,|a| = 1, and |a| = 1.01 (with σ2 = 1).

where α > 0 represents the sensitivity to error ej(t). Theknowledge of ej(t) is possible, because each node detectschannel collisions, keeps track of all successfully broadcastinformation, and runs a copy of the estimator for its local plantto learn the tracking error on other nodes. (This way, node j canknow xij(t),∀i = j, i.e., what other nodes think about its ownstate. This information is represented by the dashed link xj inFig. 2.) Then, λj(t) ≥ 0 in (13) is converted to the transmissionprobability pj(t) ∈ [0, 1] by a continuous mapping, i.e.,

pj(t) = 1 − exp (−λj(t)) (14)

where the extreme case pj(t) = 1 happens with probabilitymeasure zero for all t. We denote the tracking MSE of thispolicy as ΦE

j for (5). According to [17], the existence of ΦEj (t)

is guaranteed for tracking the process (1) with σ2 < ∞ and|a| < ∞.

The analysis in [21] applies the renewal reward theorem [2]on ΦE

j by using (4) and (5), and it shows that this policy cannot

Fig. 4. Optimal sensitivity and MSE tracking performance of the error-dependent communication policy (with n = 10 and σ2 = 0.01).

outperform round-robin scheduling, i.e., ΦEj ≥ ΦD

j , and theequality is possible only when the interval between successfultransmission, a random variable denoted as Z, has E[Z] = n.Otherwise, ΦE

j > ΦDj when E[Z] > n. If we properly choose

sensitivity α, its performance can be made close to round-robin scheduling ΦD

j ≤ ΦEj ΦP

j . When |a| = 1, the neces-sary range of α to have ΦE

j = ΦDj is given in (15) and (16),

shown below. That is, there exists 1 < δ < E[Z] such that

α∗ ≤ α ≤ α∗ +1 − a2

σ2×

ln(

n−1n−δ

)1 − 1

n

∑nl=1 a2l

(15)

where α∗ is the minimum required sensitivity, i.e.,

α∗ =1 − a2

σ2×

ln(

nn−1

)1 − 1

n

∑nl=1 a2l

. (16)

When |a| = 1, (15) reduces to α∗ ≤ α ≤ α∗ + σ−2 × ln(n −1/(n − δ)), with α∗ = σ−2 × ln(n/(n − 1)).

The optimal sensitivity and MSE tracking performance of theerror-dependent policy (based on simulation and analysis) areshown in Fig. 4. Intuitively, when α is very small, the com-munication logic is insensitive to error, and thus, no sufficientstate information can be delivered to remote estimators on othernodes. On the contrary, if α is very large, the communicationlogic becomes very sensitive, and frequent broadcasts from allnodes could result in numerous collisions in the shared channel;thus, less state information can successfully be delivered toremote estimators. Both extreme cases should be avoided.

The numerical analysis of (16) reveals that, when more nodesshare the network, α∗ should be made smaller so that each nodewould not respond to the tracking error very hard and resultin unnecessary collisions. Asymptotically, α∗ ↓ 0 as n ↑ ∞. In


practice, the number of active nodes in the network might notbe a constant, and thus, there is no fixed α∗. Taking CASS asan example, the number of neighboring vehicles (i.e., activetransmitting nodes) might greatly change with time, e.g., duringpeak or off-peak hours, and location. This observation has beenincorporated into our next communication design.

Err-Coll-Dep: The Err-Coll-Dep policy is an improved ver-sion of the error-dependent design, and its communicationintensity λj(t) for node j at step t is decided by a similar formof (13), i.e.,

λj(t) = ξ(t) × ej(t)2 (17)

with ξ(t) being a time-varying quantity (a function of collisionratio c(t)), and

ξ(t) =α

1 + β × c(t)(18)

where α > 0 is a constant as defined in (13), β > 0 is thesensitivity to collisions, and c(t) ≡ (1/γ)

∑t−1s=t−γ I(s) is the

time-averaged channel collision ratio for immediate past γ timeslots, γ ∈ N. Here, I(s) represents the channel status of the sthtime slot. When there is a collision (message loss) in the sharedchannel, I(s) = 1; otherwise, I(s) = 0. Again, λj(t) ≥ 0 in(17) is then converted to pj(t) by the same mapping in (14).

