Quantifying Content Consistency Improvements Through Opportunistic Contacts

Transcription

1 Unversty of Pennsylvana ScholarlyCommons Departmental Papers (ESE) Department of Electrcal & Systems Engneerng Quantfyng Content Consstency Improvements Through Opportunstc Contacts Kn-Wah Kwong Unversty of Pennsylvana, Augustn Chantreau Thomson Roch A. Guérn Unversty of Pennsylvana, Follow ths and addtonal works at: Part of the OS and Networks Commons, and the Systems and Communcatons Commons Recommended Ctaton Kn-Wah Kwong, Augustn Chantreau, and Roch A. Guérn, "Quantfyng Content Consstency Improvements Through Opportunstc Contacts",. August 29. Proceedngs ACM CHANTS 29 Workshop Bejng, Chna, September 29 Ths paper s posted at ScholarlyCommons. For more nformaton, please contact repostory@pobox.upenn.edu.

2 Quantfyng Content Consstency Improvements Through Opportunstc Contacts Abstract The sharng and dssemnaton of onlne content s one of the man purposes of socal network applcatons, and the amount of content accessed through them, n partcular through portable devces such as smartphones and PDAs, s expected to ncrease. Consumpton of onlne content, however, does not requre a contnuous onlne presence. Content can be downloaded, consumed, modfed, and uploaded at dfferent tmes. An opportunty to mprove a user's access to up-to-date nformaton from ts own socal network s to take advantages of opportunstc contacts between moble devces, \e wthout watng for connectvty to the network nfrastructure. In other words, users of a socal network applcaton may receve more fresh content wth no extra nfrastructure deployment, smply by communcatng wth moble devces of other users, n a delay-tolerant manner. Assessng the magntude of ths mprovement s, however, challengng. For example, the frequency and patterns of such contacts are partly a functon of the socal connectvty of users, and so wll be the avalablty of relevant nformaton to share and more mportantly the wllngness to share that nformaton. All these nfluence n non-trval ways the gans that can be realzed through opportunstc contacts. The paper's man contrbuton s n provdng a quanttatve handle through whch these gans can be estmated, whle accountng for the above factors. Keywords socal networks, delay-tolerant, optmzaton, dssemnaton Dscplnes OS and Networks Systems and Communcatons Comments Proceedngs ACM CHANTS 29 Workshop Bejng, Chna, September 29 Ths conference paper s avalable at ScholarlyCommons:

3 Quantfyng Content Consstency Improvements Through Opportunstc Contacts Kn-Wah Kwong Unversty of Pennsylvana Phladelpha, U.S.A. Augustn Chantreau Thomson Pars, France Roch Guérn Unversty of Pennsylvana Phladelpha, U.S.A. ABSTRACT Contacts between moble users provde opportuntes for data updates that supplement nfrastructure-based mechansms. Whle the benefts of such opportunstc sharng are ntutve, quantfyng the capacty ncrease they gve rse to s challengng because both contact rates and contact graphs depend on the structure of the socal networks users belong to. Furthermore, socal connectvty nfluences not only users nterests,.e., the content they own, but also ther wllngness to share data wth others. All these factors can have a sgnfcant effect on the capacty gans achevable through opportunstc contacts. Ths paper s man contrbuton s n developng a tractable model for estmatng such gans n a content update system, where content orgnates from a server along multple channels, wth blocks of nformaton n each channel updated at a certan rate, and users dffer n ther contact graphs, nterests, and wllngness to share content, e.g., only to the members of ther own socal networks. We establsh that the added capacty avalable to mprove content consstency through opportunstc sharng can be obtaned by solvng a convex optmzaton problem. The resultng optmal polcy s evaluated usng traces reflectng contact graphs n dfferent socal settngs and compared to heurstc polces. The evaluaton demonstrates the capacty gans achevable through opportunstc sharng, and the mpact on those gans of the structure of the underlyng socal network. Categores and Subject Descrptors C.2.1 [Network Archtecture and Desgn]: Wreless communcaton; C.4 [Performance of Systems]: Modelng technques The work of K.-W. Kwong was performed durng an nternshp at Thomson Research, and ts completon was subsequently supported by NSF grant CNS The work of R. Guérn was supported n part by NSF grant CNS Permsson to make dgtal or hard copes of all or part of ths work for personal or classroom use s granted wthout fee provded that copes are not made or dstrbuted for proft or commercal advantage and that copes bear ths notce and the full ctaton on the frst page. To copy otherwse, to republsh, to post on servers or to redstrbute to lsts, requres pror specfc permsson and/or a fee. CHANTS 9, September 25, 29, Bejng, Chna. Copyrght 29 ACM /9/9...