Travel Prediction-based Data Forwarding for Sparse Vehicular Networks. Technical Report

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1 Trvel Prediction-sed Dt Forwrding for Sprse Vehiculr Networks Technicl Report Deprtment of Computer Science nd Engineering University of Minnesot Keller Hll 200 Union Street SE Minnepolis, MN USA TR Trvel Prediction-sed Dt Forwrding for Sprse Vehiculr Networks Fulong Xu, Shuo Guo, Jehoon Jeong, Yu Gu, Qing Co, Ming Liu, nd Tin He July 28, 2011

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3 Trvel Prediction-sed Dt Forwrding for Sprse Vehiculr Networks Fulong Xu, Shuo Guo, Jehoon Jeong, Yu Gu, Qing Co, Ming Liu nd Tin He Deprtment of Computer Science & Engineering, University of Minnesot, USA Singpore University of Technology nd Design, Singpore Deprtment of Electricl Engineering & Computer Science, University of Tennessee, USA Deprtment of Computer Science & Engineering, University of Electronic Science nd Technology of Chin, Chin Astrct Vehiculr Ad Hoc Networks (VANETs) represent promising technologies of cyer-physicl systems for improving driving sfety nd communiction moility. Due to the highly dynmic driving ptterns of vehicles, effective pcket forwrding, especilly for time sensitive dt, hs een chllenging reserch prolem. Previous works forwrd dt pckets mostly utilizing sttisticl informtion out rod network trffic, which ecomes much less ccurte when vehicles trvel in sprse network s highly dynmic trffic introduces lrge vrince for these sttistics. With the populrity of on-ord GPS nvigtion systems, individul vehicle trjectories ecome ville nd cn e utilized for removing the uncertinty in rod trffic sttistics nd improve the performnce of the dt forwrding in VANETs.. In this pper, we propose Trvel Prediction sed Dt-forwrding (), in which vehicles shre their trjectory informtion to chieve the low dely nd high reliility of dt delivery in multi-hop crry-nd-forwrd environments. The driven ide is to construct vehicle encounter grph sed on pir-wise encounter proilities, derived from shred trjectory informtion. With the encounter grph ville, optimizes delivery dely under specific delivery rtio threshold, nd the dt forwrding rule is tht vehicle crrying pckets lwys selects the next pcket-crrier tht cn provide the est forwrding performnce within the communiction rnge. Through extensive simultions we demonstrte tht significntly outperforms existing schemes of nd with more thn 5% more pckets delivery while reducing more thn 40% delivery dely. I. INTRODUCTION Vehiculr Ad Hoc Networks(VANETs) hve emerged s one of the most promising cyer-physicl system pplictions to improve trnsporttion sfety nd efficiency [1] [5]. As n importnt component of Intelligent Trnsporttion Systems (ITS) [6], [7], it promises wide rnge of vlule pplictions including reltime trffic estimtion for trip plnning, moile Internet ccess, nd in-time dissemintion of emergency informtion such s ccidents nd wether hzrds. In this pper, we focus on the multi-hop dt forwrding prolem in VANET. In dynmic nd moile vehiculr networks, most of the dt forwrding schemes dopt the crry-nd-forwrd pproch, where vehicle crries messges temporrily until it cn rely its messges to etter next-hop vehicle using Dedicted Short Rnge Communictions (DSRC) [7], [8]. The existing protocols, such s [2] nd SADV [9], utilize mcroscopic informtion out rod network trffic (e.g., trffic density nd rod section verge speed) to guide forwrding opertion mong vehicles. This type of forwrding protocols is very effective in dense vehiculr networks where sttistics re reltively stle nd insensitive to individul vehicle s ehvior. However, it ecomes less roust when vehiculr network ecomes sprse nd unpredictle. Fortuntely, with wide doption of the GPS for nvigtion, we cn now esily otin vehiculr trjectories in the physicl world, which significntly reduces the uncertinty of multi-hop dt forwrding in sprse vehiculr network. A few recent protocols, such s [10] nd TSF [11], hve demonstrted promising performnce results y comining the physicl trjectory informtion of source vehicle nd trffic sttistics in the rest of network. Although literture is encourging till now, we found there re still rooms to improve significntly. The mjor issue out previous work such s nd TSF is tht vehicles did not fully shre nd utilize trjectory informtion ville in the network. In other words, individul vehicle only knows its own trjectory nd does not shre with other vehicles, constrining fctor leding to low performnce. Therefore, the chllenging question ddressed in this work is how we cn push performnce limits y utilizing ll trjectories ville. In this pper, we propose Trvel Prediction sed Dt forwrding () scheme, which ims t providing effective vehicle-tovehicle(v2v) communiction over multi-hops in sprse vehiculr networks. is uilt upon the concept of prticiptory services in which users of service (e.g., dt forwrding service) shre their informtion (e.g., trjectory) to estlish the service. The privcy-sensitive users cn opt out, while prticiptory users cn exchnge privcy for convenience nd performnce. The min ide of is to utilize shred trjectory informtion to predict pir-wise encounters nd then construct n encounter grph to support end-to-end dt forwrding. Bsed on the encounter grph, optimizes the forwrding sequence to chieve the miniml delivery dely given specific delivery rtio threshold. The optiml forwrding metrics llow the vehicle to lwys forwrd pckets to the vehicle in its communiction rnge tht is expected to provide the est forwrding performnce. With microscopic informtion out individul trjectories ville, cn chieve much more effective dt forwrding performnce in terms of dely nd delivery rtio thn the ones tht lrgely depend on rod trffic sttistics. Specificlly, our intellectul contriutions re s follows: To the est of our knowledge, is the first ttempt to design the dt forwrding for VANETs with the shred trjectory informtion, tightly couples informtion from oth physicl nd cyer world. We design novel sttistic method to construct vehicle encounter grph, which effectively reduces uncertinty in sprse vehiculr network. We optimize the predicted encounter grph using dynmic progrmming to chieve low delivery dely under the