Similar to many stabilization algorithms for multiaccesschannels (e.g., see [1]), c(t) is used as an indicator for thesender to infer the increase/decrease in the number of activenodes. Matlab simulation results (see Fig. 5) reveal the ro-bustness of the Err-Coll-Dep design for a time-varying num-ber of nodes. In Fig. 5, the simulated time step is 50 ms.Each point in Fig. 5 represents statistics collected from thesame node (that stays in the network for the whole simulationduration) and summarized for a 1-s interval. For example,the collision ratio shown is the average of collision indicatorI(s) within that 1 s. Simulation parameters (a, σ2, α, β, γ) =(−0.5, 0.01, 20, 29, 10). During 10–20 s, more nodes jointhe network and share the channel. The Err-Coll-Dep policyachieves a smooth MSE curve with a lower rate and fewercollisions than the error-dependent policy.

Different sets of simulations show that a good range for βis between 25 and 30, with other parameters fixed. When β isvery large, the rate is very much reduced, and the channel isthus wasted. When β is very small or when β = 0, it reduces tothe error-dependent policy. In short, this kind of rate adaption(17) and (18) helps moderate generated data flow and avoidcongestion collapse of the entire network [1]. In Section IV,we will explore the reasons that this Err-Coll-Dep rate controlis effective.

IV. PRELIMINARY SIMULATIONS AND DISCUSSIONS

In this section, we analyze different communication policiesto get insights into how the tracking accuracy can be improvedby controlling the rate of information dissemination in a sharedchannel. Because we aim at the design for VANETs and CASS,only decentralized policies are considered in this section: 1) theprobabilistic policy; 2) the error-dependent policy; and 3) the

Fig. 5. Tracking performance of the error-dependent and Err-Coll-Dep poli-cies with a time-varying number of active nodes.

Err-Coll-Dep policy. These policies will be compared in termsof tracking accuracy, resulting collisions in the channel, andstatistical multiplexing gain (i.e., channel sharing behaviors).

Monte Carlo simulations of different communication poli-cies are conducted in Matlab/Simulink. The discrete time steplength is set to 50 ms. There are n = 10 nodes for the entire100-s simulation duration. The same channel assumptions inSection III continue to hold in this section. As depicted inFig. 2, all nodes contain an identical plant, with different RNs(random numbers) as simulation seeds and a bank of model-based estimators. For the plant (1), xj is a scalar with aj =0.5, and εj follows Gaussian distribution N(0, 10−2) for all j.Each node keeps tracking other nodes and broadcasting its ownstate information according to a specified stochastic policy.Throughout the Matlab simulations, values of (β, γ) in (18)are fixed at (30, 10). By tuning the error sensitivity α in (13)


Fig. 6. Tracking performance [MSE in the sense of (5)] and averaged collisionratio for the three decentralized communication policies.

and (18), we get different average packet rates for the error-dependent and Err-Coll-Dep policies.

