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TMC: Exploiting Trajectories for Multicast inSparse Vehicular Networks

Ruobing Jiang, Yanmin Zhu∗, Member, IEEE, Xin Wang, Member, IEEE, Lionel M. Ni, Fellow, IEEE

Abstract—Multicast is a crucial routine operation for vehicular networks, which underpins important functions such as messagedissemination and group coordination. As vehicles may distribute over a vast area, the number of vehicles in a given regioncan be limited which results in sparse node distribution in part of the vehicular network. This poses several great challengesfor efficient multicast, such as network disconnection, scarce communication opportunities and mobility uncertainty. Existingmulticast schemes proposed for vehicular networks typically maintain a forwarding structure assuming the vehicles have a highdensity and move at low speed while these assumptions are often invalid in a practical vehicular network. As more and morevehicles are equipped with GPS enabled navigation systems, the trajectories of vehicles are becoming increasingly available. Inthis work, we propose an approach called TMC to exploit vehicle trajectories for efficient multicast in vehicular networks. Thenovelty of TMC includes a message forwarding metric that characterizes the capability of a vehicle to forward a given messageto destination nodes, and a method of predicting the chance of inter-vehicle encounter between two vehicles based only ontheir trajectories without accurate timing information. TMC is designed to be a distributed approach. Vehicles make messageforwarding decisions based on vehicle trajectories shared through inter-vehicle exchanges without the need of central informationmanagement. We have performed extensive simulations based on real vehicular GPS traces and compared our proposed TMCscheme with other existing approaches. The performance results demonstrate that our approach can achieve a delivery ratioclose to that of the flooding-based approach while the cost is reduced by over 80%.

Index Terms—sparse vehicular networks, multicast, trajectory, encounter prediction.

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1 INTRODUCTION

Recent advances in short-range radio technology suchas Dedicated Short Range Communications (DSRC)[1] [2] for inter-vehicle communications have driv-en significant efforts in investigating and developingvehicular networks. By sharing information amongmoving vehicles, a vehicular network can supporta wide variety of real-world applications, includingemergence alert [3], advertisement, file sharing [4] [5],data collection [6], etc.

Information and message exchanges through mul-ticast, where packets are sent from one sender toa group of receivers, have gained popular use andserve as a crucial routine operation in vehicular net-works. For example, the taxis in a city may forman information network where each taxi may collectvarious types of information such as road surfacecondition, road closure status due to maintenanceand traffic accidents. For more efficient informationdissemination, a taxi can subscribe for some types

• Manuscript received on Sep 5, 2013, and accepted on Jan 1, 2014.• Ruobing Jiang and Yanmin Zhu are with the Department of Com-

puter Science and Engineering at Shanghai Jiao Tong University andShanghai Key Lab of Scalable Computing and Systems. Xin Wang iswith the Department of Electrical and Computer Engineering at StonyBrook University. Lionel M. Ni is with the Department of ComputerScience and Engineering at Shanghai Jiao Tong University as wellas Department of Computer Science and Engineering at Hong KongUniversity of Science and Technology.

• ∗Yanmin Zhu is the corresponding author, and his email isyzhu@cs.sjtu.edu.cn.

of information of its interest, while a vehicle thatcollects the relevant information can serve as a sourceto disseminate the collected data through multicast tothe group of subscribers.

Different from conventional communication net-works, vehicular networks exhibit many unique char-acteristics, which pose several great challenges toefficient multicast. First, as vehicles may distributeover a vast area, the number of vehicles in a givenregion can be very limited. Therefore, a vehicularnetwork can be sparse and resemble a delay tolerantnetwork (DTN) [7] that relies on the ”carry-and-forward” paradigm to exchange information amongvehicles. In a sparse network, it is very difficult to finda connected path between any pair of vehicles. Second,as two vehicles can communicate only when theyencounter (i.e., within the communication range ofeach other), the encounter opportunities become thecritical network resources, which are usually scarce[8]. This makes it necessary for a multicast approachto be cost efficient. Finally, there is great uncertaintywith vehicle mobilities, which makes it difficult topredict the future location of a given vehicle.

A few approaches [9] [10] [11] have been proposedfor multicast in vehicular networks. However, stem-ming from multicast schemes proposed for MobileAd Hoc Networks (MANETs), these approaches of-ten require maintaining a costly forwarding structuresuch as a tree or a mesh. They typically assume thatvehicles in the network are densely populated andmove at a lower speed. Both assumptions may be

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invalid in a practical vehicular network which oftenhas sparse connections in an area, thus making thesemulticast approaches inefficient and even fail.

On the other hand, some potential opportunitieshave not been exploited for vehicular communica-tions. Vehicles are increasingly deployed with GlobalPositioning System (GPS) enabled navigation systems.A recent report shows that approximately 300 millionGPS devices have been shipped in 2009 alone [12].The GPS enabled navigation system can suggest apath towards a destination. When the future trajectoryof a vehicle is known in advance, its mobility uncer-tainty is greatly reduced. Two vehicles may potential-ly encounter each other if their trajectories intersectwith each other. This observation suggests that theknowledge of trajectories of vehicles may be appliedto predict future encounters, which will in turn bringvaluable information to guide more efficient messageforwarding in vehicular networks. More specifically,the forwarding may be more efficient if a message isforwarded to the set of vehicles that can potentiallyencounter more destination nodes, i.e., the relay vehi-cles would have a higher capability of delivering thismessage to destination nodes.

Motivated by this observation, we proposetrajectory-based multicast (TMC) which exploitsvehicle trajectories for more efficient multicasttransmissions in sparse vehicular networks. We focuson information dissemination among public vehiclessuch as taxis and buses which run for the mosttime of a day. We have conducted empirical studybased on real GPS traces from around 2,000 taxis inShanghai, China, and find that there are on average5.6 encounters between each pair of taxis in one daywhen the communication range is 200m.

In TMC, a novel message forwarding metric isproposed to characterize the capability of a vehicle toforward a given message to a group of destination n-odes, which is defined as a vector of delivery potentialof the message to each of the destination nodes. Withthis metric, a vehicle can simply forward a messageto a vehicle that has a higher multicast delivery gainover the vehicle itself. To compute the metric, thekey challenge is to predict the chance of encounterbetween two vehicles based only on their trajectorieswithout accurate timing information. To conquer thischallenge, we model the travel time of a vehicle as aGamma-distributed random variable and verify themodeling with real vehicular GPS traces. Then, anovel method is designed to predict the chance ofinter-vehicle encounters. The salient feature of TMC isthat it is a fully distributed approach in which vehicletrajectories are shared through inter-vehicle exchangeand a vehicle makes its message forwarding decisionbased on the trajectories it learns instead of relyingon a central point for information management.