4 required delivery rtio. With online forwrding, our design is roust to the trjectory chnge of individul vehicles. II. MODEL AND ASSUMPTIONS Our work is to design n effective dt forwrding scheme in sprse vehiculr networks sed on the following ssumptions: Vehicles re instlled with GPS-sed nvigtion system nd digitl rod mps. Trffic sttistics, such s the men nd vrince of the trvel time for ech rod section, re ville vi commercil nvigtion service [12]. A vehicle s trjectory, defined s the moving pth from the vehicle s strting position to its destintion position in rod network, is lso ville for shring when this vehicle decides to prticipte dt forwrding service. Populr crowdsource trffic nd nvigtion pplictions such s Wze [13], TomTom Crowdsourcing[14] nd icrtel [15] hve ttrcted millions of voluntry users nd support the feture of trjectory shring mong ppliction users. Further, we ssume such shred trjectory informtion cn e inccurte nd smll percentge of trjectories (e.g. less 20%) re suject to chnge fter shring. Access points (APs) re deployed t the entrnces nd rodside of rod network sprsely. They re inter-connected nd disseminte rjectory informtion of moving vehicles. With the recent developments in ITS, it hs een prcticl to instll Rodside Units(RSUs) t intersections, which communicte with On-Bord Units (OBUs) crried on vehicles for vrious purposes such s driving sfety nd electronic fee collection [7], [16]. We propose tht such RSUs cn e used s APs, which my collect trjectory nd current loction informtion from vehicles, nd lso llow vehicles to downlod the ltest trjectory informtion of others. The overhed nd dely for downloding vehicle trjectories re very limited. Assume one vehicle s trjectory size is 200 ytes (it contins the vehicle s strting time, strting loction nd series of intersections it will pss), nd the dt trnsmission rte from n AP to vehicle is 10 Mps, so the downloding of the shred trjectory informtion from n AP is very fst (i.e., the time to downlod100 trjectories is less thn 20 ms). The Vehicle-to-Vehicle communiction supported y opertes in prticiptory mnner. A vehicle is llowed to otin the V2V communiction service, only when this vehicle shres its trjectory informtion with other prticipted vehicles. Pckets re forwrded only mong prticipted vehicles. For now, we ssume the prticipted vehicles re willing to scrifice certin level of privcy in exchnge of the service. Advnced designs with enhnced privcy nd security re left s future work. III. ENCOUNTERING PREDICTION AND CONSTRUCTING A PREDICTED ENCOUNTER GRAPH Our sic ide is sed on vehiculr encounter prediction. From the trjectory informtion with certin precision, lthough it is difficult to ccurtely predict the encounter of two vehicles trveling in the sme direction, it is typiclly esier to decide the encountering proility of the two vehicles trveling in opposite directions. After we derive sufficient knowledge on vehicle encounters, we schedule messge trnsmissions so tht 3 c Fig. 1. Dt forwrding through predicted encountered vehicles messge goes from the source to the destintion hop y hop sed on our encounter prediction. Figure 1 shows n exmple of this ide, in which, V is predicted to encounter V t rod section L 12 (etween the intersection n 1 nd n 2 ) nd V is predicted to encounter V c t rod section L 34. Then, pckets generted y V nd destined to V c cn e forwrded through the encountered vehicles pth : V V V c. In the following sections, sed on this ide, we will explin this design in more detil. As the foundtion of our protocol, this section introduces how to clculte the encounter proility etween vehicles, nd further how to construct predicted encounter grph sed on proilistic encounter events. A. Trvel Time Prediction 1) Trvel Time through Rod Section: Reserchers on trnsporttion hve demonstrted tht the trvel time of one vehicle over fixed distnce follows the Gmm distriution [11] [17]. Therefore, the trvel time through rod section i in the rod network is modeled s: d i Γ (κ i, θ i ). d i is lso clled link dely for rod section i. To clculte the prmeters κ i nd θ i, we use the men nd the vrince of the link dely, which re the trffic sttisticl informtion (provided y commercil service provider). Let the men of d i e E[d i ] = µ i, the vrince of d i e V r[d i ] = σ 2 i, the formuls for κ i nd θ i re s follows: θ i = V r[d i] E[d i ] κ i = E[d i] θ i 5 = σ2 i µ i (1) = µ2 i σ 2 i 2) Trvel Time on n End-to-End Pth: Here we model the end-to-end trvel dely from one position to nother position in given rod network. As discussed ove, the link dely is modeled s the Gmm distriution of d i Γ (κ i, θ i ) for rod section i. Given specific trveling pth, we ssume the link delys of different rod sections for the pth re independent. Under this ssumption, the men nd vrince of the end-to-end trvel dely re computed s the sum of the mens nd the vrinces of the link delys tht the end-to-end pth consists of. Assuming tht the trveling pth consists of N rod sections, the men nd vrince of the end-to-end pcket dely distriution cn e computed s follows: i=1 (2) N N E[P] = E[d i ] = µ i (3) i=1 i=1 N N V r[p] = V r[d i ] = σi 2 (4) With(3) nd(4), the end-to-end pcket dely distriution cn e modeled s P Γ (κ p, θ p ) nd the κ p, nd θ p cn e clculted using E[P] nd V r[p]. i=1

5 l encounter position 1 2 Fig. 2. Vehicle nd will encounter t rod section L 12 B. Encounter Event Prediction 1) Encounter Proility etween Vehicles: Bsed on the trvel time prediction, the encounter event etween two vehicles cn e predicted. In Figure 2, suppose vehicle V nd V s trjectories overlp t rod section L 12 tht joins intersections n 1 nd n 2. V will trvel through L 12 from n 1 to n 2, while V will trvel through L 21 from n 2 to n 1. Assuming the initil time s 0, let T 1 nd T 2 e the time when V moves pst n 1 nd n 2, respectively. Let T 1 nd T 2 e the time when V moves pst n 1 nd n 2, respectively. The proility tht they will encounter ech other on this rod section: P(V 12 V ) = P(T 1 T 1 T 2 T 2 ) (5) where the 12 mens encountering t rod section L 12. As discussed ove, T 1, T 1, T 2, T 2 re stochstic vriles following the Gmm distriution. It s cler tht T 1 nd T 2 re not independent, nd T 1 nd T 2 re not independent, either. To clculte (5), they hve the following reltionship: T 2 = T 1 + t 12 (6) T 2 = T 1 t 21 (7) where t 12 is the sttistic men trvel time through L 12 from n 1 to n 2 ; t 21 is the sttistic men trvel time through L 21 from n 2 to n 1. Replce T 2 nd T 2 in (5) y (6) nd (7), we get: P(V 12 V ) = P(T 1 T 1 T 1 + t 12 + t 21 ) (8) Let f(x) nd g(y) represent the proility density function of stochstic vriles T 1 nd T 1 respectively. Becuse T 1 nd T 1 re independent, we hve: P(V 12 V ) = x+t12+t 21 0 x f(x)g(y)dydx. (9) So fr we hve discussed how to clculte the encounter proility in one rod section. If the trjectories of two vehicles overlp y more thn one rod section, we cn still clculte the overll proility y treting these djcent overlpping rods s long one. 2) Conditionl Encounter Proility Clcultion in Multihop Encounter Prediction: Dt forwrding through multi-hops of encountered vehicles should use the conditionl proility clcultion. Let s get ck to Figure 1. As discussed erlier, if vehicle V wnts to send dt to V c, it should trnsmit pckets to V when they encounter, so tht when V meets V c, pckets could e trnsmitted to V c. The success proility of this forwrding process is s follows: P(V 12 