$1.. General Terms Algorthms, Performance, Theory Keywords Socal networks, Delay-tolerant networks, Consstency, Dynamc content, Dssemnaton, Optmzaton 1. INTRODUCTION The sharng and dssemnaton of onlne content s one of the man purposes of socal network applcatons, and the amount of content accessed through them, n partcular through portable devces such as smartphones and PDAs, s expected to ncrease. Consumpton of onlne content, however, does not requre a contnuous onlne presence. Content can be downloaded, consumed, modfed, and uploaded at dfferent tmes. An opportunty to mprove a user s access to up-to-date nformaton from ts own socal network s to take advantages of opportunstc contacts between moble devces,.e., wthout watng for connectvty to the network nfrastructure. In other words, users of a socal network applcaton may receve more fresh content wth no extra nfrastructure deployment, smply by communcatng wth moble devces of other users, n a delay-tolerant manner. Assessng the magntude of ths mprovement s, however, challengng. For example, the frequency and patterns of such contacts are partly a functon of the socal connectvty of users, and so wll be the avalablty of relevant nformaton to share and more mportantly the wllngness to share that nformaton. All these nfluence n non-trval ways the gans that can be realzed through opportunstc contacts. The paper s man contrbuton s n provdng a quanttatve handle through whch these gans can be estmated, whle accountng for the above factors. There are many possble metrcs for quantfyng the performance mprovement of content delvery achevable through opportunstc contacts. One possble approach s to consder a generc network metrc that would be relevant to all applcatons: one may hence focus on the addtonal flow capacty provded by ntermttent lnks [7], or consder the tme needed to exchange data between arbtrary pars of users [4]. Unfortunately these metrcs can be both complex to defne and dffcult to nterpret, as ther values vary greatly dependng on the pars of users, the flows or the network load consdered. A dfferent approach, whch s used n the paper, s to defne a specfc applcaton metrc that descrbes drectly the performance of the network to support the requrement of a gven applcaton. The mprovement gath-

4 ered by delay-tolerant communcaton can then drectly be nterpreted n terms closer to users experence, as n a feld test. When t s possble to compute such an applcaton metrc, one can study under whch condtons opportunstc contacts sgnfcantly mprove servces provded by the network. Here, n contrast to other work, we focus on content consstency as ths content s updated over tme. We show that t s possble to accurately measure the benefts of opportunstc contacts accordng to ths applcaton-specfed metrc. Content orgnates at a server and s structured nto dfferent channels. Channels can be thought of as nformaton sources of nterest to some members of a socal network. Channel nformaton s updated accordng to a statonary renewal process, and the server seeks to keep users n sync wth the latest content of each channel, but does so under some capacty lmtatons. The value of channel nformaton to users s a functon of ts relatve age. Users can select whch channel content they are wllng to store as well as whch users they are wllng to share t wth durng opportunstc contacts 1. The benefts derved from opportunstc contacts s measured through a noton of capacty, whch measures the number of users wth access to recent nformaton on channels they are nterested n (e.g., subscrbe to). The paper makes the followng contrbutons: It develops a model for quantfyng the added capacty avalable for content updates through opportunstc contacts n moble networks. The model ncorporates the effect of users socal connectvty and socal behavor n sharng content durng those opportunstc contacts. These are shown to have a sgnfcant mpact on the potental gans achevable from opportunstc contacts. It demonstrates how a capacty-achevng polcy can be explctly constructed by solvng a convex optmzaton problem, and llustrates how ths optmal operatng pont can be realzed usng basc nformaton on users contacts and nterests. Usng actual moblty traces, the capacty benefts of opportunstc contacts to a content update applcaton operatng on cell phones carred by humans are characterzed. The expermental results further demonstrate a sgnfcant effect that users socal behavor, e.g., dfferences n wllngness to share wth other users, can have on overall performance. The rest of the paper s organzed as follows. The next secton gves a bref lterature revew. Secton 3 ntroduces the specfcaton and model of our content update system. It also presents our noton of capacty and establshes that t can be obtaned by solvng a convex optmzaton problem. The content update capacty of some real-lfe opportunstc moble networks s explored n Secton 4, and the optmal polcy s compared to several heurstcs. Secton 5 concludes the paper. 