To the best of our knowledge, this is the firstwork that exploits trajectory information to perform

efficient multicast in sparse vehicular networks. Themain technical contributions are as follows.

• We propose a novel message forwarding metricfor multicast in sparse vehicular networks, whichcharacterizes the capability for a vehicle to deliv-er the message to multiple destination nodes.

• We provide a method to predict the chance ofinter-vehicle encounters based on only trajectoryinformation by modeling the travel time of avehicle as a Gamma-distributed random variable.

• We have performed extensive simulations basedon real vehicular GPS traces, and compared ourapproach with other existing approaches. Our re-sults have demonstrated that the proposed TMCapproach can achieve a delivery ratio close to thatof the flooding-based approach while the cost isreduced by more than 80%.

The remainder of the paper is organized as fol-lows. Section 2 describes the design of our approach.We address the two key issues of our approach inSection 3 and Section 4, respectively. The performanceevaluation is presented in Section 5. Section 6 reviewsrelated work. We conclude the paper in Section 7.

2 DESIGN OF TMC

In this section we give the design details of TMC.First, we define the network model. Then, we presentthe basic idea of the design. Next, we introducethe message forwarding metrics and the messageforwarding procedure. Finally, we highlight the keyissues of TMC. Some other design issues are discussedin the online supplementary file.

2.1 Network Model

We consider a vehicular network consisting of Nnodes. Two vehicles can communicate when theyencounter each other, i.e., when they are within thecommunication range of each other. We do not requirethat the vehicles are densely populated, thus thenetwork connectivity can be unavailable.

A message m to multicast has the following at-tributes: message ID, source node sm, the set Dm

of destination nodes, and the time-to-live (TTL) limitbeyond which the message will be dropped.

As in [13] [14], the future trajectory Ti of a vehicle iis obtained from the GPS enabled navigation systemwhen the driver inputs the destination for gettingthe driving path. We assume most of the driversfollow the driving paths suggested by the navigationsystem. Trajectory Ti of vehicle i consists of a sequenceof road segments and is associated with a startingpoint. Trajectory Ti of each vehicle i and the startingpoint are disseminated in the vehicular network bytrajectory sharing when vehicles encounter each other.

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vTrajectory of v

Destination

nodes

d3

Encounters

r1

d1

d2

Message

r2

Candidate relays

Figure 1. Illustration of the basic idea of TMC.

2.2 Basic IdeaThe basic idea of TMC is to forward a message tovehicles with a higher capability of delivering themessage to more destination nodes. In another word,a relay node of a message should be able to encountermore destination nodes.

As an example, in Fig. 1, the trajectories of vehiclesv, r1, r2, d1, d2 and d3 are shown. At the intersectionsof different trajectories, encounters occur between thetwo corresponding vehicles. Vehicle v has a messageto forward to a destination set including vehicle d1, d2and d3, and it will encounter vehicle r1, r2 and d3.After encountering v, vehicle r1 will encounter d1 andd2, and vehicle r2 will encounter d2 and d3. Vehiclev is able to forward the message to the destinationnode d3 when v and d3 encounter each other. Asvehicle r1 can forward the message to both d1 andd2, v should forward the message to r1. In contrast, vwill not forward the message to r2 in spite that r2 willencounter d2 and d3 because d2 and d3 have alreadybeen taken care jointly by v and r1.

2.3 Message Forwarding MetricsFor the success of TMC, it is critical to design anefficient message forwarding metric which characterizesthe capability of a vehicle to deliver a given messageto the set of destination nodes. With the metric, avehicle v can compute the multicast delivery gain fora candidate relay node r based on which v can deter-mine if it should forward the message to r.

We next give the formal definitions of the two mes-sage forwarding metrics, the delivery potential vectorof a candidate relay node r to a message m and themulticast delivery gain of r over vehicle v.

Definition 1 (Delivery Potential Vector). Given a mes-sage m, the delivery potential vector γ⃗m(v) of a vehicle vis defined as the vector of delivery probabilities that vehiclev delivers m to the destination nodes in Dm:

γ⃗m(v) , ⟨p1(v), p2(v), · · · , pk(v)⟩, (1)

where k = |Dm|, the ith position of the vector representsthe ith destination node in Dm sorted in the increasingorder of their IDs, and pi(v) is the corresponding deliveryprobability for the ith destination node.

Note that pi(v) is zero when v has no potential ofdelivering message m to destination node i.

Definition 2 (Multicast Delivery Gain). Given a mes-sage m, the multicast delivery gain of vehicle r over vehiclev, denoted as ϕm(r, v), is defined as,

ϕm (r, v) ,k∑

i=1

αi,

where αi =

{pi(r)− pi(v), if pi(r)− pi(v) > 00, otherwise ,

(2)

From the definition, we can see that the multicastdelivery gain of r over v reflects the additional benefitfor delivering m to destination nodes if r is selectedas a relay. It is reasonable to ignore the negativeeffect of r on delivering m to destination i whenpi(r) − pi(v) ≤ 0. The justification is as follows. Inour multicast routing algorithm, message replicationis used, which indicates that a message remains inthe forwarder vehicle and a copy is replicated on therelay vehicle. With this in mind, we actually want toselect those relays which can take the message to anyone of the destination nodes with high probability. Ifa potential relay has a high delivery probability ofrelaying the message to one of the destinations whilehas low delivery probabilities for the rest destinations,this relay is still desirable since it contributes to thesuccess of the multicast of the message. On the otherhand, if we only forward messages to those relays thathave high delivery probabilities for all destinations,then the number of such relays would be very small.As a result, the overall delivery probability of themessage would be very small.

2.4 Message Forwarding Procedure

When the message forwarding metrics are available,we are ready to describe the trajectory-based multicastrouting. That is, how does the vehicular networkforward messages to their respective destination ve-hicles. Essentially, the core of the multicast routingprocess is the procedure executed by each vehicleonce it encounters another. Through period beaconsat the MAC layer, a vehicle can discover the presenceof a new neighbor and the departure of an existingneighbor. Once discovering a new neighbor, a vehicleexecutes the procedure in which the vehicle decideswhether to forward its messages to the new neighborand the order of these messages being forwarded.

