Forwarding Redundancy in Opportunistic Mobile Networks: Investigation, Elimination and Exploitation

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1 1 Forwardng Redundancy n Opportunstc Moble Networks: Investgaton, Elmnaton and Explotaton We Gao, Member, IEEE, Qnghua L, Member, IEEE, and Guohong Cao, Fellow, IEEE Abstract Opportunstc moble networks consst of moble devces whch are ntermttently connected va short-range rados. Forwardng n such networks reles on selectng relays to carry and delver data to destnatons upon opportunstc contacts. Due to the ntermttent network connectvty, relays n current forwardng schemes are selected separately n a dstrbuted manner. The contact capabltes of relays hence may overlap when they contact the same nodes and cause forwardng redundancy. Ths redundancy reduces the effcency of resource utlzaton n the network, and may mpar the forwardng performance f beng unconscously gnored. In ths paper, based on nvestgaton results on the characterstcs of forwardng redundancy n realstc moble networks, we propose methods to elmnate unnecessary forwardng redundancy and ensure effcent utlzaton of network resources. We frst develop technques to elmnate forwardng redundancy wth global network nformaton, and then mprove these technques to be operable n a fully dstrbuted manner wth lmted network nformaton. We furthermore propose adaptve forwardng strategy to ntentonally control the amount of forwardng redundancy and satsfy the requred forwardng performance wth mnmum cost. Extensve tracedrven evaluatons show that our schemes effectvely enhance forwardng performance wth much lower cost. Index Terms Data Forwardng, Opportunstc Moble Networks, Redundancy, Relay Selecton, Adaptablty. 1 INTRODUCTION Opportunstc Moble Networks, also known as Delay/ Dsrupton Tolerant Networks (DTNs) [16], consst of hand-held moble devces such as PDAs, laptops and smartphones. These devces are connected only ntermttently when they opportunstcally contact each other,.e., move nto the communcaton range of ther shortrange rados (e.g., Bluetooth, WF). Such ntermttent network connectvty can be a result of moblty, devce sparsty or power outage. Examples of such networks nclude groups of ndvduals movng n dsaster recovery areas, urban sensng [13] and Vehcular Ad-hoc Networks (VANETs) [5]. The ntermttent network connectvty among moble devces makes t dffcult to mantan end-to-end communcaton lnks or global network nformaton. To facltate communcaton n opportunstc moble networks, node moblty s exploted to let nodes physcally carry messages as relays, whch forward messages when they opportunstcally contact other nodes. The key problem s hence how to make effectve forwardng decsons, to ensure that the messages are carred by relays wth the Ths work was supported n part by the DOD Grant W911NF We Gao s wth the Department of Electrcal Engneerng and Computer Scence, Unversty of Tennessee at Knoxvlle, 1520 Mddle Drve, Knoxvlle, TN E-mal: wegao@utk.edu. Qnghua L s wth the Department of Computer Scence and Computer Engneerng, Unversty of Arkansas, Fayettevlle, AR E-mal: qnghual@uark.edu Guohong Cao s wth the Department of Computer Scence and Engneerng, Pennsylvana State Unversty, Informaton Scence and Technology Buldng, Unversty Park, PA E-mal: gcao@cse.psu.edu. best chance to contact ther destnatons. Forwardng decson n opportunstc moble networks conssts of two stages. Frst, the utlty of a node for forwardng a message s determned. Due to the lack of global nformaton about how to reach the destnaton, node s utlty s evaluated by predctng the node s capablty of contactng others n the future. Varous utlty functons evaluatng such nodes contact capablty have been proposed based on node moblty pattern [9], [40], stochastc node contact process [30], [2] or socal network concepts [10], [25], [23]. Second, node utltes are appled to varous forwardng strateges for dfferent tradeoffs between forwardng performance and cost. Epdemc [38] and RAPID [2] optmze forwardng performance by utlzng all the nodes and contact opportuntes for replcatng messages. Most strateges only replcate messages to relays wth hgh utltes and mprove forwardng performance wth lower cost. In ths paper, we envson that conventonal wsdom has been focusng on developng varous relay utlty functons or forwardng strateges for opportunstc moble networks, but generally gnore the large amount of forwardng redundancy produced by the current forwardng schemes,.e., the calculated utlty of a relay may not reflect ts actual contrbuton on forwardng a message. The major reason for such redundancy s that the utlty of a relay, n current forwardng schemes, s evaluated separately wthout consderng the exstence of other relays carryng replcas of the same message, and the contact capabltes of relays hence may overlap wth each other. The relays may contact the same node at dfferent tmes n the future, but only the frst relay

2 2 havng contacted the destnaton delvers the message. The capabltes of all other relays contactng ths node are redundant and wasted. The exstence of forwardng redundancy generally reduces the effcency of resource utlzaton n opportunstc moble networks, because some relays may have only lttle contrbuton on forwardng the message f the forwardng redundancy s unconscously neglected and napproprately grows. Message replcas carred by these relays neffectvely consume the lmted network resources ncludng channel bandwdth and local storage buffer, and further mpar the performance of forwardng other messages. On the other hand, n applcaton scenaros wth strct performance requrements such as dsaster recovery or emergency notfcaton, ntentonally mantanng and explotng such redundancy wth specfc forwardng strateges helps create a suffcent number of message replcas and satsfy the requred performance for forwardng the message. The major focus of ths paper, therefore, s to approprately address the mpact of forwardng redundancy n opportunstc moble networks, and make forwardng schemes ) beng able to correctly dentfy and elmnate unnecessary forwardng redundancy from relays utltes, so as to mprove the effcency of resource utlzaton and forwardng performance n opportunstc moble networks, and ) beng able to adaptvely mantan the amount of forwardng redundancy n the network, so as to explot such forwardng redundancy for satsfyng the specfc performance requrements of dfferent moble applcatons. Our basc dea s to develop cost-effectve methods whch dentfy the nodes that exstng relays are lkely to contact n the future, so that forwardng redundancy can be elmnated by avodng these nodes from beng contacted agan, when the contact capabltes of other relays are later evaluated. Such redundancy hence can be further exploted by adaptvely adjustng the crtera of relay selecton wth respect to the requred contact capabltes of relays. More specfcally, we made the followng contrbutons: Investgaton. We nvestgate characterstcs of forwardng redundancy from both theoretcal and expermental perspectves. We frst formulate a theoretcal framework about varatons of forwardng performance and redundancy when message replcas are created, and then conduct expermental studes usng exstng forwardng schemes over realworld moble network traces. We observe that some message replcas contrbute lttle on mprovng the delvery rato, and up to 70% of relays utltes n current forwardng schemes are redundant. Ths result serously mpars forwardng effectveness and hghlghts the necessty of redundancy elmnaton. Elmnaton. The major challenge of elmnatng forwardng redundancy s the lack of global network nformaton. Ths makes t hard to estmate the cumulatve contact capablty of exstng relays and determne forwardng redundancy. To address ths challenge, we frst propose a scheme to elmnate forwardng redundancy wth global network nformaton, and then make t dstrbuted. We provde formal analyss on the accuracy of dstrbuted redundancy elmnaton, and propose two alternatve methods to correct the possble errors durng redundancy elmnaton due to ncompleteness of network nformaton. After redundancy elmnaton, lmted resources at each relay s effectvely allocated to messages accordng to the relay s utltes for forwardng them. Evaluaton results show that the forwardng performance after redundancy elmnaton s mproved by 20% wth 40% less cost. Explotaton. The explotaton of forwardng redundancy s based on the relays utltes after redundancy elmnaton, whch reflect the actual contrbuton of relays for forwardng messages. We desgn adaptve forwardng strategy to ntentonally control the amount of forwardng redundancy n the network, and acheve the delvery rato requred by specfc moble applcatons wth the mnmum cost. Ths s acheved by adaptvely adjustng a message forwardng threshold at ndvdual relays based on the up-to-date network condton. The rest of ths paper s organzed as follows. Secton 2 descrbes our network model and motvaton of elmnatng forwardng redundancy. Based on nvestgaton results n Secton 3, our schemes for elmnatng and explotng forwardng redundancy are descrbed n Sectons 4 and 5. The performance of our proposed schemes are evaluated by trace-drven smulatons n Secton 6. Secton 7 revews related work and Secton 8 concludes the paper. 2 OVERVIEW 2.1 Network Model and Assumptons Opportunstc contacts among moble devces are descrbed by network contact graph (NCG) G(V,E), where contact process between nodes, j V s modeled as an edge e j E, ande j only exsts f and j have contacted before. We focus on effectvely forwardng messages to destnatons wth mnmum cost, measured by the average number of replcas created per message 1. We consder that each relay has only lmted resources of channel bandwdth and local buffer. When replcas of multple messages are forwarded to the same relay, ther prortes are determned to maxmze the effectveness of utlzng the relay s resources. We assume a well-defned communcaton mechansm at and below the lnk layer, and the consderaton of lnk qualty or channel nterference s beyond the scope of ths paper. We assume that each message has a fnte lfetme T. Lettng the forwardng delay be a random varable X 1. Each relay only carres one replca of a message, and hence the number of replcas created for a message s equal to the number of relays used for forwardng the message.