1 Both storage and transmsson of content to other users durng contacts have costs, e.g., memory and battery lfe tme. It s, therefore, mportant to quantfy the resultng gans to users, f only to motvate such opportunstc sharng. Fgure 1: Content update system 2. RELATED WORK Takng advantage of contacts created by moblty for delaytolerant applcatons have recently receved much attenton, typcally for routng (e.g., [1, 6, 2]), and more recently for content dssemnaton (e.g., [14, 5, 3, 12, 9]) and content updates (e.g., [1, 8, 13]). The use of socal behavor to mprove the delvery of nformaton, as n vral marketng [11], has been suggested several tmes [6, 14, 5, 8]. Most of the prevous work reles on a utlty-based crteron to optmze the dssemnaton of nformaton, and usually estmates the resultng benefts usng generc network metrcs such as propagaton delay. In partcular, [8] showed that content update systems could scale better by leveragng peer-to-peer (opportunstc) sharng of nformaton, and t developed optmal dssemnaton strateges for dfferent settngs [8, 1]. Our work shares ths focus on content update systems, but acknowledges the mpact that ndvdual connectvty patterns and sharng behavor can have, and explctly ncorporates ther effect n devsng content update solutons. Furthermore, n contrast to the prevous work, we seek to precsely characterze the benefts (here, content consstency) afforded to applcatons by dfferent opportunstc sharng schemes, ncludng the optmal soluton. Ths calls for a model that accounts for the creaton of content, ts consumpton by dfferent users, as well as users behavor when they are asked to opportunstcally share content. 3. CONTENT UPDATE SYSTEM Content s structured nto a fnte set of channels K, wth a channel dentfed by ts ndex k. The content of channel k Kconssts of a sequence of blocks created by a source and updated over tme. The set of moble hosts 2 s denoted by V. The structure of the overall content update system s shown n Fg. 1 where the arrows among the moble hosts denote ther sharng behavor, e.g., sharng only between users wthn ther communtes or wth smlar nterests. In order to clarfy where the paper dffers from the prevous work, we frst revew the propagaton of a sngle block update through the whole network as captured by the prevous models, e.g., [8]. Next, we extend sgnfcantly ths model to defne a noton of network capacty when content 2 In ths paper, the terms node, user and moble host are synonymous.

5 spans multple blocks and s updated accordng to dfferent statstcs, and users follow dfferent behavor wth regard to content subscrpton and sharng. 3.1 Propagaton of a sngle update block The socal network created among users by ther opportunstc contacts can be used to reduce the age of dynamc nformaton that all of them are nterested to mantan on ther devces. We assume that all the data from a block are over-wrtten whenever a newer block of the same channel s receved. Consequently nodes mantan only the latest block receved on each channel. We assume that blocks are atomc n terms of both content and transmsson,.e., they have a fxed sze denoted by b k (bts) whch may depend on the channel. Furthermore, whole blocks can be exchanged durng connectons wth ether the nfrastructure or other nodes. A more general update model would allow content fragmentaton. Ths adds sgnfcant complexty (partal updates need to be consdered and tracked) that s beyond the scope of ths work. Content provder. Let us assume that an updated block s avalable at the content provder. The provder has a total capacty C (bts per second) avalable for all channel updates. Ths constrans ts ablty to provde all the users wth fresh content, n partcular when a channel s popular. The provder has complete freedom n choosng whch nodes and blocks to update. We rely on a smple randomzed strategy to capture ths flexblty. At each tme slot (of duraton δ seconds), the provder attempts to send the latest block of channel k to node wth probablty δ λ k. Followng a usual assumpton, δ s assumed small enough that the tmes at whch these events occur approach a contnuous tme Posson process wth rate λ k. The capacty lmtaton of the provder mposes that λ k s satsfy λ k b k C V,k K where we recall that b k s the block sze of channel k. Moble hosts. In addton to recevng updates from the provder, moble hosts can also receve updates through opportunstc contacts. We assume that nodes are able to exchange all the blocks for whch one of them has a more recent verson. However, whle those contacts are not bandwdth lmted n our model, other factors mpact the update capacty that can be realzed through them. For example, unlke provder-moble lnks, lnks between moble hosts are only ntermttently avalable, and ther avalablty s a functon of moblty patterns that are unpredctable. We assume that the process descrbng opportunstc contacts between all pars of users (whch can be descrbed as a marked pont process wth marks n V V) s statonary and ergodc. As ths process s drven only by users moblty, t s assumed ndependent of the block update process at the provder. Contacts between dfferent pars of nodes are, however, not assumed ndependent. In order to defne capacty and optmal applcaton performance, we assume that the dstrbuton of ths opportunstc contact process s known. It s possble to fnd optmal applcaton performance from an adaptve algorthm even when ths dstrbuton s unknown (see concluson) but ths s beyond the scope of ths paper. 