V V 34 V c ) = P(V 12 V )P(V 34 V c V 12 V ) (10) Becuse the encounteretween V nd V ffects the encounter proility etween V nd V c, the two events V 12 V nd V 34 V c re not independent, therefore: P(V 34 V c V 12 V ) P(V 34 V c ) (11) It s difficult to clculte P(V 34 V c V 12 V ). However, n pproximte vlue cn e otined s follows: we first clculte the conditionl expecttion of V s pssing time through intersection n 1 (it s the outlet intersection tht V would pss fter the encountering with V in rod L 12 ), under the condition tht V encounters V t the rod section L 12. It s indicted y E(T 1 V 12 V ). Then the pproximte vlue of P(V 34 V c V 12 V ) cn e otined y clculting P(V 34 V c ) using the method in the previous susection with the precondition tht V strts its trveling from n 1 t time E(T 1 V 12 V ). The formul to clculte E(T 1 V 12 V ) is: E(T 1 V 12 V ) = h(y V 12 V )ydy (12) where h(y V 12 V ) is the conditionl proility density function of T 1 under the condition tht (V 12 V ). It cn e esily deduced. C. Constructing Predicted Encounter Grph To forwrd pckets through predicted encounter vehicles, we construct predicted encounter grph sed on these proilistic encounters. We first discuss how to clculte the expecttion of two vehicles encounter time. 1) Expecttion of Encounter Time: We cn lso clculte the expecttion of the encounter time etween two vehicles. The expecttion of encounter time is used in the process of constructing the predicted encounter grph. Let s get ck to see Figure 2, which still illustrtes the possile encounter etween V nd V t rod L 12. Suppose the encounter position is l meters wy from n 1, the men trvel speed from n 1 to n 2 is v 12, the men trvel speed from n 2 to n 1 is v 21, nd the encounter time is T, we hve: therefore: l = (T T 1 )v 12 = (T 1 T)v 21 (13) T = T 1v 12 + T 1 v 21 v 12 + v 21. (14) Formul 14 shows T is function of T 1 nd T 1. As T 1 nd T 1 re independent stochstic vriles, the expecttion of the encounter loction is: E(T V 12 V ) = T(x, y)h (x, y V 12 V )dxdy (15) Where h (x, y V 12 V ) is the joint conditionl density function of T 1 nd T 1 under the condition tht (V 12 V ). 2) Constructing the Predicted Encounter Grph: The predicted encounter grph is directed grph tht origintes from the source vehicle tht intends to forwrd pckets, nd ends t the forwrding destintion, which could e moving vehicle or fixed point t rodside. Ech node in this grph denotes vehicle. For convenience, oth node nd vehicle re used to refer to node in the grph. For node e, its child nodes re the vehicles it might encounter lter fter its prent vehicle. These child nodes re sorted in the sequence of their expected encounter time with node e. Tht is, if the expecttions of the encounter time etween node e nd its n child nodes stisfy t 1 t 2 t n, these child nodes re sorted in the sequence C t1, C t2,, C tn, where C ti (i [1, n]) is the child whose expected encounter time with node e is t i.

6 Queue: Grph: 3 Queue: Grph: c (4) d s1 c (1) 1 2 s 4 5 Fig. 3. Vehicles trvel in the rod network Queue: d Queue: c d Queue: Grph: c Grph: s2 s1 (5) d (2) Queue: Grph: Grph: (3) 6 7 Queue: Grph: c c s (6) (7) Fig. 4. construction of the predicted encounter grph The construction of predicted encounter grph is process of expnding the grph y dding new nodes into it one y one. The expnsion is performed ccording to the sequence of the expected encounter time. Tht is, when dding node into the grph, ech node denoting possile encounter event tht would hve hppened erlier thn the current node should hve een lredy hndled nd inserted into the grph. We use n ssistnt ordered queue Q to implement it. The lgorithm is represented s follows: 1) Generte the root node nd insert it into Q. The root node is the source vehicle tht hs pckets to forwrd; 2) Tke out the first node (denoted y node e here) in Q; 3) Clculte node e s child nodes using the trjectory informtion. Tht is, predict the possile encounters during its following trvel nd get its child nodes. Insert the child nodes into Q, if the expected encounter time is erlier thn TTL (Time-To-Live).Note tht ll the nodesin Q re sorted in the order of the expected time of encountering with their own prents. 4) If node e is the root node, it s the first node in the grph; otherwise, dd node e into the grph y inserting it into its prent s child-list. The nodes in the child-list re lso ordered y the expected encounter time, s stted ove. 5) If Q is not empty, go to step 2; otherwise the construction process finishes. We illustrte the construction process through n exmple. In Figure 3,,,c nd d re four vehicles in the network nd nodes from 1 to 7 re rod network intersections. For demonstrtion purpose, in Figure 3, the fixed point s t rodside is selected s the pcket destintion. In fct, the destintion could e simply replced y moving vehicle. Assuming vehicle V intends to forwrd pckets to the fixed node s. Firstly the root node is inserted into Q, s shown in Figure 4(1). When we move the node out of Q, the possile encounter vehicles V nd V d re predicted. Therefore node nd node d re inserted into Q s1 d d s d ccording to the expected encounter sequence, s shown in Figure 4(2). Figure 4(3) shows tht when the first node in Q is tken out,it spredictedthtnode couldencountervehicle V c (underthe condition tht V encounters V first). So node c is inserted into Q nd then node is dded into the grph. Suppose the expected encounter time etween V nd V c is erlier thn the encounter etween V nd V d, node c is hed of d in Q. Figure 4(4) shows the result when node c is out of Q. Note tht the node s 1 in Q indictes tht the destintion node s would e encountered y node c. We differentite the destintion nodes in Q ecuse it cn differentite the trnsmission dely of different pths. When node d is tken out of Q, its child node s 2 is inserted into Q. Node s 2 is inserted hed of s 1 ecuse it s predicted tht V d encounters destintion s erlier thn V c, s shown in Figure 4(5). Figure 4(6) nd 4(7) show tht in the grph, two links emitting from node d nd node c re pointed to the destintion node sequentilly. When forwrding pckets in high trffic density rod network, the grph construction might tke some time. Some useful methods cn e used to reduce the time, i.e., we cn limit the serch zone, nd only the encounters within the geogrphicl zone re predicted nd dopted; we cn lso delete the nodes in the grph, if the product of the encounter proilities from it up to root is smller thn threshold. More importntly, in the next section we will see tht, the expnsion process of the grph will finish erlier when it chieves the requested delivery rtio ound. IV. TRAVEL PREDICTION BASED DATA FORWARDING SCHEME Like otherschemessuchs nd, our employs theunicst strtegy.tht iswe onlykeeponecopyofthe messge in the network. After constructing the predicted