A. Time-Averaged Tracking Performance

The tracking performance [MSE in the sense of (5)] isplotted in Fig. 6, with each point representing the statisticsfrom one simulation run. First, three policies exhibit U-shapecurves: 1) When the average rate is very low, the trackingMSE is large, because less state information is transmittedto remote estimators; 2) when the average rate is very high,MSE becomes large again, because many transmitted packetsget collided in the shared channel; and 3) when the averagerate is very high, the amount of available state information toremote estimators decreases. The observation that more stateinformation transmitted results in higher tracking accuracy in[17] is not valid in a multiaccess channel because of collisions.The corresponding collision ratios are also plotted in Fig. 6 forcomparison. Second, for the probabilistic policy, the minimumtracking MSE is achieved with an average rate of 2 pkt/node/s(packets per node per second). This value corresponds to trans-mission probability pj = 1/10, for all j, which matches withthe previous analysis p∗ = 1/n, where n is the node number.Third, the probabilistic policy, i.e., no rate control, cannotachieve the same minimum MSE as the error-dependent andErr-Coll-Dep policies. The error-dependent and Err-Coll-Deppolicies achieve lower minimum MSE with a lower average rate(0.4 pkt/node/s) than the probabilistic policy.

Similar to the analysis in [17], controlled communicationpolicies result in better tracking performance, because timelydelivered state information eliminates large estimation errors.With the same average packet rate, the Err-Coll-Dep policy canachieve lower MSE compared with the Error-Dependent policy,

Fig. 7. Collision occurrence for the three decentralized policies in 2000 timeslots, with an average rate around 0.2 pkt/node/s, i.e., the channel is only lightlyloaded. The respective collision ratios are 0.95%, 2.55%, and 1.30%.

particularly when its packet rate is high. As shown in Fig. 6, theErr-Coll-Dep policy also achieves MSE close to the minimumfor a wide range of rates (0.4–3 pkt/node/s), i.e., that curve actsas if the tracking MSE is not affected by the increasing packetrate and the gradually congested channel.

B. Collision Response in the Shared Channel

This section compares short-term collision response whileusing different communication policies, which is a key perfor-mance indicator of a multiaccess channel. A higher collisionratio means a lower probability of successful transmission and,thus, much bandwidth wasted. Fig. 7 shows the collision oc-currence in 2000 time slots for the three policies, respectively.Their average packet rates are all around 0.2 pkt/node/s, whichmeans that the channel is only lightly loaded. In Fig. 7, theerror-dependent policy has higher collision ratio and moreconsecutive collisions, which can also be observed in Fig. 6when the rate is small. For the error-dependent policy, when acollision happens, it means that at least two nodes want to sendout state information at the same slot, because their estimationerrors are relatively large. In the next time slot, those nodeswould still have high broadcast probabilities, because theirestimation errors are still large (because no state information issuccessfully transmitted due to previous collision). The samesituation may go on, i.e., consecutive collisions, until all in-volved nodes can successfully transmit their state information.

The error-dependent design does not consider possible chan-nel collisions and aggressively keeps sending more packetsuntil one successful transmission, which is the main cause offrequent consecutive collisions, even when the channel is in alightly loaded condition. On the contrary, the Err-Coll-Dep pol-icy alleviates this problem by considering channel collisions:When there is a collision, all nodes throttle their rates andcollaboratively reduce consecutive collisions. Therefore, thecollision ratio of the Err-Coll-Dep design is always lower thanthe error-dependent policy, as shown in Fig. 6. Note that, al-though Fig. 6 shows that the error-dependent and Err-Coll-Deppolicies have higher collision ratios in a lightly loaded channel,they still achieve lower tracking MSE than the probabilisticpolicy (compare their performance in Fig. 6 when the averagerate is below 0.5 pkt/node/s). Again, this result shows thatthe effectiveness of using a controlled communication policycomes from the timely delivery of state information to eliminatelarge errors, although some channel bandwidth is sacrificed.


Fig. 8. Tracking performance of the three decentralized policies under adedicated channel (with 10% bandwidth) for each node (ten nodes in total)and a shared channel (with 100% bandwidth) for all ten nodes.