3.2 Content generaton and sharng For defnng the capacty of an opportunstc network to update content, several mportant dmensons need to be consdered such as content update generaton, users nterests and ther wllngness to share. Those dmensons are dscussed n the followng. Content update generaton. The prevous work, e.g., [8], assumes that content s contnuously updated, so that each new transmsson from the content provder s a new and fresher block for ths partcular channel. The mportance of ths content (or utlty measurng a user s satsfacton) s then assumed to be a functon of the propagaton delay only. In practce, however, updates are lkely to occur at fnte ntervals of tme that vary across channels. Moreover, the satsfacton of a user depends on the relatve age of the content: a block that s an hour old may be very relevant f content for ths channel s updated everyday, but less so f new content s created every mnute. To deal wth ths ssue, we dffer from the analyss of [8] n two ways: Frst, we assume that blocks of a sngle channel are updated accordng to a statonary renewal process. We assume that ths occurs ndependently of opportunstc contacts and transmsson from content provder. However, we do not assume that the processes of updates between dfferent channels are ndependent. Ths already allows varous scenaros. For example, a determnstc, perodcal update process, a Posson update process, or even update processes wth heavy taled statstcs where most updates occur n bursts and there can exst a long perod wthout updates. Second, we assume that the satsfacton of users s not a functon of the propagaton delay of ther content, but rather a functon of the consstency of ther content wth respect to recent updates (see Secton 3.3). Content nterest and sharng. The prevous work, e.g., [8], only focused on a sngle block that all nodes wsh to receve and are wllng to share wth others. In practce, popularty of dfferent channels vares greatly and power, memory, as well as trust lmtatons affect users wllngness to arbtrarly exchange blocks. Update exchanges typcally take place only between users who trust each other. It s mportant to ncorporate such factors when assessng the capacty avalable from opportunstc contacts. We ntroduce the N K nterest matrx A as: { 1 f node s nterested n channel k, A,k = otherwse. The N N sharng matrx B k for channel k s: 1 f, whenever a contact (, j) occurs, B,j k blocks from channel k can be sent = from to j, otherwse. Note that B k,j = 1 f and only f and j are nterested n channel k (.e., A,k = A j,k =1), agrees to transmt a block to j durng an opportunstc contact, and j agrees to receve a block from. Ths allows us to consder arbtrary content sharng patterns, e.g., a network where all nodes agree to store and

6 forward all blocks, a network wth a subset of selfsh nodes who may store and not forward blocks to others, a network wth cautous nodes who only receve blocks from a subset of nodes they trust. 3.3 Defnton of capacty The goal of ths paper s to offer an effectve estmate of the capacty mprovements that opportunstc contacts can offer, as well as how to realze those mprovements. The frst step towards realzng ths goal s to ntroduce a precse defnton of capacty for such a content update system. Consstency-based utlty. We do so by way of a utlty functon that expresses users satsfacton. For smplcty, we assume that for every channel k Kthe utlty of the content assocated wth channel k at node s gven by the followng bnary varable: 1 f node s nterested n channel k, U k (t) = and t has the latest block at tme t, otherwse. U k (t) measures the satsfacton of a user n the sense that how much tme the user has the latest content for channel k. There are many possble extensons to ths basc utlty functon, e.g., utlty could be a non-ncreasng functon of the block versons (score 1 f the node has the latest block, score 1/2 f t has the second latest, etc.). These dfferent extensons can stll be handled usng the convex optmzaton formulaton developed n the paper, but t becomes much harder to extract nsght from ther behavor. For ths reason, we concentrate on the above smple bnary consstency functon for the rest of the paper. Capacty regon. We can now formulate an ntutve defnton of the capacty regon of a content update system. Let u k = E [ U k (t) ] [, 1] whch measures the fracton of tme