Each vehicle gives forwarding priority to those mes-sages with higher delivery gains with respect to thenew neighbor. To explain the procedure, without lossof generality, we consider vehicle v encounters anoth-er vehicle u. Upon discovering the new neighbor u,node v should decide whether to forward its messagesto u, and the order of these messages being forwarded.Consider a message denoted by m in vehicle v. To

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Path 2

Trajectories

d

vMessage

Path 1Path 3

Destination

Node

Figure 2. Illustration of the computation of the deliveryprobability of v delivering m to a given destination d.

enable u to compute the delivery gain for m, it main-tains a vector γ⃗m of maximum delivery probabilitiesthat have been recorded in previous relays to eachdestination. The computation of delivery gain requiresencounter probabilities which needs the knowledgeof vehicle trajectories. Such knowledge is obtained byeach vehicle by sharing trajectories and correspondingstarting points each time two vehicles encounter. By vforwarding γ⃗m to u, u can compute its gain based onthe trajectories it has maintained. Only when u has apositive delivery gain over γ⃗m, v will forward m to u.

Considering v might have multiple messages toforward to u while the encounter duration might notbe long enough for all the messages to be transmit-ted, v should decide the message forwarding order.The messages are sorted according to their deliverygains. The pseudo codes of the message forwardingprocedure for both vehicle v and u can be found inthe online supplementary file.

It is possible that in the collision domain of v, theremight be other vehicles contending for the channel inaddition to u. This paper does not focus on the designof MAC protocols. Note that the adopted MAC pro-tocols for inter-vehicle communication should includeperiodic beacon mechanism for neighbor discovery.

2.5 Key Issues

To implement TMC, it is necessary for each vehiclev to compute its delivery potential vector γ⃗m(v) fora given message m. Essentially, v should compute itsdelivery probability of delivering m to each destina-tion node d, pd(v). To compute pd(v), the followingtwo key issues must be addressed.

• Computation of delivery probability. The deliv-ery probability pd(v) of vehicle v delivering m todestination node d is dependent on all the futureinter-vehicle encounters in the network. Section 3addresses this issue.

• Prediction of inter-vehicle encounters. We needto compute the encounter probability of two ve-hicles when their trajectories intersect with eachother. In spite of the knowledge of future trajec-tories, one does not know the accurate arrival

time of the vehicle at a specific location on thetrajectory, which is critical for estimating the en-counter probability of two vehicles. This issue isaddressed in Section 4.

3 COMPUTING DELIVERY POTENTIAL VEC-TOR

To derive γ⃗m(v), there is a need to calculate thedelivery probability pd(v) of delivering m to eachdestination d. In this section, we provide the detailedprocedures of deriving pd(v).

We first illustrate the main idea of computing pd(v)in Fig. 2, where trajectories of several vehicles in-cluding v and d are shown. There are three possibleforwarding pathes Path 1, Path 2 and Path 3 for themessage m carried by v to reach d. Whether themessage m can be delivered along a path is prob-abilistic because the encounter at the intersection oftwo trajectories is uncertain. Let λi denote the Path iand P (λi) denote the delivery probability along theforwarding path i. Then pd(v) can be computed as,

pd(v) = 1−∏

i=1,2,3

(1− P (λi)) . (3)

As a result, to compute pd(v) we should first obtainthe following two items.

• Item 1: The set of all possible forwarding pathsconnecting v and the destination node d, denotedby Θv(d).

• Item 2: The message delivery probability alongeach forwarding path λi ∈ Θv(d), i.e., P (λi).

We propose the trajectory-based encounter graph toderive the two items in the following.

3.1 Trajectory-based Encounter GraphWe denote the trajectory of a vehicle i by Ti, contain-ing the geographic information of the driving path ofi and associating with a starting time.

Definition 3 (Trajectory-based Encounter Graph). Atrajectory-based encounter graph G = {V,Eu, Eb} isconstructed based on a set Ψ of vehicular trajectories,including a vertex set V , a unidirectional edge set Eu anda bidirectional edge set Eb. Along a trajectory Ti ∈ Ψ, foreach intersection with another trajectory Tj , j ̸= i, there isa vertex ρij ∈ V which is associated with a random variableof vehicle i’s arrival time at the intersection. Between twosuccessive vertices ρij and ρik, k ̸= i along Ti, there is aunidirectional edge e⃗ ∈ Eu from ρij to ρik. Between anypair of vertices ρij along Ti and ρji along Tj there is abidirectional edge e ∈ Eb which indicates that the twovehicles i and j can potentially meet and exchange messagesat the intersection .

A vehicle v constructs a trajectory-based encountergraph G(v) based on the trajectory set Ψ(v) main-tained by v. Ψ(v) is updated when v encounters

5

Road

intersections

b

c

a

r

Road

segment r

I2 I3 I4

I1

Figure 3. Trajectories of vehi-cles a, b, and c in a small roadnetwork.

a

a

cr

b c

1

c

bI

c

ar

4

c

bI

1

b

cI

4

b

cI

t

Figure 4. The trajectory-basedencounter graph based onthe three trajectories shown inFig. 3.

4e

1e

1

v

aI

2

v

bI

2

b

vI

1

a

vI

3

c

bI

4

c

aI

4

a

cI

3

b

cI t

Destination node

2e

3e

1e

2e

3e

Figure 5. An example trajectory-based encounter graph to illus-trate the main process of thesearching algorithm.

other vehicles which share the trajectory informationwith v. To create the set V (v) of G(v), every twotrajectories Ti, Tj ∈ Ψ(v) are compared for locatingtheir intersections. Each intersection results in a pairof vertices ρij and ρji .

Each vertex ρij ∈ V (v) is associated with a randomvariable τ ij of i’s arrival time at the intersection ofTi and Tj . The probability distribution of the randomvariable will be discussed in the subsection 4.1. It ispossible that the same pair of trajectories have morethan one intersections, so we attach spatial and tem-poral information to each vertex for differentiation.

A unidirectional edge e⃗ ∈ Eu(v) between ρij andρik indicates that a vehicle i first meets the vehiclej and then meets the vehicle k on its trajectory Ti.As the message is carried by the vehicle i during itstraveling between the two successive intersections, theprobability of moving the message between the twointersections is 1. Thus the weight of e⃗, P (e⃗), is set to1. A bidirectional edge e ∈ Eb(v) between ρij and ρjiindicates that there is an chance for the vehicles i andj to encounter and exchange messages. The weightof e, P (e), represents the encounter probability andis less than 1. The way of estimating the encounterprobability will be introduced in Section 4.

As an example, we show the trajectories of threevehicles a, b and c in a small road network in Fig. 3.The corresponding trajectory-based encounter graphG is shown in Fig. 4. Along the trajectory Tc of vehiclec, there are two intersections with the trajectory Tb

at road intersections I1 and I4 respectively, and anintersection with the trajectory Ta on the road seg-ment r. Thus, there are three corresponding verticesρcb(I1), ρ

cb(I4) and ρca(r) in G. We differentiate the two

intersections between the trajectories of c and b, i.e.,ρcb(I1) and ρcb(I4), with the geographic positions I1and I4. Along Tc there are three successive intersec-tions represented by vertices ρcb(I1), ρ

ca(r) and ρcb(I4)

respectively. Accordingly, there are two unidirectionaledges in G, one is from ρcb(I1) to ρca(r) and the otheris from ρca(r) to ρcb(I4). There are also two successiveintersections along Tb at I1 and I4, respectively. Corre-spondingly, there is a unidirectional edge from ρbc(I1)

to ρbc(I4). For the trajectory intersection between Ta

and Tc on the road segment r, there is a bidirectionaledge between vertices ρac (r) and ρca(r).