3 3 S A S B when A determnes whether to replcate message to C at tme t 3, the redundancy between B and C on nodes J and K s hard to be elmnated. (a) Network contact graph (b) Forwardng decsons Fg. 1. Illustraton of forwardng redundancy. Utlty u ndcates the number of nodes that contacts, and the value wthn brackets s the value of u after redundancy elmnaton. Message s replcated from to j f u <u j. (0, + ], the expected delay s measured as E{X X T } and the delvery rato s P(X T ). Snce the delvery rato and expected delay are correlated and ncrease smultaneously when T ncreases, n ths paper we measure forwardng performance usng delvery rato and wll not evaluate delay separately. 2.2 Motvaton Forwardng redundancy n opportunstc moble networks s llustrated by the example n Fgure 1. Fgure 1(a) only shows part of NCG near the data source S, and none of the nodes n Fgure 1(a) has contacted the destnaton, whch s far away and not shown n the fgure. In ths case, the node s capablty of contactng other nodes s used as ts utlty for forwardng decson 2, and forwardng redundancy occurs when the relays A, B and C contact many nodes n common. In partcular, when B receves message replca at tme t 2 from S and becomes a relay, node G contacted by B s also contacted by another exstng relay A. Hence, the contact of B to G s redundant. B s utlty wthout such redundancy, measured n number of nodes that B has contacted, should be 2 nstead of 3. Smlarly, contacts of relay C to nodes J and K are redundant because of the exstence of B, and ths redundancy reduces C s utlty from 3 to 1. Ths redundancy, f beng unconscously gnored and grows napproprately, may mpar the forwardng effectveness. For example, wth the exstence of B, replcatng message from A to C at tme t 3 s neffectve because t only ncreases the cumulatve number of nodes that the relays contact by (6 5)/5 =20%, but ncreases the number of message replcas by 33%. C may also prevent node F wth hgher utlty from beng used as relay when forwardng strategy lke Delegaton [15] s used, due to the fake hgh utlty of C. Elmnaton of ths redundancy s challengng due to the lack of global network nformaton. When S replcates message to B at tme t 2, A may not know the exstence of relay B f A has dsconnected wth S. Hence, 2. Note that nodes and j are not ncluded n calculatng ther utltes when determnes whether to replcate message to j. Exstng relays are not ncluded n such calculaton ether. A C 2.3 Metrcs We measure forwardng redundancy as follows: Defnton 1: Redundancy percentage P k (t 1,t 2 ) of k exstng relays durng tme perod [t 1,t 2 ] s defned as / k P k (t 1,t 2 )=1 k N (t 1,t 2 ) N (t 1,t 2 ), (1) =1 =1 where node j N (t 1,t 2 ) f t s contacted by the -th relay durng tme perod [t 1,t 2 ].The-th relay belongs to N (t 1,t 2 ). Forwardng redundancy vares when dfferent utlty functons are used for forwardng decson. In general, the utlty of node s calculated as U = N j=1 c j, where N s number of nodes n the network and c j s the capablty of node contactng j. Utlty functons are classfed nto two categores accordng to the network nformaton used to measure c j. The frst category s observatonal utltes, n whch c j s measured by drect network observatons n the past. These observatons nclude parwse contact frequency (Freq) [14] and elapsed tme snce last contact (Elapsed- Tme) [11]. Betweenness [17] s also used n socal-aware forwardng schemes [25], and defnes c j = j 1 k=1 g jk () g jk, where g jk s the number of shortest paths between node j and k on the NCG and g jk () s the number of such paths passng node. Betweenness hence ndcates the relatve mportance of node n facltatng communcaton among other nodes. The second category s probablstc utltes, where c j ndcates parwse contact probablty derved from node contact process. PROPHET [30] ncreases c j by (1 c j ) p nt each tme when and j contact 3,andCCP [22] defnes c j =1 e λjt where λ j s the parwse contact rate. These utltes apply to varous forwardng strateges. In Compare-and-Forward [11], [14], a relay replcates messages to nodes wth hgher utlty than tself. Delegaton [15] reduces the number of replcas, such that a relay only replcates message to nodes wth hgher utlty than any exstng relay that t s aware of. In Spray-and-Focus [36], the maxmum number of message replcas s fxed and a relay forwards message to another node wthout retanng a local copy. In ths paper, we study forwardngredundancyover varous combnatons of forwardng strateges and utlty functons. Note that there are more forwardng strateges and utlty functons havng been developed than the ones mentoned above. Our goal s not to address forwardng redundancy for each of them, but to demonstrate the general mpact of ths redundancy on forwardng performance, as well as the unversal methodology for practcal redundancy elmnaton. 3. PROPHET proposed n [30] was only used between a relay and the destnaton. In ths paper we extend t to an arbtrary par of nodes.

