Trajectory Improves Data Delivery in Urban Vehicular Networks

Transcription

1 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS Trajectory Imroves Data Delivery i Urba Vehicular Networks Yami Zhu, Member, IEEE, Yuche Wu, ad Bo Li, Fellow, IEEE Abstract Efficiet data delivery is of great imortace, but highly challegig for vehicular etworks because of frequet etwork disrutio, fast toological chage ad mobility ucertaity. The vehicular trajectory kowledge lays a key role i data delivery. Existig algorithms have largely made redictios o the trajectory with coarse-graied atters such as satial distributio or/ad the iter-meetig time distributio, which has led to oor data delivery erformace. I this aer, we mie the extesive datasets of vehicular traces from two large cities i Chia, i.e., Shaghai ad Shezhe, through coditioal etroy aalysis, we fid that there exists strog satiotemoral regularity with vehicle mobility. By extractig mobility atters from historical vehicular traces, we develo accurate trajectory redictios by usig multile order Markov chais. Based o a aalytical model, we theoretically derive acket delivery robability with redicted trajectories. We the roose routig algorithms takig full advatage of redicted robabilistic vehicular trajectories. Fially, we carry out extesive simulatios based o three large datasets of real GPS vehicular traces, i.e., Shaghai taxi dataset, Shaghai bus dataset ad Shezhe taxi dataset. The coclusive results demostrate that our roosed routig algorithms ca achieve sigificatly higher delivery ratio at lower cost whe comared with existig algorithms. Idex Terms Vehicular etworks, robabilistic trajectory, routig, redictio, Markov chai INTRODUCTION A vehicular etwork is a etwork of vehicles which commuicate with each other via short-rage wireless commuicatios []. Vehicles ca therefore commuicatio with each other either directly whe there meet each other or through multiho trasmissios. Vehicles ca act as owerful sesors ad form mobile sesor etworks [2, 3]. Vehicular etworks have may aealig alicatios, such as drivig safety [4], itelliget trasort [5, 6], ifrastructure moitorig [7, 8]. ad urba moitorig [9]. Today 3G etworks are gettig more ad more oular ad ubiquitous access to 3G is ossible. Movig vehicles ca also commuicate with each other via 3G. The 3G commuicatio has advatage of ubiquitous access ad shorter delay. Comared with multiho iter-vehicle commuicatio, however, commuicatio via 3G has limitatios. First, although 3G commuicatio becomes more ad more cheaer, the cost of 3G commuicatio is still high. I Shaghai, Chia, for examle, the rate of 3G data commuicatio is aroud USD for oly 3 MByte. By cotrast, ad hoc vehicular commuicatio is for free. Secod, the badwidth of iter-vehicle commuicatio, realized through DSRC or 82., ca be higher tha that of 3G. Fially, may real-time alicatios, e.g., emerget message dissemiatio, are time critical ad direct iter-vehicle commuicatios may be more suitable. Efficiet iter-vehicle data delivery is of cetral imortace to vehicular etworks ad such imortace has bee recogized by may existig studies [-6]. I this aer we focus o such vehicular etworks that Mauscrit received o Jue 9, 22, revised o November 28, 22 ad o March 25, 23. Yami Zhu ad Yuche Wu are Shaghai Key Lab of Scalable Comutig ad Systems, ad the Deartmet of Comuter Sciece ad Egieerig at Shaghai Jiao Tog Uiversity. Their s are {yzhu, eaufavor}@sjtu.edu.c. Bo Li is with the Deartmet of Comuter Sciece ad Egieerig at Hog Kog Uiversity of Sciece ad Techology. His is bli@cse.ust.hk. are sarse ad do o assume that all vehicles o the road are member odes of the vehicular etwork. Such sarse vehicular etworks feature ifrequet commuicatio oortuities. Iter-vehicle data delivery may itroduce oeligible delivery latecy because of frequet toology discoectio of a vehicular etwork. Thus, we should stress that the iter-vehicle commuicatio i vehicular etwork are suitable for those alicatios which ca tolerate certai delivery latecy. For examle, i the cotext of urba sesig, vehicles cotiuously collect useful iformatio, such as road traffic coditios ad road closures. A vehicle may sed a query for a secific kid of iformatio ad the oe that has the iformatio should resod the queryig ode with the data. Such commuicatio require multi-ho data delivery i vehicular etworks. Other examles of such alicatios iclude eer-to-eer file sharig, etertaimet, advertisemet, ad file dowloadig. There is a great deal of ucertaity associated with vehicle mobility. Vehicles move at their ow wills. It is difficult, if ot imossible, to gai the comlete kowledge about the vehicular trace of future movemet, i.e., the ositio of the vehicle at a give oit i time. For routig i a vehicular etwork, a relay ode must decide how log a acket should be ket ad which ode a give acket should be forwarded to. Existig study [7, 8] shows that it is ossible to fid a otimal routig ath whe the kowledge of future ode traces is available, which is NP-hard though. However, it is imractical to have rior kowledge about future traces of odes. The kowledge of future vehicular trajectories lays a key role for otimal data delivery. Existig routig algorithms heavily rely o redictio of vehicle mobility. However, they have adoted oly simle mobility atters, such as the satial distributio ad iter-meetig time distributio, which suort coarse-graied redictios of vehicle movemets. Some algorithms [4, 9] assume radom mobility i which vehicles move radomly i a oe sace or a road Digital Object Idetifier.9/TPDS /3/$3. 23 IEEE