encounter grph, s shown in Figure 4, ech vehicle normlly would encounter multiple other vehicles with different proilities nd different delys during the dt forwrding process. To gurntee the system requirements such s dt delivery proility nd minimize end-to-end(e2e) pcket delivery dely in the network, we discuss how to optimize E2E messge delivery dely under specific delivery rtio threshold y only selecting suset of encountered vehicles for dt delivery. A. Clculting Expected Delivery Rtio (EDR) For ech node in the encounter grph, ll of its children tht hve pth to the destintion node re potentil next-hop forwrders. To send pcket, the vehicle looks up the predicted encounter time nd rod section ssocited with the first vehicle in its forwrding pths, nd expects to encounter it. If this vehicle encounters the first forwrding vehicle successfully t the right rod section, the pcket is trnsmitted, nd the sender no longer needs to crry this pcket. Otherwise, the sender prepres for the encountering with the next vehicle in its forwrding pths nd tries to send the pcket gin. This trnsmission process over single hop continues until the sender hs successfully sent the pcket to one of the forwrding vehicles or the sender reches the end of ll its forwrding vehicles, mening tht the pcket fils to e delivered. In this section, we discuss how to clculte the expected delivery rtio sed on the predicted encounter grph. Let p ei e the encounter proility etween vehicle e nd its i th forwrder in the predicted encounter grph. The overll proility P e (i) tht pcket is trnsmitted y vehicle e to the i th forwrder

7 when they encounter (which mens e fils to encounter with the former i 1 forwrders) cn e represented s: i 1 P e (i) = [ (1 p ej )]p ei. (16) j=1 The expected delivery rtio(edr) of given vehicle e, denoted y EDR e, is the expected pcket delivery rtio from vehicle e to its destintion. Assuming vehicle e hs n children in its predicted encounter grph nd the i th forwrder s EDR vlue is EDR i, we hve the following recursive eqution for EDR e : n EDR e = P e (i)edr i (17) i=1 To clculte the E2E expected delivery rtio t the root node in the predicted encounter grph, recursive process strts from the trget node S. At the trget node S, oviously, EDR S = 1 (i.e., no pcket loss), while EDD S = 0. To clculte EDR for the whole encounter grph, we strt from known initil conditions nd recursively pply Eqution 17. The whole process of clculting EDR vlues propgtes upwrdly from the destintion nodes to the rest of the grph until finlly reches the root node. Fig. 5. EDR Clcultion of Vehicle V To illustrte the whole EDR clcultion process for predicted encounter grph, we show wlkthrough exmple in Figure 5. From Figure 5, vehicle forwrds dt pckets towrd the destintion S through Forwrding Pth-1 (i.e., c S) nd Forwrding Pth-2 (i.e., d S). The weights on the edges in Figure 5 denote the encounter proility etween two connected vehicles. At the initil stte, the EDR S = 1 t the trget node S. Then sed on the Eqution 17, we cn recursively clculte the EDR vlue for vehicles c, d nd, respectively. Finlly for source vehicle, we cn clculte its EDR vlue s: EDR = p EDR + (1 p )p d EDR d = (1 0.9) = B. Optimizing Expected Delivery Dely (EDD) Similr to clculte EDR, we cn lso recursively clculte E2E expected delivery dely from the trget vehicle sed on the predicted encounter grph,. Formlly, we define the expected delivery dely of given vehicle e, denoted y EDD e, s the expected dt delivery dely for the pckets sent y vehicle e nd received y the destintion. EDD is defined sed on the condition tht the pckets re successfully trnsmitted to the destintion. To clculte the EDR vlue of vehicle e, let Q e (i) e the proility tht the pcket trnsmissionis successfult the i th forwrderunderthe constrint tht the pcket is received successfully y the destintion node. Clerly, Q e (i) = Pe(i)EDRi EDR e. Let EDD i e the EDD vluefor the i th forwrder in vehicle e s children nodes, nd d i e the dely (crrying time) for vehicle e to crry the pcket until it encounters forwrder vi e in V n e, then EDD e cn e represented s: EDD e = n Q e (i)(d i + EDD i ). (18) i=1 In order to optimize the expected delivery dely, we oserve tht in vehiculr network, while low delivery dely is preferle, this typiclly requires tht threshold on delivery rtio is mintined t the sme time. In fct, if there is no ound on the expected delivery rtio (EDR), the optiml dely cn e esily chieved y including only single vehicle v j tht hs the minimum (d j + EDD j ) vlue mong ll next-hop potentil encountered vehicles. Becuse the corresponding delivery rtio my e very low, such n optiml solution is not suitle for prcticl pplictions. We will next discuss how to optimize the EDD metric for the node e under the constrint tht the EDR metric is no less thn certin threshold R. As discussed ove, in the process of constructing the encounter grph, when new node is dded into the grph, ll the encounter events which re predicted to hve hppened erlier thn the new node must hve lredy een included. Therefore, in the process of constructing the grph, when the trget node is tken out from the ordered queue Q nd dded into the predicted encounter grph for the first time, the first connected pth from the source vehicle to the trget is found. Becuse of the wy tht this grph is constructed, this pth hs the miniml dely for pcket forwrding. We then clculte the EDR of the root node t the current grph extension. If the EDR vlue is greter thn the required ound R, the construction of the grph stops nd the optiml pth is cquired; otherwise the process of expnding the grph continues until the EDR of the source node stisfies the ound R or the construction is stopped y the TTL constrint. This pproch of optimizing the delivery dely is integrted into the process of constructing the encounter grph. It cn e represented s follows: 1) Intheprocessofconstructingthegrph,whentkingoutthe first node in Q nd dding it into the grph, judge whether this new node is trget node; 2) If the newly dded node is trget node, we use dynmic progrmming pproch(detil in Appendix) to clculte the mximum EDR tht the source node of the grph could chieve with the current grph expnsion; 3) If the clculted EDR is smller thn the requested EDR ound R, go to 1) nd continues; otherwise the process stops, ecuse t the current grph extension, the optiml forwrding pths hve lredy met the requirement of EDR ound R nd t the sme time optiml delivery dely. When the grph extension is over, the EDD vlue of the root vehicle cn e clculted using Eqution 18. Note tht ecuse the optiml forwrding pths re cquired in terms of mximizing the EDRmetric,insomecsestheEDDvluewegetisnotthelowest dely tht meets the EDR ound R (it s hrd to get). However, sed on the chronologicl grph expnsion, the EDD vlue we get is close to the lowest dely.