4 4 (a) Comparng E{D k } and E{ D k } (b) Redundancy percentage Fg. 2. Theoretcal varaton of delvery rato and redundancy percentage 2.4 Traces Four sets of opportunstc moble network traces are used n ths paper. They record contacts among moble devces wth Bluetooth or WF nterfaces movng n suburban areas (DeselNet [3]), conference ste (Infocom [25]) and unversty campus (MIT Realty [12], UCSD [32]). Bluetooth-enabled devces perodcally detect ther peers nearby, and a contact s recorded when two devces move close. WF-enabled devces search for nearby WF Access Ponts (APs) and assocate themselves to the APs wth the best sgnal strength. A contact s recorded when two devces are assocated to the same AP. As summarzed n Table 1, the four traces dffer n ther contact type, network scale and node contact frequency. 3 INVESTIGATION In ths secton, we nvestgate the characterstcs of forwardng redundancy from both theoretcal and expermental aspects. We frst provde theoretcal nsghts on varatons of delvery rato and redundancy percentage when the message s beng replcated, and then nvestgate these varatons on real-world traces lsted n Table 1. Our fndngs are summarzed as follows, and generally hghlght the necessty of elmnatng forwardng redundancy n opportunstc moble networks. Forwardng redundancy wdely exsts n current forwardng schemes, and serously mpars the forwardng effectveness f not beng approprately elmnated. Message delvery rato and redundancy percentage are closely correlated. Hence, forwardng redundancy can be ntentonally controlled for satsfyng the requred delvery rato. The practcal varatons of delvery rato and redundancy percentage accurately match our theoretcal expectatons. 3.1 Theoretcal Framework Delvery Rato We assume that a message s generated at tme t 0 and expres at tme t e, wth lfetme T = t e t 0.Asaresult, the message delvery rato 4 wth k relays s D k (t 0,t e )=1 k (1 n ), (2) =1 N where N s the number of nodes n the network, n = N (t,t e ) and t s the tme when the message s replcated to the -th relay. When message s replcated to another relay R k+1, D k ncreases by ΔD k =(1 D k ) n k+1 N.If n are..d. statonary random varables wth E{n } = μ c, we have E{D k } =1 (1 μ c /N ) k. (3) In Eq. (2), both the destnaton and the nodes n N are assumed to be unformly dstrbuted n the network. In socal computng applcatons wth communty structures, such dstrbuton may be hghly skewed. Relays wthn the same communty may contact the same nodes and lead to lower delvery rato. In contrast, N of relays wthn dfferent communtes may not overlap at all. Comparatvely, delvery rato wthout consderng forwardng redundancy s D k = 1 N k =1 n wth k =1 n N, and E{ D k } = kμ c /N. Fgure 2(a) llustrates the dfference between E{D k } and E{ D k } when k ncreases. Whle E{ D k } lnearly ncreases wth k, E{D k } ncreases slower. Ths dfference s larger when k ncreases or μ c s smaller. Snce the dstrbuton of node contact capablty s hghly skewed n realty [25], value of μ c s low and the actual delvery rato s much lower than that ndcated by relays utltes. TABLE 1 Trace summary Trace DeselNet Infocom MIT Realty UCSD Network type WF Bluetooth Bluetooth WF Contact type Drect Drect Drect AP-based No. devces Duraton (days) No. contacts 3, , , ,225 No. contacts per par per day Redundancy Percentage The redundancy percentage of k relays s P k =1 N D k /N k, where D k s defned n Eq. (2) and N k = k =1 n.snce E{ 1 N k } 1 kμ c,wehave E{P k } 1 N E{D k }/(kμ c ), (4) and ths upper bound s asymptotcally tght because E{P N } =1 N E{D N }/(Nμ c ) when N s suffcently large. When message s replcated to another relay R k+1, P k ncreases by ΔP k = P k+1 P k = N D k = N k N D k+1 N k + n k+1 N n k+1 N k (N k + n k+1 ) (D k N k N (1 D k)). 4. The delvery rato of a sngle message equals to ts probablty to be delvered to the destnaton before expraton. (5)

5 5 Lemma 1: For k 1, ΔP k 0. Proof: Consder functons f(n 1,..., n k ) = 1 k N =1 n = N k /N and g(n 1,..., n k ) = 1 k =1 (1 n N ) k =1 (1 n = N ) f n = 1 N D k 1 D k. For [1,k] we have g 1 and n = (1 + g(n N(1 n 1,..., n N ) k )). Snce f(0,..., 0) = g(0,..., 0) = 0, we have f(n 1,..., n k ) g(n 1,..., n k ) for n 1,..., n k (0,N] and the lemma follows. Lemma 1 shows that forwardng redundancy does not decrease each tme when message s replcated, and ths s also llustrated n Fgure 2(b) by usng ts upper bound n Eq. (4). When μ c ncreases, a node can be contacted by more relays and hence leads to hgher redundancy percentage. We also notce that replcatng message to more relays ncreases the relay coverage and redundancy percentage smultaneously. The relatonshp between the two perspectves s descrbed by the followng theorem. Theorem 1: When 1 n <N/2for [1,k], there exsts k 0 [1,N], suchthatfor k k 0, ΔP k ΔD k,and for k >k 0, ΔP k > ΔD k. Proof: From Eqs. (2) and (5), we have ΔP k ΔD k = n k+1(d k (f(k)+n) f(k))), (6) N k (N k + n k+1 ) where f(k) = N N k+n 2 k +N kn k+1 N and N k = k =1 n. Eq. (6) shows that the proof of Theorem 1 s equvalent to prove that there exactly exsts one k 0 (0, ) such that f(k 0 ) D k 0 N 1 D k0 =0. Ths s proved n the followng steps. Step 1: Let g(k) = D k N 1 D k, and we mmedately have f(0) = g(0) = 0. f(1) = N n1+n2 1 +n1n2 N,andg(1) = N n1 N n 1. Snce n [1,N/2) for [1,k], wealsohavef(1) > g(1). Step 2: It s easy to have f(k) k > 0 and g(k) k > 0 for k. Step 3: Snce n k+1 [1,N/2) and f(k +1) f(k) N k N, we have 2 f(k) k > 0. Wealsoseethat 2 g(k) 2 k 2 f(k) 2 k > 0 2 n the smlar way from Eq. (2). The theorem s proved by combnng the three steps above. Theorem 1 shows that, when the number of message replcas s small, each replca has lmted forwardng redundancy but consderably ncreases delvery rato. However, when message s replcated to more relays, the newly created replcas gradually become redundant and only contrbute lttle to the forwardng performance. 3.2 Trace Studes We nvestgate the characterstcs of forwardng redundancy n the traces lsted n Table 1. In each experment, a message s generated wth random source and destnaton over 100 smulaton runs for statstcal convergence. (a) Delvery rato (b) Redundancy percentage Fg. 3. Delvery rato and redundancy percentage n dfferent traces when message s replcated to more relays (a) Delvery rato (b) Redundancy percentage Fg. 4. Delvery rato and redundancy percentage n the Infocom trace wth dfferent utlty functons A warm-up perod s reserved before message s generated, for nodes to collect necessary network nformaton and calculate ther utltes Impact of forwardng redundancy We frst vary the number of message replcas usng the Spray-and-Focus strategy [36] and the utlty functon of CCP [22]. Message lfetme T s adaptvely determned n dfferent traces to ensure that the desgnated number of message replcas s created. As shown n Fgure 3, both delvery rato and redundancy percentage ncrease when more message replcas are created. Ths ncrease s determned by the contact patterns and frequences of moble nodes, whch are trace-dependent. In the MIT Realty trace, when the number of relays s smaller than 3, redundancy percentage s lower than 40%, and each message replca notcably mproves delvery rato by 10%. However, the other TABLE 2 Curve fttng on delvery rato Trace D max m fttng error DeselNet Infocom MIT Realty UCSD