3.2 Searching for Forwarding PathsWith G(v), an efficient searching algorithm is appliedto find all possible paths from v to each destination.

We next explain the main process of the searchingalgorithm with an example trajectory-based encountergraph shown in Fig. 5. The searching algorithm in-troduces a parameter of search depth ω ≥ 1, which isdefined as the maximum number of forwarding hopsof all resulting paths. A forwarding hop correspondsto the message transmission between two vehicles,and the number of hops on a forwarding path reflectsthe number of times the messages are forwarded fromone vehicle to another over the whole path.

The main process of the searching algorithm onG(v) given a searching depth ω is as follows.

• Initialization: The starting point ρ0 of the searchis the first trajectory intersection along Tv, i.e.,the first vertex of v. In our example, the startingvertex is ρva(I1).

• Depth-1 search: The vehicle v looks for the des-tinations that it can directly reach without needof another vehicle to forward the message. Thus,starting from ρ0, v only needs to search alongits unidirectional edges to find the vehicles thatcan be encountered in one hop, denoted by β1.Once encountering these vehicles, v can forwardthe message to them. In the example, β1 = {a, b}because ρva(I1) and ρvb (I2) are found.

• Depth-i search (1 < i ≤ ω): The search goesalong the bidirectional edges from vehicles inβi−1 to find the vehicles that can be reachedwithin i hops from ρ0. From a vehicle in βi−1,same as the Depth-1 search, the search goes alongunidirectional edges to find vehicles that havenot been included by βi−1 to create the set βi ofvehicles to encounter in i hops. In the sample,β2 = {c} and ∀i > 2, βi = ∅.

• Termination: After the search finishes, the desti-nation nodes and the forwarding path rooted at

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v are available. In our example, there are twoforwarding pathes from v to the destination nodec, i.e., ρva(I1) → e1 → ρav(I1) → e⃗2 → ρac (I4) →e3 → ρca(I4) and ρva(I1) → e⃗1 → ρvb (I2) → e2 →ρbv(I2) → e⃗3 → ρbc(I3) → e4 → ρcb(I3).

According to the searching algorithm, the searchdepth ω controls the tradeoff between the estimationaccuracy of the message delivery probability and thecomputation complexity. When a larger search depthis used, more destination nodes and more forwardingpaths from a vehicle to each of the destination nodeswould be included. However, a larger search depthleads to a higher computation complexity. We knowthat the message delivery probability through a for-warding path quickly decreases with the increasingnumber of hops. As a result, a small search depthsuffices in practice, e.g., 3 hops.

3.3 Calculating P (λi)

Suppose λi ∈ Θv(d) is a forwarding path searchedby the previous algorithm and λi contains a set ofbidirectional edges, denoted by Φ(λi), then P (λi) canbe computed as follows,

P (λi) =∏

e∈Φ(λi)

P (e). (4)

It is possible that when two vehicles, e.g., v andu, encounter with each other, neither v nor u canfind a forwarding path to deliver a message of vto one of the destinations, e.g., i. In another word,both pi(v) and pi(u) are zero. Then, the multicastdelivery gain of forwarding the message from v to u iscomputed based only on those destinations to whichu has higher delivery probabilities than v. As a result,the destination i, to which both v and u have a zerodelivery probability, will be ignored.

4 PREDICTING INTER-VEHICLE ENCOUN-TERS

The occurrence of an encounter between two vehiclesrequires two conditions. First, there is a trajectoryintersection between the two trajectories. Second, thearrival instants of the two vehicles at the intersectionposition are so close that the two vehicles will residewithin the communication range of each other. Basedon the two conditions, we compute the encounterprobability of two vehicles given their trajectories.

4.1 Modeling of Travel TimeWhen predicting inter-vehicle encounters, it is neces-sary to have the knowledge of a vehicle’s arrival timeat an intersection on its trajectory. However, vehiculartrajectories do not provide such arrival times. Fortu-nately, the vehicular travel time over a route of urbanroads follows the Gamma distribution, as suggestedin some prior research [15] [16].

0 50 100 150 200 250 3000

20

40

60

80

100

120

140

Travel Time (minutes)

Num

ble

of T

rave

l Tim

e S

ampl

es

Driving Time SampleGamma Distribution

Figure 6. Travel time distribution of a randomly select-ed road segment.

The probability density function (PDF) of the Gam-ma distribution can be expressed in terms of thegamma function parameterized in terms of a shapeparameter κ and a scale parameter θ. The equationdefining the PDF of a gamma-distributed randomvariable τ , representing the vehicular travel time, is

f (τ ;κ,θ)= 1θκ

1Γ(κ)τ

κ−1e−τθ ,

τ ≥ 0, and κ,θ>0.(5)

To verify that the vehicular travel time followsGamma distribution, we have conducted empiricalstudy based on real vehicular GPS traces from around2,058 taxis in Shanghai, China. For a randomly select-ed road segment, we compute the travel time of about1,000 vehicles which forms a sample set. Based on thesample set, we first plot a histogram in Fig. 6 whichshows the distribution of all the samples. Then weestimate the two parameters of the PDF of the Gammadistribution by conducting the maximum likelihoodestimation over the sample set. With the estimatedparameters, we plot the PDF of this specific Gammadistribution in Fig. 6, too. The Kolmogorov-Smirnov(K-S) test shows that the sample set follows Gammadistribution with a significance level of 95%.

As a result, we model the travel time over a path asa random variable following the Gamma distributionin which there are two parameters. We derive thetwo parameters We estimate the two parameters byconducting statistics on the real vehicular GPS tracesas follows. First, travel time samples for the drivingpath are collected, which include both the time onroad segments along the path and the time at cor-responding intersections. Then, maximum likelihoodestimation is conducted based on the travel timesamples to achieve the parameters.

4.2 Calculation of Encounter ProbabilitiesThe rationale behind the computation of encounterprobabilities is as follows. Suppose the trajectories ofvehicle v and u intersect at position I . The arrivaltime of v at I , denoted by τvu(I), has been introducedin the construction of encounter graphs (Section 3.1).τvu(I) can be modeled as a Gamma distributed random

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variable. This is because the starting time instant ofv’s trajectory is known and the vehicular travel timeuntil v arrives at I can be modeled as a Gammadistributed random variable as introduced in the pre-vious subsection. Similarly, the arrival time of u at I ,τuv (I), is also a random variable. We denote the timedifference between τvu(I) and τuv (I) by ∆(τvu(I), τ

uv (I)).