C. Statistical Multiplexing Gain

In this section, we study how efficient these communicationpolicies can be in sharing the finite-channel resource. Here,statistical multiplexing gain is defined as the tracking perfor-mance [MSE in the sense of (5)] improvement of using a sharedchannel with full bandwidth (i.e., accessed in an uncoordinatedmanner) instead of assigning a dedicated channel with equallypartitioned bandwidth to every node (i.e., perfectly scheduledaccess). This multiplexing gain of three policies is comparedin Fig. 8. For each communication policy, we compare itsperformance in the following two scenarios: 1) Ten dedicatedchannels, each with 10% bandwidth, are individually assignedto ten nodes for them to broadcast state information, and 2) amultiaccess channel, with 100% bandwidth, is simultaneouslyshared by all ten nodes. A communication design that workswell in the second scenario (i.e., it has statistical multiplexinggain in a shared channel) is more suitable for IVC-based CASS.

Fig. 8 shows that there is no multiplexing gain for theprobabilistic policy due to the lack of rate control and excessivecollisions in the channel. On the contrary, the multiplexing gainexists when the packet rate of the error-dependent policy is lessthan 0.6 pkt/node/s and when the packet rate of Err-Coll-Dep isless than 1.5 pkt/node/s. Once average rate is higher than thesevalues, channel collisions become dominant, and their tracking

performance degrades. The multiplexing gain for the error-dependent and Err-Coll-Dep policies exists, because plants ondifferent nodes are decoupled, their tracking error magnitudesare different, and therefore, not all nodes need to broadcast stateinformation at the same time. This behavior comes from ourdesign of on-demand rate control in (13) and (18).

In Fig. 8, the Err-Coll-Dep policy also has a wide raterange of multiplexing gain than the error-dependent policybecause of a lower collision ratio in the shared channel. Byproperly selecting parameters (β, γ) in (18) for Err-Coll-Dep,its tracking performance could be made very close to the casethat each node is assigned a dedicated channel (as shownin Fig. 8). Therefore, the Err-Coll-Dep policy has better ratecontrol structure for tracking multiple dynamical systems totrack each other over a shared channel and is more suitablefor CASS.

V. PROPOSED TRANSMISSION RATE CONTROL FOR

COOPERATIVE ACTIVE SAFETY SYSTEM

In this section, we propose a transmission rate control forthe CASS communication logic (i.e., the dashed box in Fig. 1).Our rate control algorithm follows the Err-Coll-Dep policy, asdiscussed in Sections III and IV. Some minor modificationsare introduced to address the case that there is no explicitacknowledgment (ACK) for broadcast messages in DSRC [27].The performance of our proposed algorithm will be evaluatedin Section VI.

Our rate control algorithm runs on each vehicle every50 ms, which is due to the usual 20-Hz sampling frequencyof onboard sensors [10]. At each time step t ∈ N, i.e., multiplesof 50 ms, the jth vehicle gets a measurement of its own stateand calculates the transmission probability pj(t) based on thesuspected tracking error ej(t) on neighboring vehicles towardits own position in the Euclidean sense (i.e., the usual distancedefinition for a Cartesian coordinate system). The calculationof ej(t) will be specified later. Similar to the rate control in(17) and (18), we use this scalar measure ej(t) to calculate thetransmission probability by vehicle j at time step t, which isdenoted as pj(t), as follows:

pj(t) = 1 − exp

(−α

1 + βγ

∑t−1s=t−γ Λj(s)

× ej(t)2)

(19)

where α and β are the sensitivity parameters, as in (17) and(18), and γ = 20 is the 1-s time window for evaluating recentchannel utilization. Later in simulations (see Section VI), weuse β = 0 for the error-dependent policy and β = 30 for theErr-Coll-Dep policy, respectively. In (19), Λj(s) representsclear channel assessment (CCA) [27] as reported by the jth802.11p Media Access Control/Physical (MAC/PHY) mod-ule: When the channel is sensed busy, Λj(s) = 1; otherwise,Λj(s) = 0. Because a DSRC transceiver cannot detect colli-sion, we use channel utilization in (19) as a substitute for c(t)in (18). This substitution is adequate, because the collision ratiois a monotonically increasing function of channel utilization.Based on the pj(t) given by (19), the jth vehicle stochasticallygenerates a packet (i.e., a safety message) with its latest state


information and places this packet in the 802.11p MAC queuefor transmission.