6 6 (a) Correlaton n dfferent traces (b) Correlaton wth dfferent forwardng strateges (c) Correlaton wth dfferent utltes Fg. 5. Correlaton between delvery rato and redundancy percentage. An nflecton pont s found n all cases. 6 message replcas beng created later only mprove delvery rato by another 10%, but ncrease redundancy percentage to 70%. Smlar cases are also found n other traces. These results show that napproprate growth of forwardng redundancy has only lttle contrbuton on forwardng performance but mpars the forwardng effectveness. When more message replcas are created, ncrease of delvery rato shown n Fgure 3(a) s consstent wth our theoretcal expectatons n Secton 3.1. To valdate ths consstency, we perform least-square curve fttng on Fgure 3(a) usng formula E{D k } = D max (1 (1 m) k ) where m = μ c /N, and results n Table 2 show that fttng error s lower than n all cases. Smlar consstency s also found for redundancy percentage by comparng Fgure 3(b) wth Fgure 2(b). In Fgure 4 we also nvestgate the mpact of dfferent utlty functons. Freq and PROPHET lead to lower delvery rato and hgher redundancy because they naccurately measure nodes contact capablty. CCP and Betweenness perform better, especally when more message replcas are created Correlaton Analyss We are also nterested n the correlaton between delvery rato and redundancy percentage. Fgure 5 shows that the two metrcs are closely correlated and ncrease smultaneously when message replcas are beng created. We notce that there s an nflecton pont n each curve n Fgure 5. Delvery rato ncreases faster than redundancy percentage before the nflecton pont and vce versa. Ths result also valdates our expectaton n Theorem 1. As shown n Fgure 5(a), the poston of nflecton pont s manly determned by node contact frequency and s trace-dependent. The poston of nflecton pont also depends on the forwardng strategy and utlty functon beng used. Fgure 5(b) shows that Compare-and-Forward s less effectve and Spray-and-Focus performs better, when CCP s used as the utlty functon. Smlarly, Fgure 5(c) shows that PROPHET and CCP produce more redundancy than Betweenness does, wth the Delegaton forwardng strategy. 4 ELIMINATION In ths secton, we wll elmnate forwardng redundancy from the utltes evaluatng relays contact capablty, so as to prevent ths redundancy from affectng forwardng decson and ensure effcent network resource utlzaton. Our basc dea s to keep track of Cumulatve Relay Informaton (CRI) for each message, whch records the cumulatve contact capablty of relays used for forwardng the message. The defnton of CRI depends on the amount of network nformaton avalable at ndvdual nodes, and wll be descrbed later. When a relay R determnes whether to replcate the message to node A, R compares the contact capablty of A wth the current CRI of the message, and checks whether nodes contacted by A have also been contacted by other relays. If so, ths redundancy s elmnated from A s utlty, so that A s utlty reflects ts actual contrbuton on forwardng the message. Moreover, when replcas of multple messages are forwarded to A wth lmted resources, ther prortes are also determned by A s utlty after redundancy elmnaton. We frst focus on elmnatng forwardng redundancy wth complete CRI at the global scope, and then extend ths scheme to be dstrbuted wth ncomplete CRI mantaned at ndvdual relays. Impact of ths ncompleteness to redundancy elmnaton s analyzed and addressed from varous perspectves. 4.1 Redundancy Elmnaton wth Global CRI We frst assume that each node knows the global CRI. In practce, ths nformaton can be provded va a specfc backend server, whch mantans CRI and connects to nodes va 3G or satellte lnks 5. The global CRI mantans 5. These communcaton lnks are generally expensve and have only lmted bandwdth. Hence, they cannot be used for forwardng messages.

7 7 a quantty C (k) for each node, whch ndcates the cumulatve capablty of the current k relays contactng node. C (0) =0for. Each tme when the message s replcated to another relay R k+1, C (k) for each non-relay node s updated as C (k+1) = f(c (k),c (k+1) ), (7) where c (k+1) s the capablty of R k+1 contactng, and s evaluated when the message s replcated to R k+1 wthout beng changed n the future. f( ) s a utltydependent functon wth the followng propertes: Monotoncty. For k [1,N], C (k+1) C (k). Convexty. For k [1,N], C (k+1) C (k) + c (k+1). Forwardng redundancy caused by R k+1 on node s dentfed as the dfference between C (k+1) and C (k) + c (k+1). Hence, after redundancy elmnaton, the utlty of R k+1 for forwardng ths message s calculated as U k+1 = N =1 (C(k+1) C (k) ), (8) whch ndcates the actual contrbuton of R k+1 on forwardng the message nstead of N =1 c(k+1).wedesgn f( ) for observatonal and probablstc utlty functons, respectvely Observatonal Utltes For observatonal utltes ncludng Freq, ElapsedTme and Betweenness, the contrbuton of c (k+1) to C (k+1) s reduced by the rato between c (k+1) and C (k) + c (k+1),.e., C (k+1) = C (k) + C (k) c (k+1) + c (k+1) c (k+1). (9) Eq. (9) can be nterpreted n varous ways when beng appled to dfferent utlty functons. For Freq, the chance for R k+1 to provde useful contact capablty to node s proportonally reduced due to the exstng contact capablty C (k). Ths reducton also apples to ElapsedTme, because the recprocal of elapsed tme snce last contact equvalently measures contact frequency by assumng statonary contact process. For example, f two relays A and B contact node wth the frequency 2 and 8 respectvely, the cumulatve C (2) = = 8.4 accordng to Eq. (9). For the thrd relay C contactng wth the frequency 6, C (3) = =10.9. For Betweenness, c (k+1) measures the number of nodes whch can communcate wth node va R k+1. Betweenness n opportunstc moble networks s usually calculated n an ego-centrc manner [17]. Forwardng redundancy exsts when the neghborhood of R k+1 on NCG overlap wth that of other relays, and hence can be calculated smlarly usng Eq. (9). (a) Network contact graph. Numbers on the edges are the parwse contact probabltes. (b) Message replcaton. Numbers n the brackets ndcate nodes probablstc utltes Fg. 6. The mpact of redundancy elmnaton n Eq. (10) to forwardng decson wth Delegaton strategy Probablstc Utltes For probablstc utltes ncludng PROPHET and CCP, c (k+1) s the probablty for R k+1 to contact. We assume that the contact process of each relay s ndependent, and C (k+1) =1 k+1 j=1 (1 c(j) ). Hence, C (k+1) =1 (1 C (k) ) (1 c (k+1) ). (10) The mpact of redundancy elmnaton on forwardng decson s llustrated n Fgure 6. The utltes of B and C are reduced by nearly 50% after ther redundancy of contactng G, J and K has been elmnated, and hence wll not be used as relays due to ther low utltes. Instead, A replcates message to F whch s effectve to contact more dstnct nodes and has more contrbuton on forwardng the message. 4.2 Dstrbuted Elmnaton When the global CRI s unavalable, each relay mantans CRI n a dstrbuted manner 6, only based on ts local nformaton about ts neghbors on NCG. Due to the lack of end-to-end network connectvty, the CRI mantaned at relays may be ncomplete and partally overlap wth each other. For example, n the network shown n Fgure 6, node J s contacted by three relays A, B and C. The CRI about node J mantaned at B ncludes capablty of A and B contactng J, but the CRI mantaned at C only ncludes that of A and C. Due to ths possble overlappng, relays need to merge ther mantaned CRI when they contact, and the quantty C (k) s nsuffcent for mantanng CRI n a dstrbuted manner. In the above example, t s dffcult for relays B and C to correctly dentfy ths overlappng and merge ther CRI to calculate the cumulatve capablty of A, B and C contactng J. In ths case, CRI s mantaned n a more fne-graned level. A relay mantans a lst for each non-relay node, and the lst records the capablty c (j) of each relay R j contactng. WhenrelaysB and C n Fgure 6 contact each other, ther lsts are merged to correctly calculate 6. A relay ntalzes ts CRI as ts own contact capablty.