node has the latest block created for channel k (or, equvalently, the probablty that ths occurs n steady state). One can say that a vector (f k ) k K n [, 1] K s nsde the capacty regon of the system f there exst parameters (λ k ) V,k K such that for any and k, the expected fracton of nterested nodes that hold the latest blocks on channel k s at least f k. Of course, a dffcult part s to fgure out how λ k can be chosen to test ths assumpton. The measure u k corresponds to the utlty of the system from the user s pont of vew (for channel k). The boundary of ths network capacty regon can be generally expressed by consderng any non-decreasng concave functon φ : R V K R and then solvng the followng optmzaton problem CAP: maxmze λ k, V,k K subject to φ ( ( ) u k V,k K V,k K ), λ k b k C The functon φ of all users utltes denotes the utlty of the system not from a user s pont of vew, but as a whole. Theorem 3.1. For φ non-decreasng and concave, ( ( ) ) (λ k ) V,k K φ u k s a concave functon. V,k K Theorem 3.1 establshes that the optmzaton problem CAP can be effcently solved due to ts structural propertes. Ths allows us to compute the optmal performance of the network n terms of maxmzng φ, and hence characterze the correspondng capacty regon. A consequence of ths theorem s that any locally optmum choce of (λ k ) V,k K s a global optmum, whch can hence be found through a smple gradent search. Note that u k s are the functons of λ k s, the moblty patterns of the users, the content generaton processes of the channels, as well as the nterest and sharng behavor of users (captured through matrces A and (B k ) k K ). Because the users moblty patterns and the content generaton processes of the channels are ndependent of the provder transmsson process, they do not affect the concavty result of Theorem 3.1. The proof of Theorem 3.1 can be found n Appendx A. Farness. The above defnton of φ s very general and can be used to ncorporate farness. For any α, let the α-farness functon h α be x 1 α, f α 1 h α (x) = 1 α ln (x), f α =1. For channel k, let 1 f k = V A,k V uk denote the average fracton of nodes for channel k wth the latest block. We defne the per-block α-farness as h α (f k ). (2) k K Note that when α = 1 maxmzng ths functon corresponds to ensurng proportonal farness: at ths equlbrum pont, varyng parameters to mprove the fracton of nodes for one channel wll necessarly result n a proportonal decrease n same proporton of the fracton of nodes n another channel. 4. EVALUATION WITH ACTUAL TRACES Ths secton evaluates the capacty benefts of opportunstc contacts n settngs that exhbt dfferent contact statstcs and user s sharng behavor. 4.1 Smulaton settng Data sets We use moblty traces 3 from two dfferent envronments, Infocom5 and MIT. The Infocom5 data set logs Bluetooth contacts between 41 devces carred by partcpants of the INFOCOM 5 conference. The MIT data set was bult usng GSM cell-tower assocatons of 1 cell phones carred by students and faculty durng a semester. For the latter data set, we assume that two phones are n contact whenever connected to the same GSM base staton, and we remove solated nodes (87 cell phones were ncluded). To speed-up the evaluaton, a smplfcaton was ntroduced that preserves the heterogenety n contact rates present n the traces. Frst, we extracted a contact graph from each 3 The data sets are avalable at

7 trace that explctly dentfed the average contact rates of each ndvdual par of nodes. These rates were then used to generate ndependent memoryless contact processes for all pars of nodes. Ths s an approxmaton of the real traces as t removes dependences between contact processes of dfferent pars of nodes, as well as ther detaled statstcs. However, t stll captures heterogenety n contact rates between dfferent pars of nodes. The computatonal procedure for solvng the optmzaton problem CAP can be found n Appendx B, and the computaton reles on 5 samples of contact latences between nodes 4. Matlab 7.6 was used to solve the optmzaton problem CAP. In future work, we plan to carry out nvestgaton usng actual contact traces Provder update polces We assume that blocks have all equal sze and hence the provder update capacty C s smply gven n updates per mnute. Moreover, content updates are generated for each channel k accordng to a Posson process wth rate γ k.the followng polces for allocatng (λ k ) k K, V are studed: Unform no sharng: The provder update capacty s unformly shared across blocks,.e., λ k C = A,k V,k K A.,k We further assume that there s no sharng between nodes, so that updates are only from the server. Unform: Ths s the same as Unform no sharng, except that sharng between nodes s now enabled durng opportunstc contacts, and follows a sharng behavor specfed through (B k,j) k K,,j V. Optmal no sharng: The server allocates capacty across channels and nodes n a manner that s optmal gven ts knowledge of nodes nterests and