8 C. Dt Forwrding Process in Dt forwrding in is dynmic process. When the vehicle needs to forwrd pckets, it constructs predicted encounter grph with the desired TTL nd delivery rtio ound R, nd then otins the optiml forwrding pths. Bsiclly, the forwrding cn e guided y this optiml forwrding pths nd then pckets re trnsmitted through the predicted encounter grph. As discussed ove, pckets cn e forwrded to the destintion with the performnce of the root vehicle s EDR nd EDD vlue. Besides the predicted vehicles in it s forwrding pths, it cn meet some other vehicles not in its predicted forwrding pths when the pcket crrier is moving long its trjectory. The resons re: 1) the encountering prediction only considers the cse tht vehicles encounter fce-to-fce. It doesn t include the cse tht two vehicles trvel rod in the sme moving direction (ecuse it s hrd to ccurtely predict), nd 2) there my e missing trjectory informtion mintined y the ccess points, nd some vehicles encountered y the pcket crrier re perhps not in the pcket crrier s trjectory dtse. Therefore, during the trvel time, once the pcket crrier meets other vehicles which re not in its forwrding pths, it first notifies these neighors the destintion it wnts to forwrd pckets to nd the time left for the forwrding (ecuse of the TTL constrint). Ech neighor receives the notifiction, clcultes the EDR nd EDD it could chieve using the method of optimizing dely with the requested EDR ound R, nd replies the result to the pcket crrier. During the trvel, s the EDR nd EDD of the crrier vry with time (i.e., some expected vehicles in its optiml forwrding pths re not ctully encountered, then the EDR nd EDD chnge), pcket crrier should first re-estimte its current EDR nd EDD vlue, nd then compre these vlues with ll its neighors using the following rules to select the est forwrder for pcket trnsmission: If the EDRs of ll the connected vehicles cn not meet the requested ound R, select the vehicle hving the highest EDR s the next-hop forwrder; If there exists the vehicles whose EDRs re greter thn the ound R (EDR R), within these vehicles we select the one which hs the miniml EDD vlue s the next-hop forwrder. For exmple, Figure 6 shows the forwrding protocol. Ech vehicle clcultes its own forwrding metric pir of (EDR, EDD). Using the forwrding rule, whenever the pcket crrier encounters etter forwrder, the pcket forwrding could e improved y (i) incresing the EDR (when the current crrier cnnot meet the requested EDR ound R, s shown in Figure 6()) or (ii) reducing the EDD (when the requested EDR ound R cn e chieved, s shown in Figure 6()). V. PERFORMANCE EVALUATION This section evlutes the performnce of. To our est knowledge, existing well-known protocols do not support multihop unicst etween two moving vehicles. Therefore in evlution, we minly focus on the dt forwrding from moving vehicles to fixed points, enling us to compre with, nd flooding under common settings. It cn e esily chieved for y selecting sttionry vehicles s pcket destintions. We lso compre the performnce of nd i i Prmeter Rod network Communiction rnge Numer of vehicles (N) Time-To-Live Vehicle speed (v) Vehicle trvel pth length (l) Min ville encounter proility Requested EDR ound R node3 node 2 node1 g Communiction Rnge Current Crrier j h node 7 node 6 node9 node8 node 5 node 4 hs the mximum EDR node 4 Next though ny node cnnot stisfy R Crrier () Forwrding to Mximum-EDR Node node3 node 2 node1 node 4 node 5 g Communiction Rnge Current Crrier j h node 6 node 7 Next Crrier node9 node8 node 8 hs the minimum EDD while its EDR is greter thn R () Forwrding to Minimum-EDD Node Fig. 6. Forwrding Protocol TABLE I DEFAULT PARAMETERS Description The numer of intersections is 36. The re of the rod mp is 6.75km 6km R = 200 meters. The numer N of vehicles moving within the rod network. The defult of N is 100. The expirtion time of pcket. The defult T T L is 1000 seconds. v N(µ v, σ v) where µ v = 40 MPH nd σ v = {5, 6,...,10} MPH. The defult of (µ v, σ v) is (40, 7) MPH. Let d u,v e the shortest pth distnce from strt position u to end position v in the rod network. l N(µ l, σ l ) where µ l = d u,v km nd σ l = 3 km. The miniml encounter proility we dopt when constructing the encounter grph. The defult vlue is 0.3. The requested EDR ound the forwrding should chieve. The defult is R=0.9. flooding on the vehicle-to-vehicle dt forwrding. Note tht for flooding, we ssume there is no trnsmission conflict nd vehicles hve infinite uffer to store pckets, sed on which vehicle simply forwrds pckets to every other vehicle it meets. With these ssumptions, the flooding protocol chieves the mximl delivery rtio nd miniml delivery dely. The evlution is sed on the following settings: Performnce Metrics: We use (i) pcket delivery rtio nd (ii) verge delivery dely s the performnce metrics. Prmeters: We investigte the impct of (i) vehicle speed devition, (ii) communiction rnge, nd (iii) vehiculr density. In the simultion rod network with 36 intersections is used, nd one fixed trget point (sttionry vehicle) is locted in the center of the network. Ech vehicle moves from rndomly selected source position to rndomly selected destintion position. The movement pttern is determined y Mnhttn Moility model [18]. Bsed on the chrcteristics of Mnhttn k k

9 1 1 1 Averge Delivery Rtio Averge Delivery Rtio Only through Grph Averge Delivery Rtio Vehicle Speed Devition (MPH) () Delivery Rtio vs. Speed Devition Vehicle Speed Devition (MPH) () Delivery Rtio vs. Speed Devition Communiction Rnge (m) () Delivery Rtio vs. Communiction Rnge Averge Delivery Dely (s) Averge Delivery Dely (s) Only through Grph Averge Delivery Dely (s) Vehicle Speed Devition (MPH) () Delivery Dely vs. Speed Devition Fig. 7. Impct of Speed Devition Vehicle Speed Devition (MPH) () Delivery Dely vs. Speed Devition Fig. 8. Pcket Forwrding through Predicted Grph Communiction Rnge (m) () Delivery Dely vs. Communiction Rnge Fig. 9. Impct of Communiction Rnge Moility, s shown in Tle 1, the vehicle trvel pth length l from strting position u to ending position v is selected from norml distriution N(µ l, σ l ) where µ l is the shortest pth distnce etween these two positions nd σ l determines rndom detour distnce; this rndom detour distnce reflects tht ll of the vehicles do not necessrily tke the shortest pth etween their strting position nd their ending position. After rriving t its driving destintion, vehicle