8 8 Fg. 7. Dstrbuted mantenance of CRI based on the network n Fgure 6 (a) Incomplete CRI at relays. Relays receve message replcas from ther parents, and are ndexed by ther tme recevng message replca. (b) R 7 : false postve error, R 8 : false negatve error. Numbers at the nodes ndcate relays probablstc utltes. Fg. 8. Incompleteness of CRI and ts mpact on forwardng decson. Delegaton strategy s used. CRI of node J based on Eqs. (9) or (10), and ths process s llustrated n Fgure 7. The amount of storage space for mantanng CRI s related to the number of relays, whch s much smaller than the number (N) of nodes n the network. For example, the requred space s O(N (log N) 2 ) when Delegaton strategy s used R R R R R R R R Accuracy Analyss and Improvement When CRI s mantaned n a dstrbuted manner, accuracy of redundancy elmnaton may be mpared due to ncompleteness of CRI. Ths ncompleteness appears when a relay s unaware of some other exstng relays, and s llustrated n Fgure 8(a) whch descrbes forwardng process as a Message Replcaton Tree (MRT). Wthout loss of generalty, we assume that communcaton lnks among R 1,..., R k 1 have broken when message s replcated to relay R k. In Fgure 8(a) when message s replcated from R 3 to R 7, R 7 knows R 2 because R 2 receves message replca earler from R 1 whch s also the parent of R 3 on MRT, but R 7 s unaware of the exstence of R 4 and R 5 because the lnk between R 1 and R 2 has broken. Smlarly, nether R 4 nor R 5 knows R 3, R 6 and R 7. Defnton 2: The Blnd Zone (BZ) B R (t) of a relay R at tme t s defned as a set of relays whch receve message replca before tme t, suchthatarelayr j B R (t) f R s unaware of the exstence of R j at tme t. The BZs of relay R 5 and R 7 are ndcated by dashed crcles n Fgure 8(a). Based on ths defnton, ncompleteness of CRI at tme t s measured by average sze of relays BZ as I k = 1 k k =1 B R (t), wherek s the number of relays. Ths ncompleteness of CRI may cause false postve and false negatve errors to forwardng decson. Frst, R 5 and R 7 n Fgure 8(b) contact node A wth probablty 0.5 and 0.6, and the actual utlty of R 7 should be 2.2 nstead of 2.5 accordng to Eq. (10). When Delegaton strategy s used, R 7 should not receve message replca from R 3 because R 6 becomes relay earler and 2.3 > 2.2. Hence, R 7 s a false postve error. Second, R 3 ncorrectly consders that R 7 has the hghest utlty of 2.5 among Fg. 9. MRTs wth 6 relays and dfferent combnatons of (N R,K R ) exstng relays. Ths prevents R 8 from becomng a relay and leads to a false negatve error. We propose two alternatve schemes to address these errors and mprove the accuracy of redundancy elmnaton. Frst, we pre-regulate the forwardng process before message s actually replcated to relays, so as to reduce the chance for errors to occur. Second, we opportunstcally adjust relays after they receve message replcas, when the errors are detected Pre-regulaton of Forwardng Process ArelayR k s nevtably blnd to relays whch receve message replca later and not from R k tself. Hence, we focus on ensurng that R k knows all the relays R 1,..., R k 1,.e., B Rk (t) = B Rk (t) {R 1,..., R k 1 } =0 for t T k,wheret k s the tme R k receves message replca. Ths s acheved by regulatng forwardng process represented by MRT. B Rk (t) s controlled by two parameters N R and K R. N R s the maxmum number of non-leaf relays at each level of MRT. We let the non-leaf relays at a level of MRT have larger ndces than any leaf relay at the same level, and only allow the non-leaf relays to replcate message and produce new relays. K R s the maxmum number of new relays that a non-leaf relay can produce, and we lmt that K R N R.MRTswth(N R,K R ) from (1, 1) to (2, 2) are llustrated n Fgure 9. Lemma 2: B Rk (t) =0for k 1 when N R =1. Proof: We prove ths lemma by nducton over levels of MRT.

9 9 Step 1: f R k s at the frst level, k =1and R 1 s the source node. The lemma smply holds. Step 2: we suppose that the lemma holds for all the relays at the j-th level. Snce N R =1,alltherelaysat the (j +1)-th level receve message replca from the same parent R (j) at the j-th level. For R k at the (j +1)-th level, ) t knows all the relays at the upper levels from R (j) because B R (j)(t) =0, ) t knows all the relays at the (j +1)-th level wth smaller ndex because they also receve message replca from by R (j). The lemma hence also holds for R k at the (j +1)-th level. Ths lemma s proved by combnng Steps 1 and 2. From Lemma 2, we mmedately have the followng theorem consderng that B Rk 1 (t) = B Rk (t) =0. Theorem 2: When N R = 1, I k = (k 1)(k 2) 2k for any 2 K R 1. I k ncreases wth K R when N R > 1. Non-leaf relays usually have the best capablty contactng other nodes and determne whch node to be the next non-leaf relay, so to ensure that a suffcent number of message replcas are created Posteror Adjustment of Relays The aforementoned pre-regulaton may prevent some relays from recevng message replca and affect forwardng performance. Another way s to adjust the relays n a posteror manner, when the false postve and false negatve errors are detected. These errors are detected opportunstcally when relays contact each other and update ther mantaned CRI. ArelayR k autonomously revokes tself by removng ts message replca, when t detects tself as false postve. For ths detecton, R k memorzes the stuaton at tme T k when t receved message replca. Each tme when R k contacts another relay and updates ts CRI, t recalculates ts utlty at tme T k. The false postve error s detected when R k realzes that t should not be a relay wth the new utlty. In Fgure 8(b), R 7 fnds that ts utlty should be 2.2 nstead of 2.5 when t contacts R 5,and realzes tself as false postve. After R 7 revoked tself, R 5 s responsble for notfyng other relays to remove R 7 s nformaton from ther mantaned CRI. Fgure 8(b) shows that a false negatve error only happens after a false postve error. After relay R 7 revokes tself, the false negatve error on R 8 s detected untl R 3 or R 8 s notfed about the revocaton of R 7.SnceR 3 may not be n contact wth R 8 by then, R 3 spreads the nformaton about ths error among exstng relays, so that R 8 receves message replca f t contacts any relay beng aware of ths false negatve error. In general, the delay for the errors to be corrected s determned by both the network scale and node contact pattern. Snce the selected relays have good capablty contactng other nodes, ths delay s expected to be much shorter than the nter-contact tme among moble nodes. 4.4 Local Allocaton of Relay Resources A relay has only lmted local resources. When replcas of multple messages are forwarded to a relay, ts resources should be allocated to the approprate message replcas. Such problem of local resource allocaton has been studed n [2], but wth the assumpton that each message has equal sze. Instead, we propose a generalzed soluton based on the relays utltes after redundancy elmnaton. When replcas of M messages wth szes s 1,..., s M are forwarded from relay R 1 to relay R 2 wth buffer sze B, the problem of resource allocaton at R 2 s formulated as max M (k) U k=1 2 x k s.t. M s kx k B, (11) k=1 where x k {0, 1} ndcate whether the k-th message replca s forwarded to R 2, and U (k) 2 s utlty of R 2 defned n Eq. (8) for forwardng the k-th message. Note that the forwardng redundancy between the exstng relays (ncludng R 1 ) and R 2 for forwardng the k-th message has been elmnated from U (k) 2. Eq. (11) ensures that R 2 s resources are allocated to the approprate message replcas, such that R 2 has the most contrbutons on forwardng these messages. In practce, snce B and s k n Eq. (11) are usually ntegers n numbers of bytes, Eq. (11) can be solved n pseudo-polynomal tme O(M B) usng a dynamc programmng approach [31]. Due to the lmted channel bandwdth and contact duraton, R 1 may not be able to transmt all the message replcas selected by Eq. (11) to R 2 before the contact ends. The order for message replcas to be transmtted follows ther order beng selected when solvng Eq. (11) usng dynamc programmng, due to the property of optmal substructure of Eq. (11). 5 EXPLOITATION Elmnaton of forwardng redundancy mproves the effectveness of network resource utlzaton and enhances the cumulatve forwardng performance, but the specfc performance requrements for forwardng ndvdual messages may not be satsfed due to the reduced number of message replcas beng created. The examples of such applcatons nclude emergency notfcaton, whch requre relable and tmely message delvery and have strct requrement on delvery rato. In ths secton, based on the capablty of elmnatng forwardng redundancy, we develop adaptve forwardng strategy to explot such redundancy and satsfy the delvery rato requred by each message wth the mnmum number of message replcas. We replcates messages based on relays utltes after redundancy elmnaton, and adaptvely controls the amount of forwardng redundancy accordng to the requred delvery rato and up-to-date network condton.