channel block generaton rates (γ k ) k K. However, sharng between nodes s not allowed and not taken nto account n the server capacty allocaton. Optmal oblvous: Ths s the same as Optmal no sharng but wth sharng now enabled. The mportant aspect s that the server s update polcy remans oblvous to the presence and structure of opportunstc contacts. Optmal: The provder chooses the optmal capacty allocaton (λ k ) V,k K by solvng the convex optmzaton problem CAP. Among these polces, only Optmal requres to know or estmate the contact patterns between the nodes and ther sharng behavor. Note that another possble polcy s to consder the server capacty allocaton obtaned from CAP but the sharng among nodes s actually not allowed n realty. However, we decde not to consder t as, by defnton, Optmal no sharng outperforms ths polcy. The man purpose for comparng these dfferent polces s to develop a better understandng of how socal factors, e.g., heterogeneous contact rates and users sharng behavor, affect the network s ablty to keep content up-to-date 4 Samples of contact latences are denoted by ŝ k,(l),j s n Appendx B. Fracton of nodes wth latest channel Optmal Optmal (No share) Optmal (Oblvous) Unform Unform (No share) Fracton of nodes wth latest channel 1 Fgure 2: MIT : Capacty regons. Fracton of upto-date nodes for channel 1 (x-axs) and channel 2 (y-axs). across users. As expected, Optmal always outperforms all other polces because t s cognzant of both user and channel characterstcs, and the effect of socal factors on opportunstc updates. Optmal oblvous that takes dfferences n block generaton rates nto account generally outperforms Unform, but not always. Ths s because t gnores the possblty of sharng among nodes, whch can occasonally result n an neffcent allocaton decson. 4.2 Evaluatng capacty We start by comparng the capacty regons realzed by dfferent polces. A combnaton (f 1,f 2 ) s deemed nsde the capacty regon f we can fnd parameters (λ k ) V,k K such that for any channel k, the expected fracton of nodes wth the latest blocks on ths channel s at least f k. In order to explore the space of feasble combnatons, we ntroduce a smple weghted average objectve functon: maxmze w f 1 +(1 w) f 2 for w [, 1]. λ k, V,k K By varyng the value of w, a dfferent objectve s defned and the maxmum value attanable for f 2 can be obtaned as a functon of f 1, from whch the boundary of the capacty regon can be found. Note that, for a polcy that does not ncorporate an objectve (.e., Unform no sharng, and Unform), the value of w has no effect, hence the capacty regon s essentally rectangular, based on a sngle data pont gven by the specfc (f 1,f 2 ) combnaton that ths polcy acheves. We use the MIT data set to llustrate the capacty regons of the dfferent polces n Fg. 2. For smplcty, the two channels were chosen to have the same block generaton rate γ 1 = γ 2 = 1/36mn, and all nodes n the system were nterested n recevng both,.e., the nterest matrx A s full. The sharng matrx B was, however, chosen wth 2% of non-zero entres,.e., only 2% of the nodes are wllng to share, and they were the 2% of nodes wth the hghest contact rates. The provder capacty s C =.5 update per mnute. Fg. 2 shows the performance seen by channels

8 Improvement (%) Channel 1 Channel 2 Channel 3 Channel 4 Channel Provder update capacty (updates per mnute) Fgure 3: Infocom5 : Capacty mprovement of Optmal over Optmal oblvous. 1 and 2 n terms of the average fracton of nodes wth the most up-to-date block for the channel,.e., f 1 and f 2. Each pont corresponds to a dfferent value of the weghng factor w = {,.2,.4,.5,.6,.8, 1} n the objectve functon. Note that when w =.5, Optmal no sharng overlaps wth Unform no sharng, andoptmal oblvous wth Unform. InOptmal no sharng and Optmal oblvous, the results are overlapped under some values of w and hence the number of data ponts n a correspondng polcy shown n the fgure s fewer. We see that opportunstc sharng alone yelds a sgnfcant mprovement n the fracton of nodes wth consstent,.e., up-to-date, versons of both blocks, and that Optmal yelds an addtonal mprovement of about a thrd. Ths demonstrates the benefts by ncorporatng specfc knowledge about opportunstc contacts and users behavor n allocatng the provder capacty. 4.3 Heterogeneous channels Ths secton nvestgates the benefts of the optmal server polcy when channels are heterogeneous n ther update rates. We consder a scenaro wth 5 channels usng the Infocom5 contact traces. All nodes are nterested n recevng all channels, but only 2% of nodes accept to exchanges blocks durng opportunstc contacts. We assume that the 2% of nodes wth the hghest contact rates accept to transmt blocks from channel 1 to other nodes. For channel 2, we choose the 2% of nodes wth the next hghest contact rates, and so on for the remanng channels so that each channel s assgned to a dstnct group of nodes wth decreasng contact rates. Ths creates sgnfcant heterogenety n how channels wth dentcal popularty are able to beneft from opportunstc contacts. We assume that block generaton rates across channels are: (γ 1,γ 2,γ 3,γ 4,γ 5) ( ) 1 = 2mn, 1 4mn, 1 6mn, 1 12mn, 1. 