2 2 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS etwork. This model is simle but far from the reality. Some other algorithms assume simle mobility atters such as exoetial iter-meetig times ad regular satial distributios. As a result, redictio results based o these simle atters are of limited value to efficiet data delivery i vehicular etworks. I additio, may of existig algorithms igore the fact that liks i a vehicular etwork have uique characteristics [6]. O the oe had, a lik is tyically short-lived. This suggests that the caacity of the lik is limited. Thus, the order for forwardig ackets becomes imortat. O the other had, liks i a desely oulated area may iterfere with each other. This idicates that lik schedulig becomes ecessary. To overcome the limitatios of existig algorithms, this aer rooses a aroach to exloitig the hidde mobility regularity of vehicles to redict future trajectories. By miig the extesive dataset of vehicular traces from more tha 4, taxis i Shaghai, Chia, we show that there is strog satiotemoral regularity with vehicle mobility. More secifically, our results based o coditioal etroy aalysis demostrate that the future trajectory of a vehicle is greatly correlated with its revious trajectory. Thus, we develo multile order Markov chais for redictig future trajectories of vehicles. With the available future trajectories of vehicles, we roose a aalytical model ad theoretically derive the delivery robability of a acket. Sice the otimal routig roblem with give vehicle trajectories is still NP-hard, we develo a efficiet global algorithm for comutig routig aths whe redicted trajectories are available. For more ractical situatios, we develo a fully distributed algorithm which eeds oly localized iformatio. The two algorithms joitly cosider acket schedulig ad lik schedulig. We evaluate the algorithms with extesive trace drive simulatios, based o the trace dataset collected i Shaghai ad Shezhe. The results demostrate that our algorithm cosiderably outerforms other algorithms i terms of delivery robability ad delivery efficiecy. The rest of the aer is orgaized as follows. I Sectio 2, we formally state the roblem. I Sectio 3 we reveal satiotemoral regularity with vehicle mobility. Sectio 4 resets the aalytical model ad a global algorithm. Sectio 5 details the desig of our distributed algorithm. We further discuss some desig issues i Sectio 6. Performace results are reseted i Sectio 7. We discuss related work i Sectio 8. The aer is cocluded i Sectio 9. 2 SYSTEM MODEL AND PROBLEM STATEMENT We have adoted a system of otatios throughout the aer. A table of otatios have bee summarized, which ca be foud i the sulemetary material. 2. System Model The vehicular etwork is modeled as a set of odes,. Whe two odes, ad, are i the commuicatio rage (deoted by ), i.e.,, there is a lik betwee the two odes ad they ca commuicate with each other while the lik exists. The ositio of ode at time is deoted by. The time is slotted. Therefore, the trajectory of ode is a sequece of ositios, deoted by T (), (),... ( ). () The distace betwee two odes, ad, at time is deoted by. Liks i the etwork are chagig with the relative ositios of the odes. The set of all ossible liks at time is deoted by, L( ) { l d ( ) D; i, j N }. (2) ij, ij, Liks are assumed to have the same caacity i theoretical aalysis. The vehicular etwork tries to deliver a set of ackets, deoted by, ad the ackets are of equal size. A acket has a source,, ad a destiatio,. A acket is coied ad forwarded from oe ode to aother if there is a lik betwee them. A acket grou,, is itroduced to deote all the coies of acket i the etwork. The size of acket grou,, icreases whe there is a ew coy-forward rocess of acket i the etwork. 2.2 Problem Formulatio The mai goal of data delivery is to move the ackets from their sources to resective destiatios. The delivery erformace objectives iclude delivery ratio, delay ad efficiecy. I the followig, we first aalyze the roerties of idividual ackets, ad the show the objectives i a global view. The delivery robability is the chace of a acket successfully delivered from its source to its destiatio. The delivery robability of acket, deoted by, deeds o the routig strategy,, ad the trajectories of odes, f (( ), ( ),{ T N }). (3) With give trajectories, ca be calculated at the begiig ad it does ot chage over time. But i the real world where the future traces are ucertai, this delivery robability ca be cosidered as a radom variable. The delay of a acket, deoted by, is defied as the total trasmissio time set for the etwork to deliver the acket to its destiatio. Aalysis of delay is similar to that of delivery robability. The delay cosists of two arts. Oe art is the time already set, ad the other is time to set, ( ) ( ( ), ( ),{ T }). (4) Whe, the delivery of the acket is comlete. The cost of the trasmissio of a acket, deoted by, is defied as the total umber of times that a acket is forwarded. A ew coy is created whe a acket is forwarded. Thus, the total umber of coies idicates

3 Y. ZHU ET AL.: TRAJECTORY IMPROVES DATA DELIVERY IN URBAN VEHICULAR NETWORKS 3 the delivery cost. The cost is therefore defied as ( ). (5) Oe of the commo objectives of vehicular etworks is to maximize delivery ratio. The delivery ratio is defied as the roortio of successfully delivered ackets to the total ackets to be trasmitted. The umber of total ackets is ofte omitted i calculatios because it is fixed ad ot affected by routig strategies. Thus, oe objective ca be give by max [ ]. (6) Thus, the roblem is to fid the otimal routig of the ackets through the vehicular etwork that meets (6). Two other commo objectives are miimizatio of delay ad miimizatio of total cost, which are give resectively by mi [ ], ad mi [ ]. (7) The efficiecy is defied as the ratio of total successfully delivered ackets to the total cost, give by [ ] [ ]. (8) A high efficiecy idicates that oe algorithm achieves high delivery ratio at a low cost. 2.3 Comlexity Aalysis Without loss of geerality, we take the objective of maximizig the delivery ratio for examle. Objective (6) ca be writte as, max [ f ( ( ), ( ),{ T N})]. (9) Theorem : This routig roblem with objective (9) whe the vehicular traces ad the set of ackets to trasmit are give is NP-hard. The roof of this theorem ca be foud i the sulemetary material of the aer. I ractice, the comlete kowledge is hard to be obtaied because the future kowledge of vehicular traces is usually uavailable. Followig this ractical costrait, the trajectory of a ode is