10 10 Q R U A of relays needed at tme t c for achevng D and N R s the estmated number of relays that can receve message replca durng tme perod (t c,t]. Weproposeeffectve heurstcs to estmate both N R and N R at ndvdual relays, and also explot perodcty of relays contact capablty for more accurate control of α. Q R <U A 5.2 Heurstcs (a) Comparson-based forwardng strategy (b) Dynamc values of α wth requred delvery rato D =80% Fg. 10. Explotaton of forwardng redundancy 5.1 Basc Methodology When a relay R determnes whether to replcate a message to another node A, most of current forwardng strateges can be summarzed as a unform comparsonbased framework shown n Fgure 10(a). R compares a local quantty Q R whch s called forwardng threshold wth A s utlty U A for forwardng the message, and only replcates the message to A f Q R <U A.Dfferent strateges vary n Q R they use. Compare-and-Forward mantans Q R as utlty of R, and n Delegaton Q R s the hghest utlty among all the relays that R s aware of. In all the strateges, the method of calculatng and updatng Q R s fxed durng forwardng process. Our basc dea for controllng the amount of forwardng redundancy s to adaptvely adjust Q R at each relay R by multplyng Q R wth a parameter α, as llustrated n Fgure 10(a). We assume that message s generated at tme 0 and expres at tme T.Asaresult,α at tme t c T s determned by the estmated delvery rato D(t c ) that relays at t c can acheve at T, and the remanng tme T t c for forwardng the message. Ths explotaton s llustrated n Fgure 10(b). Ideally, more relays receve message replcas when t c elapses and gradually mprove D(t c ) to the requred delvery rato D before T,sothatα 1. However, n practce the ncrease of D(t c ) maybedfferentduetothespecfc network contact pattern, and we adjust α accordngly to approxmate D(t c ) to the deal case. In Case 1 shown n Fgure 10(b) where D(t c ) at tme t c <T/2salready close to D, α ncreases to avod redundant relays. In Case 2 where D(t c ) s too low, α decreases to ensure that there s a suffcent number of relays to acheve D. Note that we mnmze the number of relays used to acheve D based on relays utltes after redundancy elmnaton. Otherwse, wthout redundancy elmnaton n Secton 4, D can stll be acheved by reducng α but the number of relays ncreases due to forwardng redundancy among relays. Moreover, ncreasng α or usng fewer relays does not necessarly reduce the amount of forwardng redundancy n the network. The value of α s calculated based on the CRI mantaned at tme t c and s used to estmate D(t c ). We calculate α as N R /N R,whereN R s addtonal number Estmatng N R N R s determned by CRI mantaned at tme t c. Suppose there are k relays a tme t c, D(tc ) = 1 N N =1 C(k) where C (k) s the cumulatve capablty of the k relays contactng node. From Secton 3 we know that the ncrease of actual delvery rato over k can be modeled as ED k = D max (1 (1 m) k ). Each tme when we have anewrelayr k, we update the parameters D max and m by least-square curve fttng over the estmated D(t c ), and N R s calculated as D D max ) N R = ln(1 ln(1 m) k Estmatng N R We estmate N R based on the ntervals T between the tmes that the -th and ( +1)-th relays receve message replca, and we propose two alternatves of heurstcs for such estmaton. The frst heurstc s based on the observaton n Fgure 13(b) that T generally ncreases wth. We estmate the next tme nterval T k+1 = max T, and N R = 1 k (T t c )/T k+1. Another alternatve s to model the varaton of T as an Auto-Regressve (AR) process wth the order of p (p < k). A p-order AR process s defned as p T k = φ T k + ε k, (12) =1 where φ 1,..., φ p are the parameters and ε k s whte nose. Based on T n the past, these parameters can be estmated ether va least-square regresson or usng Yule-Walker equatons [4]. NR can be estmated by recursvely calculatng these tme ntervals n the future, untl N R =k+1 T T t c. N R estmated by AR process s generally more accurate, but also requres more nformaton of T to estmate parameters n Eq. (12). In practce, the frst alternatve s used for estmatng N R durng ntal stage of forwardng, and s swtched to AR process after there are at least p +1 relays. 5.3 Explotaton of Perodcty The contact patterns among moble devces are related to human behavors, and lead to perodcty of forwardng performance and redundancy at varous tme scales. We