To ensure that u and v can encounter at positionI , ∆(τvu(I), τ

uv (I)) has an upper bound, denoted by

δ. When ∆(τvu(I), τuv (I)) is larger than δ, u and v

cannot encounter because they will be out of thecommunication range of each other when they arriveat I . δ can be determined based on the transmissionrange and the relative moving speed of two vehicles.

We consider two types of inter-vehicle encounters.We next explain the computation of the encounterprobability for each type. The first type of encoun-ters occur at a road intersection, e.g., the encounterbetween b and c at I1 in Fig. 3. Denoting the PDF ofa random variable τ by fτ , the encounter probabilitycan be computed as,

Pr{b encounters c at I1}= Pr{∆(τ bc (I1), τ

cb (I1)) < δ} (6)

=

∫ ∞

0

∫ t+δ

t−δ

fτbc (I1)

(t)× fτcb (I1)

(t′)dt′dt. (7)

Eq. 6 means the probability that b and c encounter atI1 is the probability that the time difference betweenthe arrival time of b and c at I1 is shorter than δ.

The second type of encounters take place whentwo vehicles move in different directions on the sameroad, e.g., the encounter between vehicles a and con road r in Fig. 3. Denoting the arrival time of aat road intersections I2 and I3 by τa(I2) and τa(I3),respectively, and those of c at I2 and I3 as τ c(I2) andτ c(I3), respectively, we have

Pr{a encounters c on road r}= Pr{τa(I3) < τ c(I3) ∩ τ c(I2) < τa(I2)} (8)

=

∫ ∞

0

∫ ∞

t

fτa(I3)(t)× fτc(I3)(t′)dt′dt

×∫ ∞

0

∫ ∞

t

fτc(I2)(t)× fτa(I2)(t′)dt′dt. (9)

This means that vehicles a and c encounter each otherwhen both the time a entering r (τa(I3)) is earlier thanthe time c leaving r (τc(I3)) and the time c entering r(τc(I2)) is earlier than the time a leaving r (τa(I2)).

5 PERFORMANCE EVALUATION

We evaluate the performance of TMC in this section.More evaluation results can be found in the onlinesupplementary file.

5.1 Methodology and Experimental SetupWe have conducted extensive simulations based onreal vehicular GPS traces, and compared our approach

with three state-of-the-art related approaches. TheGPS traces are collected from 2,058 taxis in Shanghai,China during a period of 32 days, covering the urbanarea of 130 km in length and 69 km in width.

To evaluate the routing performance, we use threemetrics: delivery ratio, transmission overhead, and de-livery delay. The metric of transmission overhead isan average over all the multicast sessions. For asingle multicast session, the transmission overhead isthe number of all the transmissions of data packetsover the number of reached destination vehicles. Thedelivery delay is the average value of all the success-fully delivered packets. The default value of systemparameters in all the simulations are shown in Table 1.

Each multicast session has a source node generatinga message with the TTL of two hours. The set ofdestination nodes are randomly selected and recordedin message header.

5.2 Compared Algorithms• Epidemic [17]. The source node floods the message

throughout the network to reach all multicastdestination nodes.

• RAPID [18]. RAPID is originally designed for u-nicast in delay-tolerant networks. With RAPID, amessage is forwarded to a relay who has a shorterexpected delay to the destination. We have re-vised RAPID where a relay node is selected ifit has a shorter delay to any of the destinationnodes. Message replication is adopted.

• STDF [19]. This algorithm is initially designedfor unicast in vehicular networks. It assumes theavailability of real-time trajectories of all the vehi-cles. Encounters of two vehicles traveling on thesame road segment and along opposite directionsare considered. For fair comparison, STDF is alsoextended to support efficient multicast.

5.3 Overhead of Trajectory SharingIn TMC, when two vehicles encounter each other, eachof the vehicles will share with the other vehicle theinformation of currently maintained trajectories thatthe other vehicle does not have. As a result, the tra-jectory sharing process incurs transmission overhead.To learn how much the actual transmission overheadfor sharing trajectories is incurred throughout the

TABLE 1Default Settings of System Parameters

Parameter Default Value# of vehicles 1,000

# of multicast groups 50# of destination nodes 20Communication range 100 meters

Search depth ω 3

8

500 1000 15000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Number of Vehicles

DeliveryRatio

EpidemicRAPIDSTDFTMC

Figure 7. Delivery Ratio vs. Num-ber of Vehicles.

500 1000 15000

20

40

60

80

100

Number of Vehicles

Transm

issionOverhead

EpidemicRAPIDSTDFTMC

Figure 8. Transmission Overheadvs. Number of Vehicles.

500 1000 15004200

4400

4600

4800

5000

5200

5400

Number of Vehicles

DeliveryDelay(s)

EpidemicRAPIDSTDFTMC

Figure 9. Delivery Delay vs. Num-ber of Vehicles.

whole process, we have conducted trace driven simu-lations to study the overhead. We emphasize that thetransmission overhead studied in this subsection onlycounts the amount of transmitted data for exchangingtrajectories each time two vehicles encounter.

The experimental simulations are conducted basedon the real vehicular GPS traces. We simulated thevehicular network for 3 hours (8:00am-11:00am). Theamount of transmitted data on each encounter forexchanging trajectories was recorded each time twovehicles encounter each other. The number of vehiclesis varied from 200 to 1,800. The communication rangeof vehicles is 100 meters. We use 140 bytes to store onevehicle trajectory because of the following analysis ofthe real traces. First, we can use four bytes to representa road segment because there are less than 35,000road segments in Shanghai, the largest city in China.Second, a trajectory of 10 hours contains about 34.2road segments. As a result, 140 bytes are sufficient torepresent a vehicle trajectory used in TMC.

Fig. 10 plots both the total transmission overhead oftrajectory sharing of the whole network and the aver-age overhead per vehicle in log scale as the numberof vehicles in the network is varied. From the figure,we can find that the overhead of trajectory sharingis as low as hundreds of kilobytes per vehicle andincreases with the number of vehicles. Therefore, thetransmission overhead caused by sharing trajectoriesin TMC is very low. The main reason is that when

500 1000 150010

1

102

103

104

105

106

Number of Vehicles

Trajectory

SharingOverhead(K

B)

Total OverheadAverage Overhead Per Vehicle

Figure 10. Trajectory sharing overhead vs. number ofvehicles.

two vehicles encounter, only the trajectories that theother vehicle does not have are actually exchanged.Thus, it is practical to share trajectories for efficientmulticast routing in vehicular networks.