divided ito two arts: the ast ad the future, deoted by ' t t { T } { T } { T }. () Let to deote the curret ositio of the acket. The objective at time for routig becomes max [ ] ' () max [ f ( ( ), ( ),{ T },{ T })]. t The secod art of the trajectory is differet from the first art. The first art has bee fixed while the secod art is ot fixed ad ukow at the time of beig. 3 SPATIOTEMPORAL REGULARITY ANALYSIS I this sectio, we quatitatively reveal the satiotemoral regularity with vehicle mobility. The quatitative aalysis is based o miig the large dataset of vehicular traces of more tha 4, taxis i Shaghai, Chia, which have a duratio of more tha two years. The GPS trace of a taxi, equied with a GPS receiver, was CDF of etroy Margial.2 K= K=2 K= Etroy (bit) Figure : The CDFs of margial etroy ad coditioal etroies of a vehicle ositioal state. The grid size is 2 m 2 m, ad the umber of vehicles is 5. collected by the vehicle eriodically sedig its istat ositio to a data collectio ceter at a iterval from secods to several miutes. The taxis oerates i the whole urba area of Shaghai, which covers a area of over 2 square kilometers. For simlificatio of discussio, the whole sace is divided ito small grids., ad is deoted by, S { s, s,.., s s s }. Q i j (2) where is the total umber of grids. The time is slotted. The locatio of a vehicle at a give time is cosidered as a radom variable which takes state values from the grid sace. Let deote the radom variable for vehicle. We reveal the satiotemoral regularity by comutig the margial ad the coditioal etroies of give the revious states. For vehicle, suose we have observed its states for time slots. The state sequece of the vehicle ca be deoted by a vector, where,- is the ositioal state of vehicle at time slot. Suose that aeares times i the vector of -. Thus, the robability of vehicle takig state ca be comuted as. The, the margial etroy of S i is Q HS ( ) ( o / L) log i j j 2 o / L. (3) j Next, we comute the coditioal etroy of give its immediately revious state which has the same distributio with. The coditioal etroy is, HS ( S) HS (, S) HS ( ). (4) i i i i i To derive the coditioal etroy, we have to derive the etroy of the joit radom variable By usig the state sequece, we derive a sequece of 2-tules,. By coutig the occurreces of, deoted by, we ca get its robalibty. Thus, the joit etroy of the two dimesioal radom variable of is, Q o j, j HS (, S) log. i i 2 (5) j L o /( L) j, j By geeralizig the revious comutatio, we ca comute the coditioal etroy of S i give its immediately revious states 2 HS ( S, S,... S K ). (6) i i i i 3

4 4 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS I essece, by showig the margial etroy we reveal satial regularity, which characterizes the ucertaity of a vehicle residig a locatio i the sace. By showig the coditioal etroy give the revious states, we reveal the satiotemoral regularity of vehicle mobility. This characterizes the ucertaity of a vehicle residig a secific locatio whe its revious states are give. This demostrates the correlatio of a vehicle s ositioal states over differet times. I Figure, the cumulative distributio fuctios (CDFs) of the margial ad the coditioal etroies for are show. The coditioal etroies are sigificatly smaller tha the margial etroy. This imlies that the ucertaity of the ositioal state becomes smaller whe the revious states are kow. We also fid that whe becomes larger, the etroy cotiues to decrease. This suggests that more revious states hel further reduce ucertaity. However, the imrovemet quickly stalls as icreases. This gives the guidace to the order selectio for trajectory redictio usig multile order Markov chais. 4 DESIGN OF GLOBAL ALGORITHM 4. Overview The global metric of a acket chages after itermediate trasfers over time. Cosider that a acket,, is forwarded from ode to at time. After the forwardig, the icremet i the global metric becomes () j () i. Nt,. Nt,, Nt,, (7) Ad the origial objective becomes max ( t ). (8) N,, Nt,, Sice the sum of icremets before time has bee fixed, it ca further be writte as max. Nt,, (9) Item ca be cosidered as the curret metric for acket. At time, there may exist a umber of liks that may iferece with each other, ad it is imossible for all the liks to be active simultaeously. The routig algorithm must schedule the liks, i.e., choose a subset of liks from all ossible liks to maximize the sum of curret metrics. Thus, the objective becomes max ( l )., ll( t) Nt,, ij, (2) The otimal routig erforms two tasks, i.e., lik schedulig ad acket schedulig. Before the routig decisio ca be made, we have to obtai the metric icremet of every acket over all ossible trasfers. Whe all the icremets are available, the otimal routig chooses such a set of liks ad a set of acket trasfers that meet (2). We should emhasize that eve whe all are available, fidig the best liks ad acket trasfers is still a NP-hard roblem. A brief roof is as follows. This roblem ca be cosidered as a weighted maximum ideedet set roblem that has bee roved to be NP-hard. To solve this roblem, a umber of existig heuristic algorithms [2] ca be used, i which are cosidered as lik weights. As metioed before, we take delivery robability maximizatio as examle. The delivery robability of acket,, deeds o the ecouter robability of every two odes, deoted by. I the followig we derive the relatioshi betwee metric icremets ad ecouter robability. The robability for the acket to be delivered i o more tha oe ho is. (2) ( ), ( ) The, for a two ho delivery with the two-ho route of, the robability is ( ),, ( ). ( ),, ( ) (22) Thus, the robability for acket beig delivered i two hos is 2 ( ),, ( ) ( ) N, ( ), ( ) (23) ( ). N, ( ), ( ) ( ),, ( ) The delivery robability of the acket with the h-ho route is ( ),,.., 2 h, ( ) h. (24) ( ), i i, i h, ( ) The the set of all h-ho routes (deoted by ) which starts from ad eds at is deoted by h (, ) {,,..,, N ;, }. (25) h i i Thus, the h-ho delivery robability is calculated by h r ( ( ), ( )) h r ( ). (26) Therefore, the total delivery robability