11 11 (a) DeselNet (b) Infocom (c) MIT Realty (d) UCSD Fg. 11. Perodcty of delvery rato and redundancy percentage. The perodcty n the DeselNet and Infocom traces s at daly scale, and that n the MIT Realty and UCSD traces s at weekly scale. TABLE 3 Parameters of perodcty of delvery rato Trace T p A μ σ error DeselNet Infocom MIT Realty UCSD explot such perodcty for more accurate control of forwardng redundancy. We frst nvestgate such perodcty n real-world traces. We dvde each trace nto 100 peces wth equal tme length, generate message at the begnnng of each pece, and nvestgate delvery rato and redundancy percentage at the end of pece. Ths perodcty s shown n Fgure 11, wth Delegaton and Betweenness used for forwardng decson. Perodcty of delvery rato s approxmated by perodc functon G(t) =G(t mod T p ), where T p s ts perod and G(t) =A e (t μ)2 σ 2 s Gaussan functon. Parameters of G(t) are lsted n Table 3, where T p and μ are n number of days. Table 3 exhbts perodcty of relays contact capablty and motvates us to adjust Q R accordng to transent contact capablty of relays durng tme perod [t c,t]. For example, n the DeselNet and Infocom traces, nodes contact each other more often durng daytme and have hgher chances to be used as relays. Q R should be ncreased accordngly to reduce the amount of forwardng redundancy. In contrast, Q R should decrease durng nghttme when node contact capablty s low. Our basc dea s to apply an addtonal coeffcent β beng multpled to parameter α, andβ s calculated by comparng the transent contact capablty of relays durng [t c,t] wth ther cumulatve contact capablty. Based on the Gaussan formulaton of perodcty descrbed above, β s calculated as T β = 2T p Aσ π 1 G(t)dt, (13) T t c t c where Aσ π/(2t p ) ndcates cumulatve contact capablty of relays, because T p. G(t)dt = Aσ π/2 when 0 G(k T p ). =0for k 0. In practce, parameters of G(t) are estmated based on D(t c ), whch s calculated from the mantaned CRI. 6 PERFORMANCE EVALUATION In ths secton, we evaluate the performance of our redundancy elmnaton schemes, usng the realstc moble network traces lsted n Table 1. The frst half of each trace s used for nodes to collect network nformaton and all the messages are generated at randomzed tmes afterwards. We assume that the channel bandwdth s 1 Mbps (Bluetooth v1.2), and the message sze s unformly dstrbuted n [10Mb,50Mb]. As reported n [18], most of contacts n the traces we use last long enough to transmt at least one message replca. The buffer sze of nodes s unformly dstrbuted n [50Mb,500Mb] so that each node can carry at least one message replca. 6.1 Performance of Redundancy Elmnaton We frst evaluate the performance of redundancy elmnaton wth global and dstrbuted CRI. We generate a message every hour wth random source and destnaton, and the evaluaton results over all the messages are shown n Fgure 12, where Betweenness and CCP are used to represent observatonal and probablstc utlty functons, respectvely. Fgure 12(b) shows that our schemes effectvely elmnate forwardng redundancy by more than 50%. Ths elmnaton enables effectve utlzaton of the relays resources, and hence leads to 20% mprovement of the cumulatve delvery rato and 40% reducton on the forwardng cost 7. Note that the contact capabltes of selected relays after redundancy elmnaton may stll overlap, but ths remanng redundancy s very lmted compared to the useful contact capablty provded by relays. Fgure 12 also shows the mpact of CRI ncompleteness to redundancy elmnaton and forwardng performance. When CRI s mantaned n a dstrbuted 7. We consder the overhead of mantanng CRI as neglgble because t only happens when relays contact and the sze of CRI metadata s very small compared wth the messages beng forwarded.

12 12 (a) Delvery rato (b) Redundancy Percentage (c) Number of replcas created per message Fg. 12. Performance of redundancy elmnaton wth global and dstrbuted CRI. Compare-and-Forward strategy s used n the MIT Realty trace. Our schemes elmnate forwardng redundancy by more than 50%, and mprove the cumulatve delvery rato by 20% wth 40% less cost n number of replcas created per message. (a) Change of relays utltes (b) Intervals of message replcaton (a) BZ szes n dfferent traces (b) BZ szes n MIT Realty trace Fg. 13. Detaled effects of redundancy elmnaton Fg. 14. Average BZ sze of relays manner at ndvdual relays, the CRI ncompleteness ncreases redundancy percentage by 10%, and leads to 20% ncrease of forwardng cost. We also evaluated values of relays utltes and ntervals of message replcaton after redundancy elmnaton, as shown n Fgure 13. For each message, we use the utlty and replcaton nterval of the frst relay for normalzaton. We observe that relays utltes after redundancy elmnaton are reduced by up to 40%, and ths s the major reason for reducton of forwardng cost shown n Fgure 12(c). It also takes longer tme for each message to be replcated. 6.2 Effectveness of Accuracy Improvement As dscussed n Secton 4.3, the accuracy of redundancy elmnaton may be mpared due to CRI ncompleteness at ndvdual relays. Varous technques have been proposed n Secton 4.3 to detect and correct the possble errors durng redundancy elmnaton. Such CRI ncompleteness, whch s measured by average sze of relays BZ, s shown n Fgure 14 wth Compare-and-Forward and CCP used for forwardng decson. Fgure 14(a) shows that the average BZ sze can be up to 35%. We also evaluate the effects of pre-regulaton of forwardng process on reducng the average BZ sze, and the results are shown n Fgure 14(b). As expected by Lemma 2, the average BZ sze s reduced by up to 50% when N R =1, but ncreases when N R or K R ncreases. The performance of error detecton and correcton schemes proposed n Secton 4.3 are evaluated n Fgure 15. Fgure 15(a) shows that the majorty of errors s false postve, and false negatve errors are only notceable when many message replcas are created. Our schemes can effectvely detect both types of errors, and lmt the cumulatve error percentage lower than 10%. Fgure 15(b) also evaluates the delay of error detecton. Obvously ths delay s closely related wth data lfetme. When data lfetme s set as 1 week for the MIT Realty trace, Fgure 15(b) shows that both types of errors can be detected and corrected wthn 20% of the data lfetme. Usng the same strategy and utlty functon, the performance of schemes proposed n Secton 4.3 for mprovng the accuracy of dstrbuted redundancy elmnaton s evaluated n Fgure 16. Frst, by comparng Fgure 12 and Fgure 16, we see that posteror adjustment of relays effectvely corrects errors durng dstrbuted redundancy elmnaton, and mproves forwardng performance to the level of global elmnaton. Second, Fgure 16(b)

13 13 (a) Delvery rato (b) Redundancy Percentage (c) Number of replcas created per message Fg. 16. Performance of mprovng the accuracy of dstrbuted redundancy elmnaton n the MIT Realty trace (a) Performance of error detecton (b) Error detecton delay (a) Dfferent T wth D =50% (b) Dfferent D wth T =24hours Fg. 15. Performance of error detecton n MIT Realty trace. Data lfetme s set as 1 week (168 hours). shows that pre-regulaton of forwardng process furthermore reduces forwardng redundancy over 10%, but t also prevents some relays from recevng message replca and reduces delvery rato by 3%. Fgure 16 ndcates that the two schemes have dfferent tradeoff between forwardng performance and redundancy, and should be used accordng to the specfc applcaton scenaro and requrements. 6.3 Performance of Redundancy Explotaton We frst evaluate values of α n practce, and the results n Fgure 17 show that values of α are proportonal to T.WhenT ncreases to 48 hours, the average value of α ncreases over 100%. We notce that values of α are generally lower than 1 when T 12 hours, whch means that more relays are needed to acheve D durng the short message lfetme. In contrast, when T =48hours, α quckly ncreases to avod redundant relays. Smlarly, Fgure 17(b) shows that hgher D reduces α so that more relays can be used for forwardng the message. For evaluatng the performance of our proposed forwardng strategy, we use the same experment settngs as n Secton 6.1. The requred delvery rato for each message s unformly dstrbuted n [0.5D avg, 1.5D avg ], and D avg vares n our experments. The evaluaton Fg. 17. Values of α for achevng the requred delvery rato D n Infocom trace. Delegaton and CCP are used for forwardng decson. results are shown n Fgure 18 where Delegaton and CCP are used for forwardng decson. When D avg =40% and T 12 hours, our strategy creates more message replcas to ensure that the requred D can be acheved. When T ncreases, our strategy avods redundant relays and acheves D wth 40% less relays. Comparatvely, when D avg =70%, redundancy percentage ncreases to create more message replcas. Fgure 18(a) shows that the actual delvery rato only acheves 65% due to lmted node contact capablty. In ths case, our strategy ensures that best-effort forwardng performance s provded. 7 RELATED WORK The research on data forwardng n DTNs orgnates from Epdemc routng [38] whch floods the entre network. Later studes develop data forwardng strateges to approach the performance of Epdemc routng wth lower forwardng cost, whch s measured by the number of data copes created n the network. Whle the most conservatve approach always keeps a sngle data copy and Spray-and-Wat [35] holds a fxed number of data copes, most schemes leave such numbers as dynamc and make data forwardng decson by comparng the