In the rest of performance evaluation, the reportedtransmission overhead values all include the overheadcaused by sharing trajectories among vehicles.

5.4 Impact of Number of Vehicles

We evaluate the performance of various schemes asthe number of vehicles is varied from 200 to 1,800.Fig. 7, Fig. 8, and Fig. 9 plot the evaluation results.

In Fig. 7, we can see that TMC has a delivery ratioclose to those of Epidemic and STDF and better thanthat of RAPID. For example, when there are 1,800vehicles, the delivery ratio of TMC is only 6.4% and8.0% lower than that of Epidemic and STDF, respec-tively. The delivery ratio of each scheme increasesas the number of vehicles becomes larger becausemore nodes lead to a higher delivery capability of thenetwork. STDF performs best because of the adoptionof real-time vehicular trajectories. With the knowledgeof real-time trajectories, inter-vehicle encounters arebetter estimated and and contribute to high deliveryratio. On the other hand, Epidemic floods data packetsblindly. Thus, transmission chances cannot be effi-ciently used to achieve high delivery ratio. For TMC,the reason that the delivery ratio is lower than STDFis that the trajectories are shared through inter-vehicletransmissions. Thus, trajectories are not completelyavailable to all the vehicles. For RAPID, it performsworst because it estimates the expected delay of relaysbased on less efficient statistic results of encounterhistory instead of real-time information.

As expected, in Fig. 8, TMC has the lowest trans-mission overhead among the compared algorithms.As TMC estimates not only the encounters betweentwo vehicles on the same road segment, but alsoaround road intersections which is ignored by STDF,TMC can find better sequences of relays with higherencounter probabilities. As a result, TMC deliverpackets much more efficiently than STDF. When thereare 1,800 vehicles in the network, the transmission

9

50 100 150 200

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

Number of Multicast Sessions

DeliveryRatio

EpidemicRAPIDSTDFTMC

Figure 11. Delivery Ratio vs. Num-ber of Multicast Sessions.

50 100 150 2000

10

20

30

40

50

60

Number of Multicast Sessions

Transm

issionOverhead

EpidemicRAPIDSTDFTMC

Figure 12. Transmission Overheadvs. Number of Multicast Sessions.

50 100 150 2004400

4600

4800

5000

5200

5400

Number of Multicast Sessions

DeliveryDelay(s)

EpidemicRAPIDSTDFTMC

Figure 13. Delivery Delay vs. Num-ber of Multicast Sessions.

overhead of TMC is 85.2%, 90.2% and 90.9% lowerthan that of STDF, RAPID and Epidemic, respectively.We can also find that trajectory based routing al-gorithms perform better than algorithms not usingtrajectories. This is because, with the knowledge oftrajectories, packet transmissions to those vehicleswith less probabilities to delivery the packet are re-duced and precious encounter chances can be moreefficiently used.

Fig. 9 shows that the delivery delay of four algo-rithms decrease as the number of vehicles decreasesand TMC has the shortest delivery delay amongall the compared algorithms. As mentioned above,the average delivery delay is computed over all thesuccessfully delivery packets. In other words, for amulticast packet, the delivery delay for the packet toreach each received destination should be taken intocomputation. We can find that the trajectory basedalgorithms, i.e., TMC and STDF, have shorter delaythan other algorithms. This is also because that, withthe knowledge of trajectories, relay sequences withhigher delivery probabilities are selected which avoid-s blind transmissions. When there are 600 vehicles, thedelivery delay of TMC and STDF are 10.7% and 6.2%shorter than that of Epidemic, respectively.

5.5 Impact of Number of Multicast SessionsIn order to illustrate the sparse property with precioustransmission chances in vehicular networks and toemphasize the importance of high efficient routingalgorithms, we explore the impact of traffic load byvarying the number of concurrent multicast sessions.Fig. 11, Fig. 12 and Fig. 13 show the results.

In Fig. 11, the delivery ratio of all the algorithmsdecrease as more concurrent multicast sessions exist.The most important feature in the figure is that the de-livery ratio of Epidemic decreases dramatically withheavier traffic load. When there are 200 concurrentmulticast sessions, Epidemic has the lowest deliveryratio which is 35% lower than that of STDF. As Epi-demic blindly floods packets in the network withoutefficiently using the precious transmission chances,traffic loads higher than the transmission capacity ofthe network necessarily result low delivery ratio.

In Fig. 12, algorithms keep stable transmission over-head to successfully deliver a packet under differenttraffic loads. From the figure, we can find that trajecto-ry based algorithms are more efficient than Epidemicand RAPID. For example, when there are 150 mul-ticast sessions, the transmission overhead of TMC is85.9% lower than that of Epidemic. We can also findthan TMC is much more efficient than STDF. Thereare two reasons. First, TMC considers more encountertypes than STDF. Thus, TMC can select better relayswith higher delivery probabilities. Second, TMC isdesigned for multicast. TMC evaluates the deliveryability of a candidate relay based on its integrateddelivery probabilities for all the destinations of amulticast packet. While STDF selects a relay only if ithas a higher delivery probability for any destination.

As shown in Fig. 13, the average delivery delay ofTMC for successfully delivery packets is the shortest.When the traffic load increases, the delivery delays ofthe three compared algorithms only increase slightly.This is because only a small ratio of packets aresuccessfully delivered under heavy traffic load.

6 RELATED WORK

We review related work in this section. Additionaldiscussion on other related work including multicastalgorithms in mobile ad hoc networks and previousstudies in vehicular ad hoc networks are provided inthe online supplementary file.

6.1 Multicast in Vehicular Networks

A few algorithms have been designed for multicastrouting in vehicular networks, but most of them areextended from typical multicast routing protocols forMANETs, which makes them inappropriate for sparsevehicular networks.

ROVER [9] is a tree-based geographical multicastrouting algorithm for vehicular networks. Vehicles inthe zone of forwarding (ZOF) discover a forwardingtree reaching all the nodes in the zone of relevance(ZOR) rooted at the source node. It is clear that a highdensity of nodes is necessary for this protocol.

10

MDDV [11] is also a dissemination tree based al-gorithm. For each forwarding path to a specific des-tination region, a dynamically maintained group ofnodes which locate closest to the destination regionare forwarders.

6.2 Trajectory-based Routing in Vehicular Net-worksVehicular trajectories have been exploited for packetdelivering in vehicular networks [20] since the avail-ability of future trajectories significantly reduces theuncertainty with vehicular mobility.