is h. (27) hh Costat acts as the ho limit. The revious aalysis idicates that ecouter robability is the key to comutig the overall delivery robability of a acket. Sice it is imossible to kow future movemets of vehicles, the kowledge of ecouter robability of each air of vehicles is ot immediately available. Fortuately, we have observed that there is strog satiotemoral regularity with vehicle mobility. Based o this observatio, we roose the otio of mobility atters to characterize this regularity. With the mobility atter, we are eabled to redict the trajectory of a vehicle. With trajectories of vehicles, we ca effectively comute the ecouter robability of two vehicles. Let the mobility atter of ode deoted by. We develo the followig mobility atter for characterizig the satiotemoral regularity of vehicle mobility. For vehicle i, its mobility atter is defied as, where H is a vector of ast ositioal states,,, ad is the future ositioal state. The mobility atter characterizes the frequecies of followig i the vehicle s traces by comutig the robability distributio of the two-dimesioal radom variable. This ca be

5 Y. ZHU ET AL.: TRAJECTORY IMPROVES DATA DELIVERY IN URBAN VEHICULAR NETWORKS 5 a b s c ac, bc, s2 s3 s4 s5 ( )( ) a, c b, c Figure 2: A illustratig examle of calculatio for ecouter robability ad delivery robability. Figure 3: A illustratig examle with four odes for exlaiig the global algorithm. The liks formed amog ode a, b, c should comete for the media. achieved by aalyzig the historical traces of the vehicle, as discussed i Sectio Predictio of Future Trajectories Predictig the future trajectory of vehicle at time is to comute the future trajectory,, give the trajectory before,. A trajectory,, ca be described by a sequece of ositioal states, T s, s,, s,. (28) Because of the ucertaity of vehicle mobility, there may exist a umber of ossible future trajectories. Defiitio. The set of all ossible trajectories of ode is defied as a trajectory budle, deoted by, which ca be characterized by TB D (), D (2),, D ( ),. (29) where is the robability distributio of satial states at future time. D ( ): P ( ) s S. (3) s where is the robability of the ode aearig i state s at time. To redict the trajectory of a vehicle, it is essetially to calculate the trajectory budle of the vehicle. For trajectory redictio, we develo multile order Markov chais for redictios. The key is to establish the matrix of trasitio robabilities. The trasitio robabilities are comuted o a idividual vehicle s basis, sice differet vehicle ossesses differet regularities. For a vehicle, we ca easily derive its trasitio matrix (deoted by X) from its mobility atter. Whe we are usig a K-order Markov chai, a elemet,, reresets the trasitio robability from to, where is a sequece of ositioal states,, ad is a sigle state. The,, where is the robability distributio fuctio of the mobility atter of the vehicle. By alyig the K-order Markov chai, we ca comute the trajectory budle as follows. Give the curret trajectory of ode is, the iitial distributios for are P ( ) s D ( ):,( ). (3) P ( ), s s s The distributios of satial state at future times ca be iteratively calculated. For a sigle trajectory (deoted by, its robability is P ( ) x P ( K i ). (32) s,.., s, s s,.., s, s K K i si are derived from the revious distributios ad is defied i the trasitio matrix. The, ca be derived by s all s s, s i i K D ( ): P ( ) P ( ),. (33) 4.3 Aalysis of Delivery Probability With the redicted trajectories, we are able to derive the ecouter robabilities which are required for comutig the evetual delivery robabilities. Give the trajectory budles of ode ad, ad are kow. Let deote the ecouter robability of the two odes at time. It ca be calculated by ( ) P i ( ) P j ( ). (34) ij, ss s s The, the ecouter robability, is give by ( ( )), (35) ij, t ij, T where deotes the max redictio rage of time. If the overall objective is to miimize the delivery delay, the estimated ecouter time for the two odes ca be derived by T ( )/ ( ). (36) ij, ij, ij. t t Therefore, the estimated delay of a acket ca be calculated through trajectories i a similar way with delivery robability comutatio. A examle for calculatig ecouter robability ad delivery robability is show i Figure 2. There are three vehicles, a, b ad c. Vehicle a ecouters b while a wats to deliver acket to c. To simlify the examle, we cosider oly oe redicted trajectory for each vehicle, which is show as a lie with a arrow alog roads. Thus, the ecouter robability betwee a ad c,, ca be calculated by where s is the overlaed grid betwee the trajectories of a ad c ad stads for the robability of a to aear i grid s. There are several overlaed girds betwee the trajectories of b ad c. The ecouter robability,, ca be calculated by T. 5

6 6 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS ractical, distributed algorithm with which a vehicle requires oly limited ad localized kowledge. Figure 4: A illustratig examle for exlaiig the distributed algorithm at ode. The lik betwee ad may comete for the media with the lik betwee b ad d. If a coies acket to b, b cotributes to acket delivery because it may ecouter c as well. I this case, the delivery robability of acket, whe a ad b forward it ideedetly, is. 4.4 Algorithm Descritio The global algorithm is described as follows. Accordig to Subsectios 4.2, each vehicle which has a trasitio matrix obtaied from historical data ca calculate its future trajectory budle usig its curret ositio. With the trajectory budles, the ecouter robability of every two vehicles is kow from (34). The, the delivery robability of each acket i the etwork through each ossible ath ca be calculated by (35) ad (27). With these robabilities, the global algorithm solves a otimizatio roblem to determie which the best ext ho for each acket is. The algorithm reeatedly schedules the delivery util all the ackets are delivered. A illustratig examle for exlaiig the global algorithm is give as follows. Suose at a small area of the vehicular etwork, there are oly four vehicle, a, b, c ad d i each other s commuicatio rage as show i Figure 3. Vehicle a has oe acket ad vehicle b has oe acket q. Both a ad b wat to deliver their ackets to their destiatios. The algorithm first calculates the delivery robabilities of acket of each ossible ext ho (b, c, ad d) ad the fids that c is the best ext ho. I the same way, d is the best ext ho for acket q. Because the wireless liks betwee a, c ad b, d will iterfere each other, the algorithm selects the acket with the largest delivery robability to be forwarded. 