will e deleted; nd t the sme time nother fresh vehicle is generted into the rod network, so the totl numer of vehicles in the rod network is constnt. The vehicle speed follows the norml distriution of N(µ v, σ v ) [19], nd vehicle my chnge its speed t ech rod section. During the simultion, pckets re dynmiclly generted from rndomly selected vehicles in the rod network. The simultion continues until ll of these pckets re either delivered or dropped due to TTL expirtion. Unless otherwise specified, the defult vlues in Tle 1 re used. A. Impct of Vehicle Speed Devition σ v As is trvel prediction-sed, the ccurcy of prediction will ffect its performnce. Intuitively, trffic minly ffects the trveling time, mking the encounters proilistic. In our simultion, for simplicity we use vehicle speed devition to reflect the trffic condition, nd intend to study to wht extent the speed devition could ffect. As shown in Figure 7, for, with greter speed devition, the pcket delivery rtio hs slight decrese, ut the verge dely oviously increses. This is ecuse in, we set the defult vlue of Requested EDR ound R to 0.9. tries to stisfy this EDR ound, nd t the sme time to forwrd pckets through pths with lower dely. In generl, s the vehicle speed devition ecomes lrger, the predicted encounter proilities etween vehicles decrese (our simultion result in Figure 10 verifies this). Therefore, to meet the requested EDR ound, pckets my hve to e forwrded through pths which hve longer delys. Comprtively, other protocols re slightly ffected y speed devition. However, even when the speed devition is s lrge s 10 MPH, still outperforms nd significntly in terms of oth delivery rtio nd dely, nd is closer to the performnce of flooding. As discussed erlier, flooding chieves the theoreticl mximl delivery rtio nd miniml dely in the network with the ssumptions of infinite uffer nd collision-free trnsmission. These ssumptions, however, re not resonle in relity due to hrdwre nd cost issues, so flooding is hrd to work in rel life. Generlly, for different protocols, if more informtion is used, etter performnce could e chieved. Since utilizes more informtion thn y llowing vehicle employing its own trjectory for dt forwrding, it performs etter thn. In, we tke step further nd dopt more trjectories thn, using the optimized encounter prediction s guidnce so tht pckets cn e forwrded through etter pths to destintions. Our simultion results indicte tht utilizing more informtion indeed chieves etter performnce. To further lern the impct of the speed devition on, nother experiment is performed, in which pcket cn only e forwrded to its destintion through the source vehicle s predicted encounter grph. In Figure 8 we find tht, for the dt forwrding only through the encounter grph, oth the delivery rtio nd the delivery dely re oviously ffected y the vehicle speed devition. Becuse cn forwrd pckets through more vehicles with etter performnce metrics, the impct of the speed devition on the delivery rtio of is reltively less. B. Impct of Communiction Rnge The Figure 9 shows the impct of communiction rnge on the performnce. As expected, when the communiction rnge is lrger, the pcket delivery rtio of ll the protocols increses, nd the verge delivery dely decreses. This is ecuse with lrger communiction rnge, vehicle hs more opportunities to meet other vehicles in the rod network, therefore pckets hve more

10 1 1 1 Averge Delivery Rtio Averge Delivery Rtio Averge Delivery Rtio Numer of Vehicles () Delivery Rtio vs. Vehicle Numer Communiction Rnge (m) () Delivery Rtio vs. Communiction Rnge Percent of vehicles chnging trjectory(%) () Delivery Rtio vs. Chnging Percentge Averge Delivery Dely (s) Numer of Vehicles () Delivery Dely vs. Vehicle Numer Averge Delivery Dely (s) Communiction Rnge (m) () Delivery Dely vs. Communiction Rnge Averge Delivery Dely (s) Percent of vehicles chnging trjectory(%) () Delivery Dely vs. Chnging Percentge Fig. 11. Impct of Vehicle Numer Fig. 12. Pcket Forwrding from Vehicle to Vehicle Fig. 13. Pcket Forwrding with Trjectory chnge Averge Encounter Proility Vehicle Speed Devition (MPH) Fig. 10. Averge Predicted Encounter Pro vs. Speed Devition opportunities to e forwrded to destintions. For the sme reson, the crrying time of pckets is lso reduced. With the lrgest communiction rnges (300 m), the performnces of nd re close to. However, when the communiction rnge reduces to 100 m, the performnce of nd decrese hevily, while chieves delivery rtio of 93.7% with low verge dely (315 s). The results show tht esides sttisticl trffic informtion, if detiled trveling informtion of individul vehicles cn e employed, pcket forwrding could e more ccurte nd effective. C. Impct of Vehiculr Density The vehiculr density cn e expressed y the numer of vehicles in the network. We investigte the effectiveness of under different vehiculr densities y incresing the vehicle numer from 60 to 140. As shown in Figure 11, ll of the protocols hve etter performnce in terms of oth delivery rtio nd delivery dely when the density ecomes higher. This is ecuse higher vehiculr density could increse the connectivity mong vehicles nd then promote the dt forwrding in the network. We lso find tht, with different densities lwys performs etter thn nd. Especilly, when the vehicle density is low, still chieves good performnce (e.g., when vehicle numer is 60, its delivery rtio is 90% nd dely is 346 s), which is much etter thn nd. Since the microscopic trjectory informtion provides more ccurte knowledge thn sttistics, is more suitle for dt forwrding thn nd in sprse vehiculr networks. D. Dt Forwrding from Vehicle to Vehicle Now we show the vehicle-to-vehicle dt forwrding performnce of. Becuse the trgets re moving, it s comprtively more chllenging for oth trget loction nd next-hop selection. As no other protocol is found for vehicle-to-vehicle communiction through multi-hops, we only compre with flooding under different communiction rnges. Note tht in our simultion the vehicle tht rrives t its destintion will e deleted, so we only select the moving vehicles whose following trvel time is longer thn 1000 s s dt destintions. As shown in Figure 12, lrger communiction rnge cn improve the performnce of oth nd flooding. With the defult communiction rnge (200 m), the delivery rtio of is 84.7%, nd its verge delivery dely is s. When the communiction rnge is 300 m, chieves higher delivery rtio of 90.3% with the verge dely of s. VI. DISCUSSION As trjectory informtion plys n importnt role tht directly ffects the fesiility nd effectiveness of, we discuss in this section numer of prcticl issues ssocited with the process of shring trjectory informtion, including communiction overhed, trjectory chnge, nd the use of APs. A. Roustness ginst Trjectory Chnge In rel driving process, trvel trjectory would e temporrily chnged for mny resons. If vehicle chnges its trjectory without disseminting it in time, other vehicles tht re clculted (sed on the old trjectory informtion) to meet this vehicle will definitely miss it. To see how roust our is ginst