At each moment, the suspected error ej(t + 1) [used in (19)]propagates from the previous ej(t+) based on the known plantmodel. Because there is no explicit ACK for broadcast-typetransmission in DSRC, a subject vehicle uses the perceivedchannel packet erasure rate (PER) at time t, which is denoted asΩj(t), to stochastically decide the suspected error ej(t+) rightafter each message transmission, i.e.,

ej(t+) = (1 − ζj(t)) × ej(t) (20)

where ζj(t) is the Bernoulli trial with the failure proba-bility Pr(ζj(t) = 0) ≡ Ωj(t). If the outcome ζj(t) = 1, thissuspected error ej(t+) is reset, i.e., ej(t+) = 0; otherwise,ej(t+) = ej(t). Note that this suspected error ej(t) is not theactual tracking error; it is merely a measure used by the jthvehicle to infer/simulate the tracking error evolution on itsneighbors and to accordingly adjust its own message transmis-sion rate in (19).

The estimated PER, i.e., Ωj(t), used by the Bernoulli trialin (20) is derived on the fly by checking the inconsistencyin the sequence number of recently received packets from allcorresponding neighbors within the 1-s history log of vehicle j.That is, the jth vehicle uses the number of lost packets dividedby the number of total packets sent from a certain neighborto estimate the recent channel loss rate, and Ωj(t) is thisempirical measure averaged over all its neighbors. Assumingnetwork symmetry, Ωj(t) tells the jth vehicle the likelihood ofits previous transmitted packet being erased in the channel.

The on-demand nature of (19) responds to the case thata higher transmission rate, and, thus, probability, is requiredfor a subject vehicle that has more unexpected movements,which translate to a higher tracking error at the neighboringvehicles. In addition, (19) takes the channel status into account,as discussed in Section IV, to temporarily reduce the messagerate of all vehicles in the same geographical area when channelcongestion is detected, and thus, this design increases thesuccessful reception probability of messages from all vehicles.

VI. PERFORMANCE EVALUATION USING LARGE-SCALE

TRAFFIC/NETWORK SIMULATIONS

This section presents large-scale traffic/network simulationsfor IVC-based CASS and discussions on simulation results. Wefocus on the tracking performance while using different de-centralized communication policies. Simulation results confirmthat the proposed algorithm in Section V achieves better accu-racy than the standard solution by VSCC [31] and robustnessunder various traffic conditions.

A. Simulation Settings and ImplementedCommunication Policies

Our main simulation stage is a straight 1-km highway. Forvehicle dynamics, 20-Hz trajectory profiles of [position, speed,heading] are produced by SHIFT [29], which is a microscopictraffic simulator. The total simulation time is 30 s for each

run. In the first part of our evaluation, we consider four lanesof identical traffic flows, with an average velocity of 30 mphand a mean gap of 0.8 s between vehicles in the longitudedirection. During the simulation, every 50 ms, each vehiclegets a measurement of its own status and decides whether togenerate a message, according to a specified policy, to dissemi-nate its own state information. The onboard measurement noiseis modeled exactly the same way as in [15] and [16], whichwas, in turn, based on the experimental data in [10]. Uponreceiving information from the channel, each vehicle updatesits estimated states of neighboring vehicles using a first-orderkinematic model, i.e., a constant speed predictor. Based on thismodel, a sending vehicle is assumed to run with the same speedand heading after its last safety message was received by thepredictor on a receiving vehicle.