5 DESIGN OF DISTRIBUTED ALGORITHM The global algorithm requires the comlete kowledge of all ackets ad vehicles. More secifically, for each acket, the kowledge of its source ad destiatio, ad the curret ositio must be kow. For each vehicle, the kowledge of its ositio ad the mobility atter must be kow. These ieces of kowledge are ot available i a distributed settig. Thus, we desig a 5. Overview The distributed algorithm cosists of two fudametal buildig blocks. I the first block, the ew objective for each idividual vehicle is desiged, sice it is imractical for idividual vehicles to comute the global objective. I the secod block, we defie the metadata for vehicles to exchage with each other at meetigs. I the distributed settig, the kowledge of odes ad ackets is usually icomlete. Therefore, a global otimizatio (9) is hard for it is imossible to comute the global metric ad the curret metric (defied i () ad (7)). I this case, we have to desig a ew metric based o which a idividual vehicle makes routig decisios. Let the icomlete set of odes ad ackets be deoted by ad, resectively. The, the ew objective becomes max. ' N, ', t (37) becomes the ew metric of acket at time t, which is local ad ca be comuted by idividual vehicles for each acket. Whe makig routig decisios, a ode maximizes the sum of local metrics of all the ackets it kows. It would be better for a ode to have more kowledge about odes ad ackets. Sice it is difficult for a ode to have the comlete kowledge, we desig a distributed rotocol for the odes to exchagig iformatio whe they meet each other. By this way, the kowledge ca be roagated throughout the etwork. For exchagig iformatio, we defie metadata, which iclude two arts of iformatio. The first art is about the mobility atter ad the most udate ositio of each vehicle (time stamed). The secod art is about the ackets that the ode carries. Note that for a relatively stable set of vehicles, the mobility atter reflects the regularity of a vehicle s mobility. Thus, it is relatively stable ad therefore it is o eed to udate the mobility atters frequetly. 5.2 Algorithm Descritio As a distributed algorithm, each vehicle executes the routig algorithm ideedetly. For each vehicle, a routie rocedure is ivoked each time it fids a ew commuicatio eighbor. For eighbor discovery, it is required that every vehicle eriodically broadcasts hello messages so that other vehicles ca discover it whe it eters their commuicatio rages. I the followig we describe the rocedure, suosig that vehicle fids aother vehicle,, eterig its commuicatio rage. The Pseudo code descritio of this rocedure is show i Figure 5.

7 Y. ZHU ET AL.: TRAJECTORY IMPROVES DATA DELIVERY IN URBAN VEHICULAR NETWORKS 7 Procedure ( ) Variables : the ode; : ew eighbor; : metadata; : ackets of ode ; : eighbors of ; : curret time; : total odes., 2. exchages metadata with :, 3. calculates from 4. For every acket, calculate metric 5. Sort all ackets accordig to metric for all i the decreasig order 6. Trasmit the ackets i this order Figure 5: Pseudo code of the rocedure of the distributed algorithm, which is executed uo each cotact with a vehicle. First, ode udates its eighbor set ( ). The, ode ad exchage their metadata. The metadata of a ode,, deoted by iclude two metadata sets, ad. Set cotais the metadata about the ackets that ode carries, icludig idetificatio ad source-destiatio air. Set cotais the metadata about the vehicles kow to ode, icludig ID, most udate ositio ad mobility atter. Next, it recalculates the metrics for all the ackets it carries, ad sort the ackets resect to the ew metrics i the decreasig order. The ackets will the be trasferred i the sorted order. Note that if the ode has already bee trasferrig a acket, the trasmissio of this acket is ot iterruted. After its comletio, the ackets shall be trasmitted accordig to the ew order. By orderig the ackets, we are essetially doig the lik schedulig i a distributed way. However, before a acket trasfer ca be started, a vehicle has to follow media access cotrol to avoid otetial collisios. As ackets are trasferred betwee vehicles, the acket set,, is udated wheever the vehicle receives a ew acket from its eighbors. A illustratig examle for exlaiig the distributed algorithm is show i Figure 4. At first, the vehicles exchage their short metadata with each other. With these metadata ad the metadata obtaied from other vehicles i the revious rouds, vehicle a ad c calculate the delivery robabilities of ad q, resectively. The, they comete for the wireless media with each other followig a media access cotrol rotocol. The wier seds the acket to the chose ext ho. The distributed algorithm is efficiet ad its comlexity is aalyzed. The aalysis ca be foud i the olie sulemetary material. 5.3 Other Desig Issues For the desig of the distributed algorithm, there are some other issues, icludig use of historical data, divisio of grids, ad rivacy issue. Due to the age limit, we leave the hadlig of these desig issues i the olie sulemetary material. 6 PERFORMANCE EVALUATION I this sectio, we first reset the methodology of erformace evaluatio, describe the settigs of simulatios, itroduce the comared algorithms ad fially reset evaluatio results. 