24mn Specfcally, the generaton rate for channel 1 s the largest so that t s hardest to mantan the latest copy for ths channel, but at the same tme t s assocated wth the sharng nodes wth the hghest contacts rates. In order to allow tradng effcency for farness across blocks n the network, we chose to maxmze the block-based objectve functon wth α = 1 (Eq. (2)) that corresponds to the per-block proportonal farness. Fg. 3 plots the relatve mprovement rato of f k, k = 1, 2,..., 5, under Optmal over Optmal oblvous across channels as a functon of the provder update capacty. We observe that the mprovement acheved by Optmal s substantal for all channels, and sometmes multples the fracton of nodes that have the latest content by a factor of up to four. Ths s because Optmal explots the users sharng behavor and opportunstc contacts to effcently dssemnate up-to-date content. On the other hand, Optmal oblvous gnores these factors and smply reles on relatve dfferences n content generaton rates when makng transmsson choces. Ths often results n shortsghted choces that prevent t from leveragng opportunstc transmssons. 5. CONCLUSION Recent work has advocated usng opportunstc contacts between moble nodes to mprove users access to content. Although promsng, ths has left open a dffcult ssue: Accurately measurng the mprovements ths affords applcatons as a functon of user connectvty patterns and socal behavor (e.g., nterest n content and wllngness to share t). Ths paper makes a novel and mportant contrbuton to ths problem for a tme-senstve content update applcaton, for whch t provdes a complete characterzaton of the capacty avalable through opportunstc updates. Realzng ths capacty s shown to crtcally depend on how the content provder allocates ts own updates to nodes. In partcular, ths allocaton depends on content generaton rates, node contact rates, as well as nodes nterests and sharng behavor. Surprsngly, despte these complex dependences, t s actually possble to compute an exact optmal polcy that realzes capacty. Our results further establsh that n the presence of heterogeneous contact rates and sharng behavor among nodes, smple heurstcs that are oblvous to those parameters can translate nto subpar performance. Our result ponts to several mportant research challenges that reman to be addressed: Although our model deals wth general statstcs of content creaton and contacts between nodes, we have studed quanttatve performance mprovement n a smple case: content and meetng generated accordng to memoryless statstcs. It would be mportant to understand analytcally as well as emprcally how other statstcs mpact the mprovement provded by opportunstc contacts. Computng optmal server allocaton polcy requres knowledge about dstrbuton of latences between users contact tmes n the network. However, snce ths problem follows a convex optmzaton, t s possble to come up wth a dstrbuted scheme whch targets the optmal allocaton wth lmted nformaton about processes of contacts (see [8] for an example). We assume that the content provder follows a smple randomzed memoryless strategy for updates (essentally choosng to update blocks n nodes ndependently wth dfferent probabltes). A more complex

9 strategy may take nto account tme of content creaton and the current age of content n nodes, t would be mportant to understand how that mpacts the role of opportunstc contacts. Smlarly, we assume that nodes decde to always share wth a subset of other nodes, as captured n the sharng matrx. A more complex strategy may be developed to reflect other crtera such as mnmzng energy consumpton n opportunstc sharng whle provdng users wth suffcently fresh content. We hope that the concrete evdence of these quanttatve benefts presented n the paper wll foster other contrbutons amed at mprovng applcaton performance n opportunstc moble networks. 6. REFERENCES [1] E. Altman, P. Nan, and J. Bermond. Dstrbuted storage management of evolvng fles n delay tolerant ad hoc networks. In Proc. IEEE INFOCOM, 29. [2] A. Balasubramanan, B. Levne, and A. Venkataraman. DTN routng as a resource allocaton problem. In Proc. ACM SIGCOMM, 27. [3] N. Banerjee, M. D. Corner, D. Towsley, and B. N. Levne. Relays, base statons, and meshes: enhancng moble networks wth nfrastructure. In Proc. ACM MobCom, 28. [4] A. Chantreau, A. Mtbaa, L. Massoule, and C. Dot. The dameter of opportunstc moble networks. In Proc. ACM CoNEXT, 27. [5] P. Costa, C. Mascolo, M. Musoles, and G. P. Pcco. Socally-aware routng for publsh-subscrbe n delay-tolerant moble ad hoc networks. IEEE JSAC, 26(5), 28. [6] E. M. Daly and M. Haahr. Socal network analyss for routng n dsconnected delay-tolerant manets. In Proc. ACM MobHoc, 