For OPNET [30] simulations, we modify the 802.11a PHYmodule to work at 5.9 GHz with 10-MHz bandwidth. We followthe DSRC channel model reported in [5] and simplify the fardistances as Rayleigh fading instead of pre-Rayleigh. The rea-son for this simplification is that we consider a straight-highwayscenario, while [5] considers urban scenarios with intersectionsand corners, which lead to pre-Rayleigh fading observations.We specify the path loss exponent to be 2.31 (as suggestedin [5]). The transceiver operates with 3-Mbps raw data rate,−87-dBm receiver sensitivity, and 600-mW transmissionpower. The payload size of each safety message is 300 B. Theimplemented algorithms run at every 50 ms on top of 802.11pMAC/PHY (as depicted in Fig. 1) as follows:

• beaconing at a fixed 100-ms interval, as suggested byVSCC [31];

• a probabilistic policy, which uses fixed transmissionprobability to generate messages;

• a threshold policy, which triggers communication whenthe perceived tracking error violates a predefined threshold[15], [16];

• the proposed on-demand rate control algorithms, i.e., theerror-dependent (with β = 0) and Err-Coll-Dep (withβ = 30) policies.

B. Simulation Results and Performance Comparison

In this section, we present the simulation results and com-pare the performance of different decentralized policies. Theproximity or neighborhood of a subject vehicle is defined asthe circular area of a 150-m radius to satisfy most safetyapplications identified in [31].

After each simulation run, statistics are collected from neigh-boring vehicles, and we calculate the Euclidean positioningerror over all vehicles to explore the law of a large number (seeFig. 9 for a typical tracking error distribution). In particular,95% cutoff error (as indicated by the arrow in Fig. 9) meansthat 95% of the Euclidean error population fall below thisnumber (i.e., only 5% error population is larger than 1.07 m),which represents the tracking accuracy of the communicationpolicy used. In this section, we use the measure 95% Euclid-ean cut-off error as the main performance metric for CASSsimulations. This metric is different from the MSE definitiongiven in (5). The main advantage of this performance measure


Fig. 9. Statistical distribution of the Euclidean tracking error while using the100-ms beaconing policy proposed in [31].

over (5) and others (e.g., mean or standard deviation of thetracking error) is that it possesses a statistical sense similar to aconfidence interval (CI). Note that the error statistics presentedin Figs. 9 and 10 is the ground-truth tracking error (in meters)collected during our simulations and not the suspected errorej(t) perceived by vehicle j and used in (19).

The tracking performance (i.e., 95% cutoff error) of bea-coning in Fig. 9 is used as the baseline for comparison. InFig. 10, the performance of different policies is plotted withsecond-order least squares fitting to indicate the trend. For theprobabilistic policy, its tracking accuracy is shown with respectto different transmission probabilities; the accuracy observedhas a U-shape curve (similar to Fig. 6), and the optimalprobability for this traffic scenario is 0.6, with minimum 95%cutoff error around 0.8 m. The probabilistic policy, althoughan uncontrolled policy, achieves better tracking performancethan beaconing by introducing randomness in its transmissionbehavior. For the threshold policy, its packet transmission rate isdependent on the selected error threshold. When this thresholddecreases, it triggers more broadcasts and causes more colli-sions in the channel. Its 95% cutoff error also shows a U-shapecurve, and the optimal threshold for this scenario is 0.4 m, witha minimum 95% cutoff error around 0.6–0.7 m, which is afurther improvement from the probabilistic policy.

The performance of the error-dependent policy (i.e., theproposed algorithm with β = 0) is also shown in Fig. 10 withdifferent error sensitivity α values and corresponding trackingaccuracy. As we increase α, we increase the packet rate; theoptimal rate is around 4 pkt/node/s when α = 5. Its 95%cutoff error also shows a U-shape curve, and this accuracydegrades as the average rate increases. The error-dependentpolicy achieves similar minimum 95% error (i.e., 0.6–0.7 m)as in the threshold policy. Finally, the last plot in Fig. 10shows the tracking performance of the Err-Coll-Dep policy(i.e., the proposed algorithm with β = 30). Its 95% cutofferror has similar curve as in the error-dependent policy andachieves the same minimum 95% cutoff error when the rate isaround 4 pkt/node/s. Compared with beaconing, the controlledcommunication policies (i.e., the threshold, error-dependent,and Err-Coll-Dep policies) all achieve significant improvementin tracking accuracy. However, the benefit of using the Err-Coll-

Fig. 10. Tracking performance (95% cutoff error, in meters) of the proba-bilistic, threshold, error-dependent (the proposed algorithm with β = 0), andErr-Coll-Dep (the proposed algorithm with β = 30) policies.