TBD [14] is a routing approach for using trajectoriesto forward data from vehicles to a given roadsideaccess point (AP) in a light traffic vehicular network.Each node estimates the delivery delay to the APbased on its trajectory, which is then used as themetric for making forwarding decisions. Wu et al. [21]propose to predict the future location of a vehicleby modelling the mobility of a vehicle as a multi-order Markov chain, and then estimate the encounterprobability of each pair of vehicles. TSF [22] makesuse of road side units (RSUs) and trajectories toforward data from a fixed roadside unit (RSU) to amoving vehicle.

In our work we also exploit vehicular trajectoriesfor data delivery, but consider a different problem, i.e.,multicast routing in sparse vehicular networks. Thus,our work is complementary to existing approaches.

7 CONCLUSION

In this paper we have presented an approach calledTMC for efficient multicast in sparse vehicular net-works. TMC employs a forwarding metric whichcharacterizes the capability for a candidate relay n-ode to deliver a message to each destination nodein the multicast group. We predict the pairwise en-counters of a vehicle with other vehicles to evaluateits delivery probability. TMC is a fully distributedapproach, with which vehicles share their trajectoriesas they encounter each other. This makes TMC ap-pealing for practical use in real vehicular networks.Our performance results demonstrate that TMC canachieve the packet delivery ratio close to that of abroadcast scheme with a much lower transmissionoverhead. We introduce our future work in the onlinesupplementary file.

ACKNOWLEDGEMENTS

This research is supported by China 973 Pro-gram (2014CB340303), NSFC (No. 61170238, 60903190,61027009, 60933011, 61202375), Doctoral Fund of Min-istry of Education of China (20100073120021), Na-tional 863 Program (2009AA012201, 2011AA010500and 2013AA01A601), HP IRP (CW267311), SJTU SMCProject (201120), STCSM (08dz1501600, 12ZR1414900),

Shanghai Chen Guang Program (10CG11), SingaporeNRF (CREATE E2S2), and MSRA funding for UrbanComputing and for Star Track program. This work isalso supported by Program for Changjiang Scholarsand Innovative Research Team in University(IRT1158,PCSIRT), China.

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Ruobing Jiang is a PhD student in theDepartment of Computer Science and En-gineering at Shanghai Jiao Tong University.She received her BEng. degree from theDepartment of Computer Science and Engi-neering at Southeast University in 2010. Herresearch interests include vehicular ad hocnetworks and mobile computing. She is astudent member of the IEEE.

Yanmin Zhu is an Associate Professor in theDepartment of Computer Science and En-gineering at Shanghai Jiao Tong University.He obtained his PhD from the Departmentof Computer Science and Engineering at theHong Kong University of Science and Tech-nology in 2007. Prior to joining Shanghai JiaoTong University, he worked as a ResearchAssociate with the Department of Computingat the Imperial College London, UK. His re-search interests include vehicular networks,

wireless sensor networks and mobile computing. He is a member ofthe IEEE and the IEEE Communication Society.

Xin Wang received the B.S. and M.S.degrees in telecommunications engineeringand wireless communications engineeringrespectively from Beijing University of Postsand Telecommunications, Beijing, China, andthe Ph.D. degree in electrical and computerengineering from Columbia University, NewYork, NY. She is currently an Associate Pro-fessor in the Department of Electrical andComputer Engineering of the State Universi-ty of New York at Stony Brook, Stony Brook,

NY. Before joining Stony Brook, she was a Member of Technical Staffin the area of mobile and wireless networking at Bell Labs Research,Lucent Technologies, New Jersey, and an Assistant Professor inthe Department of Computer Science and Engineering of the StateUniversity of New York at Buffalo, Buffalo, NY. Her research interestsinclude algorithm and protocol design in wireless networks and com-munications, mobile and distributed computing, as well as networkedsensing and detection. She has served in executive committee andtechnical committee of numerous conferences and funding reviewpanels, and is the referee for many technical journals. Dr. Wangachieved the NSF career award in 2005, and ONR challenge awardin 2010.

Lionel M. Ni is the chair professor in theDepartment of Computer Science and En-gineering at the Hong Kong University ofScience and Technology (HKUST). He alsoserves as the special assistant to the presi-dent of HKUST, dean of the HKUST Fok YingTung Graduate School, and visiting chair pro-fessor of the Shanghai Key Lab of ScalableComputing and Systems at Shanghai JiaoTong University. He has chaired more than 30professional conferences and has received

six awards for authoring outstanding papers. He is a fellow of theIEEE.

13

APPENDIX APSEUDO CODES OF THE MESSAGE FOR-WARDING PROCEDURE

The pseudo codes of the message forwarding pro-cedure are shown in Algorithm 1 and Algorithm 2.The procedure in Algorithm 1 is executed by everyvehicle each time it discovers a new neighbor u.The procedure in Algorithm 2 is triggered by the dis-covering vehicle. The procedure includes the processfor sharing trajectories between node v and u. Thedeparture of the neighbor prematurely terminates theexecution of the procedure.

APPENDIX BADDITIONAL PERFORMANCE EVALUATIONON THE IMPACT OF COMMUNICATION RANGE

In this set of simulations, we vary the communicationrange from 50 m to 250 m. Fig. 14, Fig. 15, and Fig. 16plot the delivery ratio, transmission overhead anddelivery delay, respectively.

As expected, in Fig. 14, the delivery ratio of each al-gorithm increases when larger communication rangeis adopted. This is because a larger communicationrange results more inter-vehicle contacts and a largernetwork capacity of packets delivery. Same as previ-ous simulations, STDF has the best performance andTMC has a delivery ratio close to those of Epidemicand STDF. When the communication range is 150 m,the delivery ratio of TMC is only 12.2% lower thanthat of Epidemic, and 27.5% higher than that ofRAPID. We can also find that STDF has similar de-livery ratio as Epidemic. However, they use differentschemes to achieve the best delivery ratio among allthe approaches. Epidemic floods the messages overthe network, taking full advantage of inter-vehicleencounters. Thus, Epidemic achieves high deliveryratio but with high transmission overhead, which willbe shown later. While STDF relays messages in a moreefficient way by assuming that each vehicle has theaccess to all the vehicular trajectories. Thus, STDF canlargely reduce the transmission overhead.