11 Flooding s Overhed / s Overhed Dt Pcket Size (KB) Fig. 14. Rtio of Flooding s Communiction Overhed to s Communiction Overhed vs. Dt Pcket Size trjectory chnge, n experiment is performed in which certin percentge of vehicles chnge their trvel route silently. As shown in Figure 13, the performnce of in terms of oth delivery rtio nd delivery dely decreses s more vehicles chnge their trjectories. However, even when 15% of totl vehicles chnge routes, still chieves shorter delivery dely nd similr delivery rtio compred with nd. In, since pre-clculted forwrding sequence contins mny forwrders, if one forwrder is missed ecuse of trjectory chnge, the forwrding would not e ffected hevily ecuse pckets could e trnsmitted through the following forwrders. In ddition, the dt forwrding of could utilize other vehicles not in the forwrding sequence during trvel, which lso wekens the impct of trjectory chnge. Figure 13 lso shows tht nd re less sensitive to the trjectory chnges. B. Communiction Overhed We discuss the communiction overhed of cused y cquiring the trjectory informtion. Since the verge frequency tht vehicle meets n AP cn e otined through sttistics (it is ctully decided y the density nd the deployment of APs), this overhed cn e esily clculted. With defult prmeters, we simulte the dt forwrding process nd compre the communiction overhed etween nd flooding, which diffuses pckets in n immoderte wy. Since different pplictions require different dt pcket sizes, we first estimte the communiction overheds of nd flooding with different dt pcket sizes. In this experiment, 2500 pckets re forwrded within 60 minutes, nd the result is shown in Figure 14. As we cn see, when the dt pcket size is only 1 KB, the communiction overhed of flooding is 3 times more thn tht of. With lrger pcket size, the increse of flooding s communiction overhed is much greter thn tht of s, so the rtio of flooding s overhed to s overhed increses. It mens tht hs greter dvntge thn flooding in term of trnsmission overhed for pplictions requiring lrger dt pcket (i.e., multimedi pplictions). Considering the different complexity of implementtion nd communiction overheds etween this two protocols, when the dt pcket size is igger thn 8 KB, is etter thn flooding for dt forwrding ecuse of its competitive low communiction overhed (less thn 10% of flooding s overhed); otherwise if the pcket size is smller thn 8 KB, flooding could lso e selected ecuse it is simple to implement, while its overhed is cceptle. C. Using APs to Form Wormhole Bckone In our sic design, APs re used to provide only trjectory informtion to vehicles, nd the dt forwrding is done exclusively through vehicles. In prctice, APs re interconnected with fst cles, creting shortcuts in crry-nd-forwrd vehiculr network. We cn consider the interconnections etween APs s wormhole ckone, which cn e used to expedite vehiculr-tovehiculr delivery process. If we remodel the topology of rod network with zero-dely rod sections etween APs nd model ech AP s sttionry vehicle, the design cn e used without modifiction. For evlution purpose, we intentionlly do not llow APs to involve in the dt forwrding in order to show the effectiveness of the vehicle trjectory shring t the microlevel. We expect improved performnce cn e chieved with APs involvement in dt forwrding. VII. RELATED WORK The reserch on vehiculr networks hs ecome populr in terms of driving sfety, efficient trveling, nd the dt service through infrstructure [2] [5], [20] [22]. In vehiculr networks, the dt forwrding is key function for the communictions etween vehicles or etween vehicle nd infrstructure. It cn tke dvntge of the following two types of informtion: (i) Mcroscopic informtion out rod network trffic sttistics (e.g., trffic density nd rod section verge speed), nd (ii) Microscopic informtion out individul vehicle (e.g., vehiculr trjectory). This informtion mke it possile to design new dt forwrding schemes. New dt forwrding schemes hve een recently developed for multi-hop vehicle-to-infrstructure communictions. investigtes the dt forwrding using stochstic model sed on vehiculr trffic sttistics. The ojective is to chieve the lowest delivery dely from moile vehicle to sttionry destintion. Dely-Bounded Routing hs the ojective to stisfy the userdefined dely ound. Also, this scheme pursues the minimiztion of the chnnel utiliztion. SADV[9] is forwrding scheme sed on sttionry nodes, it cn provide more stle, expected dt delivery dely using the sttionry nodes., Dely-Bounded Routing, nd SADV re using the mcroscopic informtion out the rod network trffic. With the microscopic informtion out vehiculr trjectory, we developed [10] for more efficient dt forwrding. cn compute forwrding metric (i.e., expected End-to-End dely) with oth vehiculr trffic sttistics nd vehicle trjectory informtion, nd further improve communiction dely nd delivery proility y selecting the est next-pcket crrier with the smllest metric vlue mong neighor vehicles. is lso the dt forwrding scheme for vehicle-to-sttic-destintion communictions. For the reverse dt forwrding, such s multi-hop infrstructure-to-vehicle communictions, we took step further with TSF [11]. TSF cn provide n efficient solution for forwrding messges from fixed point (i.e., AP) to moile node (i.e., vehicle) using the destintion vehicle s trjectory. TSF selects pcket destintion point on the rod network long the destintion vehicle s trjectory, considering the rendezvous proility of the pcket nd the destintion vehicle. However, TSF needs dditionl sttionry nodes t intersections in rod networks s pcket uffer to reduce the delivery dely vrince. Unlike the dt forwrding scheme mentioned so fr, in this pper we tke in-depth usge of shred trjectory informtion, which mkes the effective pcket forwrding for the multi-hop vehicle-to-vehicle communictions in sprse VANETs. Note tht