Dep policy needs to be understood from the following designperspective.

Although the 802.11p MAC layer helps reduce collisions,the rate control algorithms considered still have similar be-havior as in the policies analyzed in Sections III and IV. Thereason is that collision still exists for broadcast-type safetymessages, and the hidden-node phenomenon [4] degrades theeffectiveness of carrier sense multiple access with collision


TABLE ISIMULATED BIDIRECTIONAL-HIGHWAY TRAFFIC SCENARIOS

avoidance (CSMA/CA) of the 802.11p MAC [27]. Therefore,the advantages of a controlled communication policy, as dis-cussed in Section IV, still apply to VANETs here. Both theerror-dependent and threshold policies could outperform thebeaconing and probabilistic policies if one properly choosestheir parameters.

However, as suggested by (16), the optimal sensitivity orthreshold may greatly vary with vehicle densities; thus, theseparameters cannot easily be chosen by offline calculations.The Err-Coll-Dep policy alleviates the aforementioned designproblem and makes parameter selection easier. By comparingα values in the error-dependent and Err-Coll-Dep policies inFig. 10, we can notice that, when β = 30, as long as we pickα ≥ 20, the tracking accuracy of the Err-Coll-Dep policy canoperate around optimal performance for a wide range of α.

C. Robustness of the Proposed Algorithm

To further verify the robustness of the Err-Coll-Dep policy,in the second part of our evaluations, we simulate ten differenttraffic scenarios in a bidirectional 1-km highway with fourlanes of identical traffic in each direction (i.e., eight lanes intotal). As listed in Table I, cases H1–H4 have homogeneoustraffic in both directions, whereas cases M1–M6 have differenttraffic conditions for each direction (the mean flow speed islisted for reference). Again, the 100-ms beaconing policy isused as the performance baseline. Fig. 11 shows that it doesnot scale well in different traffic conditions due to excessivechannel collisions. Our proposed algorithm, with fixed parame-ters (α, β) = (20, 30), is shown to be robust in achieving bettertracking accuracy in all scenarios, and its 95% cutoff error isalways below 2 m.

In addition, the worst case scenario, in terms of trackingaccuracy, is case M3, where one direction is congested, andthe other direction is free flowing. This case is the mostchallenging, because on one hand, the high density of cars onthe congested side means that the wireless medium is heavilyloaded with large amount of safety messages; on the otherhand, vehicles on the free-flow side move very fast, and theirstates may change very quickly. In such situations, the already-saturated DSRC channel cannot support the more frequentinformation exchanges required by cars on the free-flow side.Therefore, cars on the free-flow side experience poor trackingperformance (see case M3 in Fig. 11, Dir#2). Interestingly, caseM3 happens quite often during commute hours in metropolitanareas.

Fig. 11. Tracking performance (95% cutoff error) of the 100-ms beaconingpolicy and the proposed algorithm with fixed parameters (α, β) = (20, 30)under different traffic conditions in Table I.

With the results in Fig. 11, we show that it is possibleto achieve better tracking performance (than the uncontrolled100-ms beaconing policy proposed by VSCC [31]) using theproposed design with a fixed set of parameters (α, β). However,the appropriate values for (α, β) need further investigation.We are currently implementing prototypes and conducting fieldexperiments to improve the proposed on-demand rate controlalgorithm.