6. Methodology ad Settigs We evaluate our algorithms with the erformace metric of delivery ratio, delay, cost ad efficiecy. These metrics have bee defied i Sectio 2. We comare our algorithms with several other algorithms, which is to be itroduced shortly. The simulatios are coducted with the three datasets of real GPS vehicular traces. Oe dataset icludes the vehicular traces of more tha 4, taxis collected i Shaghai, the secod dataset is the traces of more tha 2, buses i Shaghai ad the third dataset cosists of vehicular traces of more tha 2, taxis collected i Shezhe. The Shaghai dataset covers a duratio of two years ad the Shezhe dataset a duratio of oe moth. The whole urba area of Shaghai is 33 kilometers i legth ad 69 kilometers i width, ad that of Shezhe is about 27 kilometers i legth ad 97 kilometers i width. The whole sace is divided ito grids, ad the grid size is three kilometers by default ad will be varied i the imact study of grid size. The commuicatio rage is 3 meters. We cosider lik iterfaces, ad each ode ca commuicate with oe eighbor at ay time. We radomly select a subset of 4 taxis or buses from the comlete trace for simulatios. For each acket, we radomly select its source ad destiatio. The ackets are ijected at differet times. Every acket has the same size ad riority. The maximum ho ad the maximum time-to-live (TTL) of each acket is set to 2 ad 2 hours, resectively. The umber of ackets is varied from to 8 to study differet loads of the etwork. The order of Markov chais is set to two. From coditioal etroy aalysis, we have already foud that a higher order beyod two gives little reductio i ucertaity. To build the mobility atter for each vehicle, its vehicular trace of the ast 5 days is used. Each data oit is the average over five differet rus of trace-drive simulatios. 6.2 Comared Algorithms Floodig [2], also kow as eidemic routig, is a simle algorithm. Each ode forwards all the ackets it carries to ay ode it meets. This algorithm rovides a uer boud o delivery ratio ad a lower boud o delivery delay. It itroduces very high cost, which is the major defect. [8] is a oortuistic routig algorithm, which radomly decides whether to forward a acket to aother ode. I simulatios, the robability is set to.4. This algorithm reresets the algorithms without redictios. [4] is a routig algorithm for delay tolerat etworks. It obtais the robability of each ode residig i each ossible locatio by aalyzig the his- 7

8 8 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS Relative delivery ratio Figure 6: Delivery ratio vs. amout of ackets, with Shaghai taxi dataset. Average delay /s Figure 7: Average delay vs. amout of ackets, with Shaghai taxi dataset. Total cost Figure 8: Total cost vs. amout of ackets, with Shaghai taxi dataset. Efficiecy Figure 9: Efficiecy vs. amout of ackets, with Shaghai taxi dataset torical trace data. It assumes that every ode has the full kowledge of such robabilities of all vehicles. It the comutes the cotact robability of every two vehicles based o the robability distributio, ad the routig decisios ca be made. tributio [6] is a routig algorithm usig a simle mobility atter that oly cosiders the iter-meetig times of exoetial distributio. This atter makes redictio ideedet of the curret locatio of a vehicle. 6.3 Comarative Results We reset erformace results of our algorithms comared agaist other algorithms. First, we show the results usig the Shaghai dataset of real taxi traces. To characterize the mobility atter, the vehicular trace of the recet 5 days is used. We vary the amout of ackets ad comare the six algorithms i terms of delivery ratio, average delay ad total cost uder differet loads of etwork. For a give settig of amout of ackets, the same set of ackets ad the set of odes are used for all the six algorithms. Sice the delivery ratio is largely affected by the simulated time legth, we use the metric of relative delivery ratio istead of bare delivery ratio, which is the delivery ratio of each algorithm ormalized by that of Floodig. I Figure 6, the erformace of the six algorithms i terms of relative delivery ratio is show. We ca see that our algorithms erform better tha, ad Max-cotributio. Amog the six algorithms, Floodig erforms the best, as exected. I geeral, the algorithms that use redictios roduce better delivery ratios tha the algorithms that make o redictios. Our algorithms are better tha ad tributio because our algorithms use ot oly the historical traces iformatio but also the curret state ad the revious states. Predicted trajectories of vehicles hel to fid better routig aths. The global algorithm is better tha the distributed oe sice it has the global, comlete etwork iformatio. We ca also fid that whe the amout of ackets icreases, the overall delivery ratios of all algorithms decrease. The reaso is that the overall caacity of the etwork is limited. By ijectig more ackets, the ackets may comete for etwork resources ad as a result, fewer ackets ca be delivered i the ed. I Figure 7, average delay agaist amout of ackets is lotted. Our algorithms have a lower delay tha, ad tributio. As exected, Floodig has the smallest delay. The average delays of our algorithms are slightly larger tha that of floodig. This erformace gai of our algorithms is maily due to the fact that routig aths with high delivery robabilities usually lead to shorter delays. Sice our algorithms ca select routig aths of high delivery robabilities, the resultat delay is low. Figure 8 shows the costs of the six algorithms. We ca fid that our algorithms have lower costs, better tha all the other algorithms. The mai reaso is that by effectively redictig the trajectories of vehicles, we oly cosider the aths that lead to evetual delivery with high robability. Therefore, uecessary acket trasfers are greatly reduced. I Figure 9, we comare the efficiecies of the six algorithms. We ca see that our algorithms have higher efficiecy, better tha all the other algorithms. Floodig ad have a similar efficiecy ad are much worse tha the rest four. This is due to the blidess of Floodig ad whe they are makig trasfer decisios. tributio ad have larger efficiecy tha Floodig ad P-radom, but have lower efficiecy tha our algorithms, sice tributio ad merely uses a simle mobility atter of iter-meetig time. 6.4 Effect of Trace Datasets To validate the erformace of the