14 14 (a) Delvery rato (b) Redundancy Percentage (c) Number of replcas created per message Fg. 18. Performance of explotng forwardng redundancy n the Infocom trace. When D avg =40%, we furthermore reduce the amount of forwardng redundancy as well as the forwardng cost. When D avg = 70%, the amount of forwardng redundancy ncreases to create more message replcas and provdes best-effort forwardng performance. nodes utlty functons. Representatve strateges nclude Compare-and-Forward [11], [14], Delegaton [15] and Spray-and-Focus [36], whch were exploted when studyng forwardng redundancy n ths paper. Other forwardng strateges [37], [39], [8], [29] also am to acheve varous tradeoffs between the data forwardng performance and cost. The utlty functons of moble nodes, whch measure the nodes contact capabltes, are generally ndependent from the data forwardng strateges mentoned above [20]. Varous utlty functons can be appled to the same forwardng strategy for dfferent performance requrements. Some schemes predct node contact capablty by estmatng ther co-locaton probabltes n dfferent ways, such as the Kalman flter [9] and sem- Markov chans [40]. In some other schemes, node contact pattern s exploted as abstracton of node moblty pattern for better predcton accuracy, based on the expermental [7], [27] and theoretcal [6] analyss on the node contact characterstcs. Such node contacts are detected va energy-effcent perodc probng methods [1], [21], [24], and the detected contact hstory s then used to predct the nodes capablty of contactng others n the future. MaxProp [5] estmates the node contact lkelhood based on the contact counts n the past, and PodNet [28] forwards data to nodes based on ther receved data queres n the past. Socal propertes of human moblty ncludng centralty and communty structures are also exploted for forwardng messages [25], [22]. SmBet [10] uses egocentrc betweenness as relay selecton metrc, and BUB- BLE Rap [25] consders node centralty herarchcally n socal communty structures. [22] exploted both centralty and socal communtes for multcastng, and proposed Cumulatve Contact Probablty (CCP) as the utlty functon for data forwardng based on the cumulatve node contact rates and the assumpton of exponental dstrbuton of parwse node nter-contact tme. Such CCP metrc was also used n ths paper. [19] furthermore extends CCP to the mult-hop network scope. Socal communty structure n opportunstc moble networks, on the other hand, s usually used to determne the network scope for evaluatng node centralty, and can be detected n a fully dstrbuted manner n varous ways [26]. k-clque-based [34] method enables the detecton of overlappng communtes, and modulartybased method [33] works on weghted network contact graph. Based on such communty detecton technques, BUBBLE Rap [25] exploted socal communty structures for data forwardng n opportunstc moble networks based on the cumulatve node contact characterstcs. Node centralty s evaluated at varous network scopes accordng to the communty boundary of the destnaton, and data s hence forwarded n a herarchcal manner. 8 CONCLUSIONS In ths paper, we study forwardngredundancynopportunstc moble networks, whch may serously mpar the forwardng performance. We nvestgate ts characterstcs from both theoretcal and expermental perspectves, and propose effectve schemes to elmnate ths redundancy wth lmted network nformaton. We furthermore explot ths redundancy adaptvely to satsfy specfc performance requrements of moble applcatons. Extensve trace-drven smulatons show that our schemes effectvely mprove forwardng performance wth much lower cost. REFERENCES [1] M.Bakht,M.Trower,andR.H.Kravets. Searchlght:Won tyou be my neghbor? In Proceedngs of the 18th annual nternatonal conference on Moble Computng and Networkng (MobCom), pages ACM, [2] A. Balasubramanan, B. Levne, and A. Venkataraman. DTN Routng As a Resource Allocaton Problem. In Proceedngs of SIGCOMM, [3] A. Balasubramanan, R. Mahajan, A. Venkataraman, B. Levne, and J. Zahorjan. Interactve wf connectvty for movng vehcles. In Proceedngs of ACM SIGCOMM, pages , [4] G.Box,G.M.Jenkns,andG.C.Rensel. Tme Seres Analyss: Forecastng and Control. Prentce-Hall, 3rd edton, 1994.

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Hero: A home based routng n pocket swtched networks. In Wreless Algorthms, Systems, and Applcatons (WASA), pages [40] Q. Yuan, I. Carde, and J. Wu. Predct and relay: an effcent routng n dsrupton-tolerant networks. In Proc. MobHoc, pages , member of the IEEE. of the IEEE. We Gao receved the BE degree n electrcal engneerng from the Unversty of Scence and Technology of Chna n 2005 and the PhD degree n computer scence from the Pennsylvana State Unversty n He s currently an assstant professor n the Department of Electrcal Engneerng and Computer Scence at the Unversty of Tennessee, Knoxvlle. Hs research nterests nclude wreless and moble network systems, moble socal networks, moble cloud computng, and cyber-physcal systems. He s a Qnghua L receved the BE degree from Xan Jaotong Unversty, the MS degree from Tsnghua Unversty, and the PhD degree from The Pennsylvana State Unversty. In 2013, he joned the Unversty of Arkansas, where he s currently an Assstant Professor n the Department of Computer Scence and Computer Engneerng. Hs research nterests are securty and prvacy n networkng and computng systems ncludng moble sensng, smart grd, moble cloud computng, and healthcare systems. He s a member Guohong Cao receved the BS degree n computer scence from Xan Jaotong Unversty and receved the PhD degree n computer scence from the Oho State Unversty n Snce then, he has been wth the Department of Computer Scence and Engneerng at the Pennsylvana State Unversty, where he s currently a Professor. Hs research nterests nclude wreless networks, wreless securty, vehcular networks, wreless sensor networks, cache management, and dstrbuted fault tolerant computng. He has served on the edtoral board of IEEE Transactons on Moble Computng, IEEE Transactons on Wreless Communcatons, IEEE Transactons on Vehcular Technology, and has served on the organzng and techncal program commttees of many conferences, ncludng the TPC Char/Co-Char of IEEE SRDS 2009, MASS 2010, and INFOCOM He was a recpent of the NSF CAREER award n He s a Fellow of the IEEE.