VII. SUMMARY AND FUTURE WORK

In this paper, we have analyzed the problem of how multiplescalar LTI dynamical systems track each other over a multi-access channel, which is motivated by the IVC-based CASS.Based on the analysis, we proposed a transmission rate controlalgorithm for each vehicle to disseminate its state information.The proposed algorithm has an on-demand nature and adaptsthe V2V message rate for each vehicle in a decentralizedfashion. Performance evaluations, both in Matlab and in large-scale traffic/network simulations, confirm that the proposedalgorithm achieves better tracking accuracy than existing so-lutions and is more robust to channel congestion.

Throughout this paper, we have assumed uniform trans-mission power for all vehicles and adjusted their individualmessage rates to enable statistical multiplexing. Based on the


work of Gupta and Kumar on the capacity of wireless net-works, there could be further performance improvement if avariable transmission power is used by each vehicle to reduceinterference and explore channel spatial reuse. Our future workincludes such a joint design to simultaneously adapt rate andpower for safety-driven information dissemination in VANETs.

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Ching-Ling Huang received the B.S. and M.S. de-grees in electrical engineering from the NationalTaiwan University, Taipei, Taiwan. His M.S. studywith the Computer Science Group, Department ofElectrical Engineering, National Taiwan University,focused on networking and mobile communication.He is currently pursuing the Ph.D. degree in systemsengineering with the Department of Civil and En-vironmental Engineering, University of California,Berkeley.

His research interests include control and estima-tion over an unreliable channel, vehicular networks, and cooperative activesafety designs for intelligent transportation systems.

Yaser Pourmohammadi Fallah received the Ph.D.degree in electrical and computer engineering fromthe University of British Columbia, Vancouver, BC,Canada, in 2007.

He is currently a Postdoctoral Research Fellowwith California Partners for Advanced Transit andHighways, Institute of Transportation Studies, Uni-versity of California, Berkeley. His current researchactivities are focused on networked cyberphysi-cal systems and wireless networking for intelligenttransportation systems. His research has been sup-

ported by numerous grants and awards, including a Natural Sciences andEngineering Research Council of Canada (NSERC) postdoctoral fellowship,an NSERC postgraduate scholarship, and a Bell Canada graduate scholarship.


Raja Sengupta (M’02) received the Ph.D. degreefrom the University of Michigan, Ann Arbor,in 1995.

He is currently an Associate Professor withthe Systems Engineering Program, Department ofCivil and Environmental Engineering, University ofCalifornia, Berkeley, where he is also the Directorof the California Partners for Advanced Transit andHighways Wireless Laboratory and the Deputy Di-rector of the Center for Collaborative Control ofUnmanned Vehicles. He is an Associate Editor for

the Journal of Intelligent Transportation Systems.Dr. Sengupta is an Associate Editor for the IEEE Control Systems Magazine.

He was the Program Chair of the 2003 IEEE Conference on AutonomousIntelligent Networked Systems and a General Cochair of the First ACMInternational Workshop on Vehicular Ad Hoc Networks.

Hariharan Krishnan (M’92) received the B.E. de-gree from Anna University, Chennai, India, the M.S.degree from the University of Waterloo, Waterloo,ON, Canada, and the Ph.D. degree from the Univer-sity of Michigan, Ann Arbor.

From 1993 to 2000, he was an Assistant Pro-fessor with the National University of Singapore,Singapore. He is currently with the Electrical andControls Integration Laboratory, General Motors(GM) R&D Center, Warren, MI, where he is theThrust Area Lead of the GM research program on

vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) communications.He works on various research projects in V2X communication, including theVehicle Safety Communications—Applications Project conducted by GM,Ford, Mercedes, Toyota, and Honda under a cooperative agreement with theUnited States Department of Transportation. He is an Associate Editor forTransportation Research—Part C: Emerging Technologies. He has contributedto more than 60 publications in internationally refereed journals and conferenceproceedings and more than 300 citations.

Dr. Krishnan serves as an Associate Editor for the IEEE Control SystemsSociety.

Documents

Intervehicle Transmission Rate Control for Cooperative Active Safety System