606 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 6, NO. 6, JUNE 2007. Impact of Human Mobility on Opportunistic Forwarding Algorithms

66 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 6, NO. 6, JUNE 27 Impac of Human Mobly on Opporunsc Forwardng Algorms Augusn Canreau, Pan Hu, Jon Crowcrof, Fellow, IEEE, Crsope Do, Rcard Gass, and James Sco Absrac We sudy daa ransfer opporunes beween wreless devces carred by umans. We observe a e dsrbuon of e nerconac me (e me gap separang wo conacs beween e same par of devces) may be well approxmaed by a power law over e range [1 mnues; 1 day]. Ts observaon s confrmed usng eg dsnc expermenal daa ses. I s a odds w e exponenal decay mpled by e mos commonly used mobly models. In s paper, we sudy ow s newly uncovered caracersc of uman mobly mpacs one class of forwardng algorms prevously proposed. We use a smplfed model based on e renewal eory o sudy ow e parameers of e dsrbuon mpac e performance n erms of e delvery delay of ese algorms. We mae recommendaons for e desgn of well-founded opporunsc forwardng algorms n e conex of umancarred devces. Index Terms Compuer sysems organzaon, communcaon/neworng and nformaon ecnology, moble compung, algorm/ proocol desgn and analyss, moble envronmens, maemacs of compung, probably and sascs. Ç 1 INTRODUCTION THE ncreasng populary of devces equpped w wreless newor nerfaces (suc as cell pones or PDAs) offers new communcaon servces opporunes. Suc moble devces can ransfer daa n wo ways by ransmng over a wreless (or wred) newor nerface and by ang advanage of e user s mobly. Tey form a Poce Swced Newor [1]. Communcaon servces a rely on s ype of daa ransfer wll srongly depend on uman mobly caracerscs and on ow ofen suc ransfer opporunes arse. Terefore, ey wll requre neworng proocols a are dfferen from ose used on e Inerne. Snce wo (or more) ends of e communcaon mg no be conneced smulaneously, s mpossble o manan roues or o access cenralzed servces suc as e DNS. In order o beer undersand e consrans of opporunsc daa ransfer, we analyze eg dsnc daa ses colleced n newors w moble devces. Tree daa ses come from expermens we conduced ourselves. We defne e nerconac me as e me beween wo ransfer opporunes for e same devces. We observe n e eg races a e nerconac me al dsrbuon s slowly varyng over a large range. Insde s range, e nerconac me dsrbuon can be compared o a power law.. A. Canreau and C. Do are w Tomson Researc, 46 qua A. Le Gallo, 92648 Boulogne, France. E-mal {augusn.canreau, crsope.do}@omson.ne.. P. Hu and J. Crowcrof are w e Unversy of Cambrdge, 15 J J Tomson Av., Cambrdge, CB3 FD. E-mal {pan.u, jon.crowcrof}@cl.cam.ac.u.. J. Sco s w Mcrosof Researc, 7 J J Tomson Av., CB3 FB, UK. E-mal james.sco@mcrosof.com.. R. Gass s w Inel Researc, 472 Forbes Avenue, Psburg, PA 15213. E-mal rcard.gass@nel.com. Manuscrp receved 1 June 26; revsed 2 June 26; acceped 16 Mar. 27; publsed onlne 28 Mar. 27. For nformaon on obanng reprns of s arcle, please send e-mal o mc@compuer.org, and reference IEEECS Log Number TMCSI-151-66. Dgal Objec Idenfer no. 1.119/TMC.27.16. We sudy e mpac of ose large nerconac mes on e acual performance and eorecal lms of a general class of opporunsc forwardng algorms a we call oblvous forwardng algorms. Algorms n s class do no use e denes of e devces a are me, nor e recen sory of conacs, nor e me of day n order o mae forwardng decsons. Insead, forwardng decsons are based on sacally defned forwardng rules a bound e number of daa replcas or e number of ops. Based on our expermenal observaons, we develop a smplfed model of opporunsc conac beween umancarred wreless devces. Our model maes several ndependence assumpons wc are common n e leraure of moble ad oc roung. We do no clam a s model capures e performance of dfferen forwardng algorms accuraely. Raer, serves our purpose, wcs o demonsrae ow e al of nerconac mes nfluences e performance of oblvous forwardng algorms and ow ese sould be confgured o offer reasonable guaranees. Expermenal resuls are presened n Secon 2. In Secon 3, we model conac opporunes based on our observaons and we analyze e delay a wreless devces would experence usng a class of forwardng algorms prevously suded n e leraure. Secon 4 s dedcaed o relaed wor. Te paper concludes w a bref summary of conrbuons and a presenaon of fuure wor, ncludng a dscusson of e mplcaons of our assumpons. 2 EXPERIMENTAL RESULTS 2.1 Daa Ses In order o conduc nformed desgn of opporunsc forwardng algorms, s mporan o analyze e frequency and duraon of conacs beween uman-carred communcang devces. Ideally, an expermen would cover a large user base over a large me perod, as well as nclude daa on connecon opporunes encounered 24 ours a day. 1536-1233/7/$25. ß 27 IEEE Publsed by e IEEE CS, CASS, ComSoc, IES, & SPS