27. [7] D. Hay and P. Gaccone. Optmal routng and schedulng for determnstc delay tolerant networks. In Proc. IEEE WONS, 29. [8] S. Ioannds, A. Chantreau, and L. Massoule. Optmal and scalable dstrbuton of content updates over a moble socal network. In Proc. IEEE INFOCOM, 29. [9] E. Jaho and I. Stavrakaks. Jont nterest- and localty-aware content dssemnaton n socal networks. In Proc. IEEE WONS, 29. [1] S. Jan, K. Fall, and R. Patra. Routng n a delay tolerant network. In Proc. ACM SIGCOMM, 24. [11] D. Kempe, J. Klenberg, and E. Tardos. Maxmzng the spread of nfluence n a socal network. In Proc. KDD, 23. [12] J. Leguay, A. Lndgren, J. Scott, T. Fredman, and J. Crowcroft. Opportunstc content dstrbuton n an urban settng. In Proc. ACM SIGCOMM workshop on Challenged networks, 26. [13] V. Lenders, G. Karlsson, and M. May. Wreless ad hoc podcastng. In Proc. IEEE SECON, 27. [14] E. Yonek, P. Hu, S. Chan, and J. Crowcroft. A soco-aware overlay for publsh/subscrbe communcaton n delay tolerant networks. In Proc. ACM/IEEE MSWM, 27. APPENDIX A. PROOF OF THEOREM 3.1 We frst ntroduce the concept of block propagaton delay Y k (t) whch measures the latency for node to receve the latest block of channel k. There are two ways that node can receve the latest block for channel k. One way s to drectly receve t from the provder, and the another way s through opportunstc sharng wth other users. It can be shown from [8] (Lemma 2) that for any y [ ] [ P Y k >y = E e ] j V λk j (y sk,j ) + (3) where ( ) + denotes max(, ), s k,j s defned as the mnmum value s such that a message created at tme t s n j can reach before tme t, usng any opportunstc contacts (,j ) such that B k,j = 1, and the expectaton on the rght-hand sde s taken over all the values of s k,j. Note that all s k,j s do not depend on (λ k ) V,k K, or the content generaton process. Let us consder how to compute E [ U k (t) ] for node and channel k. Ifnode s not nterested n channel k (.e., A,k = ), then ths expected value s null. Otherwse, assumng A,k =1,wehave { U k (t) =I Y k } (t) Γ k (t), where I { } s the ndcator functon and Γ k (t) s the tme elapsed snce the creaton of the latest blocks on channel k. Snce the process of block creaton s assumed ndependent of the provder update process and the process of opportunstc contacts between moble hosts, thus we have [ E U k (t) Γ k (t) ] = F Y k ( ) Γ k (t) where F Y k denotes the cumulatve dstrbuton functon of Y k,.e., F Y k (y) =P [ Y k y ]. Note that, as a consequence of Eq.(3), one can easly deduce (see [8]) that the functon (λ k ) V,k K F Y k (y), for any y, s concave, and E [ ] U k (t) = E = [ E [ ]] U k (t) Γ k (t) [ ] [ P Γ k (t) =y E U k (t) Γ k (t) ] dy. Snce the ntegral of a famly of concave functons wth respect to a postve measure s a concave functon, t proves that (λ k ) V,k K E [ U k (t) ] s a concave functon. The theorem then follows from the fact that a composton of a non-decreasng concave functon φ wth a concave functon s concave and non-decreasng. Note that Eq. (4) can be further smplfed when the process of block creaton follows smple statstcs, e.g., If blocks are created accordng to a Posson process wth rate γ k, then E [ ] U k (t) = = E (4) γ k e γk y F Y k (y) dy [ ] exp( γ k Y k ). (5)

10 If blocks are created accordng to a determnstc perod of 1/γ k, then E [ ] U k (t) = = E 1/γk γ k F Y k (y) dy [ ] max(, 1 γ k Y k ). (6) B. COMPUTATIONAL PROCEDURE We descrbe how the servce provder can solve the optmzaton problem CAP and compute the optmal values of (λ k ) V,k K. Frst, the provder needs to be aware of the rate (γ k ) k K and the statstcs of the content generaton process for each channel. It also needs to know the nterest of nodes for each channel va the matrx A. Last, n order to compute the expected utltes seen by each node on each channel, we assume that t knows a certan number of samples for (s k,j) k K,,j V. Samples are ndexed by l =1,...,L,and denoted by (ŝ k,(l),j ) k K,,j V,l=1,,L. Note that the provder does not need to know the sharng matrces (B k ) k K explctly, because they are mplctly contaned n the samples of ŝ k,(l),j s whch are suffcent to run the procedure. Second, the provder needs to use these samples to estmate expected utlty. Note frst that for any y,, andk the provder can estmate P [ Y k >y ], seen as a functon of ( ) λ k, based on Eq. (3): V,k K P [ ] Y k >y 1 L L l=1 e j V λk j (y ŝk,(l),j ) +. (7) Accordng to ths expresson, the utlty for a gven node and channel can be expressed as a functon of (λ k ) V,k K. As an example, f blocks are created accordng to a Posson process, we have by Eq. (5), E [ ] U k (t) γ k e γ k y (1 1 L L l=1 e j V λk j (y ŝk,(l),j ) + )dy. Ths allows us to derve an estmator for any objectve φ as a functon of (λ k ) V,k K. As ths functon s concave, a maxmum can be found usng convex optmzaton technques. The estmator becomes closer to the expectaton as the number of samples gets large.