roosed algorithms, we also show the erformace results with the Shaghai bus dataset ad Shezhe taxi dataset. It should be oted that the whole area of Shezhe is oly oe third of that of Shaghai. Thus, the Shezhe dataset rovides a better etwork coectivity tha the Shaghai taxi dataset does. The Shaghai bus dataset has the best etwork coectivity because buses ted to ru o the same routes ad the buses are more desely distributed alog the routes. I Figure ad Figure 4, the erformace of relative delivery ratio for the six algorithms is show. We ca see the similar tred as show i Figure 6 that the roosed global algorithm outerforms the distributed algorithm ad that both of the algorithms achieve better delivery ratio erformace tha the rest four other algorithms. O average, the distributed algorithm achieves several times larger delivery ratio tha ad is about 75% of the delivery ratio achieved by the Floodig. However, we also fid that the imacts of

9 Y. ZHU ET AL.: TRAJECTORY IMPROVES DATA DELIVERY IN URBAN VEHICULAR NETWORKS 9 Relative delivery ratio Figure : Delivery ratio vs. amout of ackets, with Shaghai bus dataset. Average delay /s Figure : Average delay vs. amout of ackets, with Shaghai bus dataset. Total cost x 4 Figure 2: Total cost vs. amout of ackets, with Shaghai bus dataset. Efficiecy Figure 3: Efficiecy vs. amout of ackets, with Shaghai bus dataset. acket amout i Shaghai bus dataset ad Shezhe taxi dataset are ot as large as i Shaghai taxi dataset. This is because the better etwork coectivity i both Shaghai bus dataset ad Shezhe taxi dataset leads to a higher etwork caacity. The erformace of average delay for the six algorithms is show i Figure ad Figure 5. We ca see that the result is cosistet with that i Shaghai taxi dataset. The roosed algorithms roduce a average delay that is close to the delay of Floodig. The average delay of is much larger tha the rest of algorithms. We ca see the average delay for all algorithms icrease slightly as the acket amout icreases, sice the delivery caability is limited. I Figure 2 ad Figure 6, the total cost for the six algorithms is show. It is show that the roosed algorithms itroduce much lower cost tha,, ad. I additio, as the acket amout icreases, the costs of the roosed global ad distributed algorithm icrease with a lower rate tha the rest algorithms. I Figure 3 ad Figure 7, we comare the efficiecy erformace of the six algorithms. The global algorithm achieves the highest efficiecy ad the distributed algorithm is the secod best amog all the algorithms. I summary, the erformace results usig the Shaghai Bus ad Shezhe Taxi dataset are cosistet with those usig the Shaghai Taxi dataset. This cofirms that the roosed algorithms ca still achieve good erformace for differet tyes of vehicles ad for differet desities of vehicles. Note that taxis ad buses caot rereset all tyes of vehicles. Mobility atters of taxis may be differet from those of other tye of vehicles. We do ot have access to traces of rivate vehicles. Thus, we are ot able to show the erformace of our algorithm whe traces of rivate cars are used. However, our algorithm should work well if there exist mobility atters for rivate cars. 6.5 Additioal Evaluatio Results It is clear that other imortat system arameters icludig grid size ad legth of historical trace make imact o the erformace of our algorithms. We have also erformed additioal simulatios to study such imact of the two system arameters. The evaluatio results ca be foud i the olie sulemetary material of the aer. 7 RELATED WORK We classify existig routig algorithms for vehicular etworks ito two categories. For first class of routig algorithms, there is o eed to make estimatio or redictio o vehicular traces. They take advatage of avigatio systems, i which vehicular traces are riori kow before they begi to travel []. This model ad assumtio work well i traditioal Delay Tolerat Networks, such as iterlaetary etworks or satellite etworks. The odes i such etworks have simle ad stable mobility atters. These algorithms ca oly be alicable to those vehicular etworks, i which drivers must tell the avigatio system the destiatios before their joureys ad must follow the lead of the system [2]. Some work assumes artial kowledge about the vehicular traces. I TBD [22], a routig roblem is cosidered to deliver a acket from a mobile vehicle to a static AP. The movemet ath of a vehicle from the source to the destiatio is kow by itself through a avigatio system. It the rooses a lik model for comutig the exected delay of a road segmet, based o which the ed to ed delay ca be comuted. The secod class of routig algorithms makes estimatios about routig metrics, sice there is o further iformatio about ode future traces. Delegate Forwardig [23] demostrates that forwardig with a metric of good quality ca reduce etwork cost. This is doe by the strategy of oly forwardig ackets to those odes which lead the acket to the highest quality. RAPID [3] treats the routig of DTNs as a resource allocatio roblem ad rooses a routig rotocol to maximize the erformace of a secific routig metric. The algorithms metioed above care about calculatio of metrics by estimatig delay or iter-meetig time based o the simle model of exoetial iter-meetig times. tributio [6] cosiders the joit otimizatio of lik schedulig ad acket forwardig. It illustrates that this otimizatio is better tha former algorithms. [4] characterizes mobility atters with aearace frequecies of odes over a sace. The algorithm idicates that odes with the similar frequecies of aearaces have more oortuities to coect. This brigs beefits to routig i DTNs. 9