12 is totlly different from nd TSF in the forwrding design, lthough ll of them tke dvntge of microscopic informtion out vehiculr trjectory. As is known, enhnces the vehicle-to-infrstructure communictions y employing vehicles own trjectories, which is sed on the protocol; TSF supports infrstructure-to-vehicle communictions using the destintion vehicle s trjectory, nd it is chieved with the help of sttionry nodes deployed t ech intersection. For our, dt forwrding is performed sed on the prediction of encounters etween vehicles, which works in n prticiptory mnner to shre trjectories etween vehicles. VIII. CONCLUSION It is widely elieved tht vehiculr networks cn ring gret enefit to driving sfety nd mny prcticl pplictions. For the dt forwrding in VANETs, existing protocols minly tke dvntge of mcroscopic informtion out rod trffic sttistics nd chieve effective performnces in dense networks. However, when the vehiculr network ecomes sprse, the trffic sttistics ecome unrelile nd re sensitive to individul vehicle s trveling, thus the performnces of these protocols re ffected. To ddress this prolem, we dopt informtion out vehiculr trjectories nd propose trvel prediction-sed dt forwrding scheme () for multi-hop communictions etween vehicles in sprse VANETs. Different from nd TSF which use only vehicles own trjectories, utilizes the shred trjectory informtion in prticiptory mnner, which cn overcome the uncertinty of sttistics nd mke the forwrding more ccurte. predicts the encountering events etween vehicles nd constructs predicted encounter grph. With the dynmic expnsion of encounter grph, optimizes the forwrding sequences in terms of delivery rtio nd delivery dely, nd guides dt forwrding y llowing vehicles to lwys forwrd pckets to the est forwrder in communiction rnge. Simultion results demonstrte the effectiveness of. Since our current work minly concerns on the dt forwrding prolem, the privcy issue cused y shring trjectories with pulic hs not een ddressed. As future work, we will consider this issue nd design n dvnced protocol which cn provide etter security nd privcy-protection. REFERENCES [1] Q. Xu, R. Sengupt, nd D. Jing, Design nd Anlysis of Highwy Sfety Communiction Protocol in 5.9 GHz Dedicted Short Rnge Communiction Spectrum, in VTC. IEEE, Apr [2] J. Zho nd G. Co, : Vehicle-Assisted Dt Delivery in Vehiculr Ad Hoc Networks, IEEE Trnsctions on Vehiculr Technology, vol. 57, no. 3, pp , My [3] A. Skordylis nd N. Trigoni, Dely-ounded Routing in Vehiculr Ad-hoc Networks, in MOBIHOC. ACM, My [4] J. Ott nd D. Kutscher, Drive-thru Internet: IEEE For Automoile Users, in INFOCOM. IEEE, Mr [5] J. Eriksson, H. Blkrishnn, nd S. Mdden, Cernet: Vehiculr Content Delivery Using WiFi, in MOBICOM. ACM, Sep [6] Reserch nd I. T. A. (RITA), IntelliDrive: Sfer, Smrter nd Greener, [7] ETSI DSRC, [8] A. Crter, The Sttus of Vehicle-to-Vehicle Communiction s Mens of Improving Crsh Prevention Performnce, Tech. Rep , 2005, [9] Y. Ding, C. Wng, nd L. Xio, A Sttic-Node Assisted Adptive Routing Protocol in Vehiculr Networks, in VANET. ACM, Sep [10] J. Jeong, S. Guo, Y. Gu, T. He, nd D. Du, : Trjectory-Bsed Dt Forwrding for Light-Trffic Vehiculr Networks, in ICDCS. IEEE, Jun [11] J. Jeong, S. Guo, Y. Gu, T. He, nd D. Du, TSF: Trjectory-sed Sttisticl Forwrding for Infrstructure-to-Vehicle Dt Delivery in Vehiculr Networks, in ICDCS. IEEE, Jun [12] Grmin Ltd., Grmin Trffic, [13] Wze, [14] TOMTOM, [15] icrtel, [16] T. M. C. (TMC), TMC Develops Onord DSRC Unit to Improve Trffic Sfety, [17] A. Polus, A Study of Trvel Time nd Reliility on Arteril Routes, Trnsporttion, vol. 8, no. 2, pp , Jun [18] F. Bi, N. Sdgopn, nd A. Helmy, IMPORTANT: A frmework to systemticlly nlyze the Impct of Moility on Performnce of RouTing protocols for Adhoc NeTworks, in INFOCOM. IEEE, Mr [19] D. S. Berry nd D. M. Belmont, Distriution of Vehicle Speeds nd Trvel Times, in Proceedings of the Second Berkeley Symposium on Mthemticl Sttistics nd Proility, Jul [20] H. Wu, R. Fujimoto, R. Guensler, nd M. Hunter, MDDV: A Moility- Centric Dt Dissemintion Algorithm for Vehiculr Networks, in VANET. ACM, Oct [21] V. Numov nd T. R. Gross, Connectivity-Awre Routing (CAR) in Vehiculr Ad Hoc Networks, in INFOCOM. IEEE, My [22] P. Rodriguez, R. Chkrvorty, J. Chesterfield, I. Prtt, nd S. Bnerjee, MAR: A Commuter Router Infrstructure for the Moile Internet, in MOBISYS. ACM, Jun APPENDIX In this section, we riefly introduce dynmic progrmming pproch to find the optiml forwrding pths within the predicted encounter grph. The sic ide to decide whether child node v i should e included in the forwrding pths cn e descried s judgement. Tht is, when vehicle e crries the pcket nd encounters the forwrder v i, if it does not forwrd the pcket to v i, how mny chnces re left to successfully forwrd the pcket using the ltter forwrders in the predicted encounter grph? Let V o (k) denote the optiml set of forwrding nodes in terms of mximizing EDR from child node set of node e, (v n k+1, v n k+2,, v n ), which is suset of ll child nodes with its lst k forwrders, nd EDR e (V o (k)) denotes the optiml EDR vlue of vehicle e sed on V o (k). Clerly, EDR e (V o (k)) is the mximl EDR vlue the vehicle e cn chieve using its susequence contining the lst k forwrders. Therefore, fter the forwrder v i, the chnces left for pcket forwrding from vehicle e using the lter n i forwrders of V n is EDR e (V o (n i)). If EDR i EDR e (V o (n i)), mening tht vehicle v i cn offer higherexpecteddeliveryrtiothn EDR e (V o (n i)),so v i should eincludedintotheoptimlpthsndthenformsthe V o (n i+1). Using Eqution 17 it s cler tht EDR e (V o (n i + 1)) EDR e (V o (n i)), indictingtht the inclusion of v i increses the EDRvlueofvehicle e.otherwiseif EDR i EDR e (V o (n i)), v i should not e included into V o. Bsed on the judgement, s the lst vehicle v n in the child node set V n is the lst chnce for vehicle e to trnsmit the pcket, so v n must e included in V o. The optimizing process strts ckwrdly from the lst forwrder, judges every forwrder one y one to otin V o. For ech ckwrd ugmenttion of the forwrding sequence, we gurntee the mximum dt delivery rtio of the sequence etween the newly ugmented vehicle nd the lst vehicle. This forwrding sequence, then, serves s n optiml sustructure for ugmenting dditionl forwrders until the process reches the first vehicle in the sequence.