In Fig. 15, Epidemic and RAPID keep stable trans-mission overhead under different communicationranges while trajectory based algorithms have slightlyhigher transmission overhead when the communica-tion range increases. For example, the transmissionoverhead of TMC when the communication range is150 m is 20.6% higher than that when the communi-cation range is 100 m. The reason that trajectory basedalgorithms have higher transmission overhead underlarger communication range is as follows. When larg-er communication range is adopted, more potentialrelays are available each time when a packet holderencounters with other vehicles. Before the best re-lay sequence is found, vehicles with higher deliveryprobabilities are selected as relays to improve the

Algorithm 1: Message Forwarding Procedure Ex-ecuted on v

Notations Mi: the set of messages of vehicle iΨi: the set of trajectories maintained by vehicle iI : maximum number of retransmissions

1: for iter=1, iter< I do2: ∀m ∈ Mv , broadcast IDm, Dm, and γ⃗m3: Share trajectories Ψv with u4: if Receive delivery gains from u then5: Decide the message forwarding order6: Broadcast messages in order7: ∀m ∈ Mv , update γ⃗m,8: return9: end if

10: end for

Algorithm 2: Corresponding Procedure Executedon u

Notations Mi: the set of messages of vehicle iΨi: the set of trajectories maintained by vehicle i

1: if Receive message information from v then2: Share trajectories Ψu with v3: Compute delivery gains to messages involved in the

received message information4: Broadcast delivery gains5: if Receive messages from v then6: Update Mu and γ⃗m, ∀m ∈ Mu

7: end if8: end if

delivery ratio. Thus, more unnecessary transmissionsare generated when larger communication range isadopted.

In Fig. 16, we can find that a larger communicationrange results in a shorter delivery delay for eachalgorithm. And when the communication range islarge enough, the delivery delay of all the comparedalgorithms are close. When the communication rangeis 250 m, the delivery delay of Epidemic is only 3.7%and 6.7% higher than that of STDF and TMC, re-spectively. This is because a larger communicationrange leads to more inter-vehicle contacts and a largernetwork capacity of data delivery. Thus, the efficiencyof algorithms becomes less important.

APPENDIX CMULTICAST IN MANETS

Multicast routing in mobile ad hoc networks(MANETs) has been extensively studied. The major-ity of multicast protocols can be classified into fourcategories, i.e., tree-based, mesh-based, cluster-basedand stateless multicast routing.

A tree-based protocol constructs a forwarding tree[23] from the source to all multicast receivers. Therouting performance will be significantly affectedwhen network nodes are highly dynamic which re-sults in frequent route failures. At the same time, alarge number of control messages are generated toconstruct and maintain the forwarding tree, leadingto a high overhead. MAODV [23] and its successorSRMAODV [24] are examples of tree-based protocol.

14

50 100 150 200 2500.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Communication Range (m)

DeliveryRatio

EpidemicRAPIDSTDFTMC

Figure 14. Delivery Ratio vs. Com-munication Range.

50 100 150 200 2500

10

20

30

40

50

60

Communication Range (m)

Transm

issionOverhead

EpidemicRAPIDSTDFTMC

Figure 15. Transmission Overheadvs. Communication Range.

50 100 150 200 2503500

4000

4500

5000

5500

Communication Range (m)

DeliveryDelay(s)

EpidemicRAPIDSTDFTMC

Figure 16. Delivery Delay vs. Com-munication Range.

Instead of constructing a tree which has a singlepath to each destination node, a mesh-based multicastprotocol [25] [26] has more than one paths betweenthe source node and each multicast receiver. Themesh topology thus can better cope with link failure[27], and mesh-based routing has a higher deliveryratio and lower delivery delay. However, redundancyforwarding paths bring heavy traffic load in a sparsenetwork with constrained communication chance.

A cluster-based multicast protocol [28] builds localclusters or cohorts [29] of connected nodes to efficient-ly make multicast routing decisions.

Different from the previous categories, the statelesscategory of multicast protocols [30] [31] [32] does notrely on routing structures, thus minimizing the over-head for constructing and maintaining these routingstructures. This category of protocols are especiallysuitable for highly dynamic networks.

APPENDIX DVEHICULAR NETWORKS

Many research efforts have been devoted to differentaspects of vehicular networks. In [33], vehicle mobilityin urban environments has been studied by lookingat the inter-contact time which is reported to beexponentially distributed. Lu et al. [34] analyze theasymptotic capacity and delay performance of social-proximity urban vehicular networks with inhomoge-neous vehicle density.

Some work focus on the link layer performance ofvehicular networks. In [35], the performance of a C-SMA based broadcast protocol in vehicular networkshas been analyzed. And in [36], Martelli et al. studythe beaconing performance of IEEE 802.110 based ve-hicular networks by analyzing the real measurementscollected from field tests.

Many approaches for data delivery in vehicularnetworks have been proposed. In [5], a cooperativecontent distribution system called CCDSV is present-ed, which is based on a network of infrastructureAPs to collaboratively distribute contents to vehicles.Zhu et al. find that there is temporal dependencyfor inter-vehicle contacts between vehicles and then

design a prediction method to predict the next contactfor a given pair of vehicles. with predicted contacts,vehicles can make better forwarding decisions. In [37],the optimal replication strategy has been studied forpacket delivery in vehicular networks. In [6], sensordata fusion algorithms are developed to aggregatedata collected vehicles.

In [38], Li et al. consider service scheduling prob-lems in which a vehicle may not be able to obtainmore than one service within a short period of time,and scheduling algorithms have been proposed. Andurban vehicular networks are vulnerable to Sybil at-tacks and attack detection techniques are reported in[39].

APPENDIX EDISCUSSION

In the real world, vehicles may change their futuretrajectories. The possible reasons are traffic jams oraccidents on their previous trajectories. When a vehi-cle changes its trajectory, the outdated ones that havebeen distributed in the network should be updated.Otherwise, the estimated delivery probabilities of avehicle based on the information of the outdatedtrajectory would be inaccurate.

However, the impact of trajectory changes on theperformance of our approach is limited. The mainreasons are as follows. First, the outdated trajectoriescan be replaced quickly through our trajectory sharingmechanism. When a vehicle has a new trajectory,it shares its new trajectory with vehicles it will en-counter. Gradually, the new trajectory will spreadover the whole network to replace the outdated ones.We have conducted trace-driven simulations on thespread speed of trajectories sharing based on our realvehicular traces. The setting of the simulations followsthe default values, as specified in our main file. Thesimulation results show that it only takes half an hourto spread 70% of all the trajectories to more than 73.2%of the vehicles in the network. Second, according tothe computation of the message delivery probability(as described in the main file), this probability of avehicle is determined by all the forwarding paths. If

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only one forwarding path is changed, the messagedelivery probability is only slightly changed. Finally,the fraction of vehicles which change their trajectoriesis usually small.

APPENDIX FFUTURE WORK

We will carry our future work by investigating theprivacy issue that may arise in our approach. Thetrajectory of a vehicle may disclose some sensitiveprivacy information of the vehicle driver. The cur-rent design does not consider the privacy issue insharing vehicular trajectories. We will study privacyprotection for individual trajectory in future work.Possible solutions include anonymization of vehicletrajectories [40] and restricted sharing among autho-rized vehicles [41].