10 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS Relative delivery ratio Figure 4: Delivery ratio vs. amout of ackets, with Shezhe taxi dataset. Average delay /s Figure 5: Average delay vs. amout of ackets, with Shezhe taxi dataset. Total cost x 4 Figure 6: Total cost vs. amout of ackets, with Shezhe taxi dataset. Efficiecy Figure 7: Efficiecy vs. amout of ackets, with Shezhe taxi dataset. 8 CONCLUSION I this aer, we demostrate the strog satiotemoral regularity with vehicle mobility by etroy aalysis with the extesive datasets of real taxi ad bus traces. By develoig multile order Markov chais, we redict vehicle trajectories. Based o the aalytical model, we derive delivery robability with the redicted robabilistic trajectories. The roosed algorithms take full advatage of redicted robabilistic vehicle trajectories. Extesive simulatios based o the large datasets of real vehicular GPS traces. Performace results verify that our algorithm outerforms other algorithms. This demostrates that redicted trajectories do hel data delivery i vehicular etworks. ACKNOWLEDGEMENTS This research is suorted by Shaghai Pu Jiag Talets Program (PJ458), Shaghai Che Guag Program (CG), NSFC (No , 6939, 6279, 6933, , 67237), MIIT of Chia (29ZX36--), Doctoral Fud of Miistry of Educatio of Chia (27322), Natioal 863 Program (29AA22 ad 2AA5), HP IRP (CW2673), SJTU SMC Project (22), STCSM (8dz56, 2ZR449), Sigaore NRF (CREATE E2S2), NSFC/RGC (N-HKUST6/), HKUST (RPCEG29, SRFIEG7-C ad SBI9/.EG-C), ad Guagdog Bureau of Sciece ad Techology (GDSTEG6). REFERENCES [] F. Bai, D. D. Stacil, ad H. Krisha, "Toward uderstadig characteristics of dedicated short rage commuicatios (DSRC) from a ersective of vehicular etwork egieers," Proc. ACM MOBICOM, 2. [2] Z. Li, Y. Liu, M. Li, J. Wag, ad Z. Cao, "Exloitig Ubiquitous Data Collectio for Mobile Users i Wireless Sesor Networks," IEEE TPDS, vol. 24(2),, , 23. [3] M. Li ad Y. Liu, "Redered Path: Rage-Free Localizatio i Aisotroic Sesor Networks with Holes," IEEE/ACM Trasactios o Networkig, vol. 8(),, , 2. [4] L. Chisalita ad N. Shahmehri, "A eer-to-eer aroach to vehicular commuicatio for the suort of traffic safety alicatios," Proc. The 5th IEEE Coferece o Itelliget Trasortatio Systems, 22, [5] Z. Li, Y. Zhu, H. Zhu, ad M. Li, "Comressive Sesig Aroach to Urba Traffic Sesig," Proc. IEEE ICDCS, 2. [6] H. Zhu, Y. Zhu, M. Li, ad L. M. Ni, "SEER: Metroolita-scale Traffic Percetio Based o Lossy Sesory Data," Proc. IEEE INFOCOM, 29. [7] J. Eriksso, L. Girod, B. Hull, R. Newto, S. Madde, ad H. Balakrisha, "The Pothole Patrol: Usig a Mobile Sesor Network for Road Surface Moitorig," Proc. ACM MobiSys, 28. [8] P. Gibbos, B. Kar, Y. Ke, S. Nath, ad S. Sesha, "Iriset: A architecture for a worldwide sesor web," IEEE Pervasive Comutig,, 22-33, 23. [9] U. Lee, B. Zhou, M. Gerla, E. Magistretti, P. Bellavista, ad A. Corradi, "Mobeyes: Smart Mobs for Urba Moitorig with a Vehicular Sesor Network," IEEE Wireless Commuicatios, vol. 3(5),, 52-57, 26. [] I. Leotiadis ad C. Mascolo, "Geos: Geograhical oortuistic routig for vehicular etworks," Proc. IEEE WoWMoM, 27,. -6. [] G. Marfia, M. Roccetti, C. E. Palazzi, ad A. Amoroso, "Efficiet vehicle-to-edestria exchage of medical data: a emirical model with relimiary results," Proc. ACM MobiHoc Worksho o Pervasive Wireless 2. [2] I. Leotiadis, P. Costa, ad C. Mascolo, "Extedig access oit coectivity through oortuistic routig i vehicular etworks," Proc. IEEE INFOCOM, 2. [3] A. Balasubramaia, B. Levie, ad A. Vekataramai, "DTN routig as a resource allocatio roblem," Proc. ACM SIGCOMM, 27. [4] J. Leguay, T. Friedma, ad V. Coa, "DTN Routig i a Mobility Patter Sace," Proc. ACM SIGCOMM Worksho o Delay-tolerat Networkig, 25, [5] J. Krumm ad E. Horvitz, "Predestiatio: Where Do You Wat to Go Today?," Comuter, vol. 4(4),, 5-7, Aril 27. [6] K. Lee, Y. Yi, J. Jeog, H. Wo, I. Rhee, ad S. Chog, "Max-cotributio: O otimal resource allocatio i delay tolerat etworks," Proc. IEEE INFOCOM, 2. [7] J. Burgess, B. Gallagher, D. Jese, ad B. N. Levie, "Maxro: Routig for vehicle-based disrutio-tolerat etworks," Proc. IEEE INFOCOM, 26. [8] S. Jai, K. Fall, ad R. Patra, "Routig i a delay tolerat etwork," Proc. ACM SIGCOMM 24. [9] Z. Che, H. Kug, ad D. Vlah, "Ad hoc relay wireless etworks over movig vehicles o highways," Proc. ACM Mobihoc, 2,. 25. [2] Y. Yi, A. Proutière, ad M. Chiag, "Comlexity i wireless schedulig: Imact ad tradeoffs," Proc. ACM MobiHoc, 28, [2] R. Ramaatha, R. Hase, P. Basu, R. Rosales-Hai, ad R. Krisha, "Prioritized eidemic routig for oortuistic etworks," Proc. ACM MobiSys worksho o Mobile Oortuistic Networks (MobiO), 27,. 66. [22] J. Jeog, S. Guo, Y. Gu, T. He, ad D. Du, "TBD: Trajectory-based data forwardig for light-traffic vehicular etworks," Proc. IEEE ICDCS, 29. [23] V. Erramilli, M. Crovella, A. Chaitreau, ad C. Diot, "Delegatio forwardig," Proc. ACM MobiHoc, 28,

11 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS Yami Zhu (M 2) is a Associate Professor i the Deartmet of Comuter Sciece ad Egieerig at Shaghai Jiao Tog Uiversity. He obtaied his PhD i comuter sciece from the Deartmet of Comuter Sciece ad Egieerig at the Hog Kog Uiversity of Sciece ad Techology i 27. His research iterests iclude vehicular etworks, sesor etworks ad mobile comutig. Prior to joiig Shaghai Jiao Tog Uiversity, he was a research associate with the Deartmet of Comutig at the Imerial College Lodo. He is a member of the IEEE ad the IEEE Commuicatios Society. Yuche Wu obtaied his bachelor degree from the Deartmet of Comuter Sciece ad Egieerig at Shaghai Jiao Tog Uiversity i 2. He is a master studet i the Deartmet of Comuter Sciece ad Egieerig at Shaghai Jiao Tog Uiversity i 2. His research iterests iclude vehicular etworks ad mobile comutig. Bo Li (F ) is a rofessor i the Deartmet of Comuter Sciece ad Egieerig, Hog Kog Uiversity of Sciece ad Techology. He is a Cheug Kog Chair Professor i Shaghai Jiao Tog Uiversity, Chia, ad the Chief Techical Advisor for Chia Cache Cor. (NASDAQ:CCIH). He was reviously with IBM Networkig System Divisio, Research Triagle Park, ad a adjuct researcher at Microsoft Research Asia. His recet iterests iclude: large-scale cotet distributio i the Iteret, Peer-to-Peer media streamig, the Iteret toology, cloud comutig, gree comutig ad commuicatios. He received his B. Eg. Degree i the Comuter Sciece from Tsighua Uiversity, Beijig, ad his Ph.D. degree i the Electrical ad Comuter Egieerig from Uiversity of Massachusetts at Amherst.