CHAINTREAU ET AL. IMPACT OF HUMAN MOBILITY ON OPPORTUNISTIC FORWARDING ALGORITHMS 67 TABLE 1 Comparson of Daa Colleced n e Eg Expermens We examned wo ypes of daa ses. Frs, we use publcly avalable races measurng connecvy beween clens and access pons (APs) n several wreless newors (usng WF or GSM ecnology); conacs beween e clens were deduced from e races followng an assumpon a we dscuss below. Second, we colleced our own races of drec conacs recorded usng small porable wreless rado devces (Moes) a were dsrbued o dfferen groups of people. We found a few oer races of drec conacs and we ave ncluded em for comparson w ours. In oal, ere are eg daa ses and eac of er caracerscs are summarzed n Table 1. 2.1.1 AP-Based Daa Ses Te Unversy of Calforna, San Dego (UCSD) [2] and Darmou Unversy [3] races mae use of WF neworng, w e former ncludng clen-based logs of e vsbly of access pons (APs), wle e laer ncludes SNMP logs from e access pons. Te duraons of e dfferen logs races are ree and four mons, respecvely. Snce we requred daa abou devce-o-devce ransmsson opporunes, e raw daa ses were unsuable for our expermen and requred preprocessng. For bo daa ses, we made e assumpon a moble devces seeng e same AP would also be able o communcae drecly (n ad oc mode). Consequenly, a ls of ransmsson opporunes was deduced for eac par of devces, wc corresponds o e me nervals for wc ey sare a leas one AP. Te races from e Realy Mnng projec [4] a e Massacuses Insue of Tecnology (MIT) Meda Lab nclude records of vsble GSM cell owers, colleced by 1 cell pones dsrbued o sudens and faculy on e campus durng 9 mons. We ave assumed, as above, a wo devces are n conac wenever ey are conneced w e same cell ower. Unforunaely, e assumpons we ave made for all ese daa ses nroduce naccuraces. On e one and, s overly opmsc snce wo devces aaced o e same (WF or GSM) base saon may sll be ou of range of eac oer. On e oer and, e daa mg om connecon opporunes, suc as wen wo devces pass eac oer a a place were ere s no nsrumened access pon. Anoer poenal ssue w ese daa ses s a e devces are no necessarly colocaed w er owners a all mes. Despe ese naccuraces, ese races are a valuable source of daa spannng many mons and ncludng ousands of devces. In addon, consderng wo devces conneced o e same base saon as beng poenally n conac s no alogeer unreasonable. Tese devces may ndeed be able o communcae locally roug e base saon. 2.1.2 Drec Conac Daa Ses In order o complemen e prevous races, we dd our own expermen usng Inel Moes, wc are embedded devces smlar o Crossbow moes, 1 excep a ey communcae va Blueoo. We programmed e Moes o log conac daa every 12 s for all vsble Blueoo devces (ncludng Moes as well as oer Blueoo devces suc as cell pones). Eac conac s represened by a uple (MAC address, sar me, and end me). Te expermenal sengs are descrbed n deal n [1]; an anonymzed verson of our daa s now avalable o oer researc groups n e CRAWDAD 2 arcve. We nclude n s paper e resuls from ree Moebased expermens. We frs obaned daa from 12 docoral sudens and faculy comprsng a researc group a e Unversy of Cambrdge. Te second expermen ncluded a group of 37 parcpans n Hong Kong seleced n suc a way a ey do no belong o e same wor or socal group and, n parcular, a none of em nows eac oer. Te rd expermen was conduced durng e IEEE INFOCOM 25 conference n Mam, were Moes were carred by 41 aendees for 4 days. Te conacs colleced by Moes are classfed no wo groups e sgng of anoer Moe s classfed as an nernal conac, wle e sgng of oer ypes of Blueoo devces s called an exernal conac. Te exernal conacs are numerous and ey provde a measure of e wreless neworng opporunes presen a a me. Inernal conacs, on e oer and, represen e daa ransfer opporunes among parcpans f ey were all equpped w devces wc are always-on and always-carred. In addon o our own expermen, we found wo daa ses w drec conacs and ncluded em for comparson A researc group from e Unversy of Torono as colleced drec conac races usng 23 Blueoo-enabled PDAs dsrbued o a group of sudens. Tese devces performed a Blueoonqury every 12 seconds and s daa was logged. Ts meodology does no requre devces o be n range of any AP n order o collec conacs, bu does requre a e PDAs are carred by e 1. See www.xbow.com. 2. See crawdad.cs.darmou.edu.

68 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 6, NO. 6, JUNE 27 Fg. 1. Aggregaed dsrbuon of e nerconac me n eg daa se expermens (a) Moe-based expermens a Cambrdge and Hong Kong, and e Torono expermen, (b) Moe-based expermen a INFOCOM, and (c) daa colleced a UCSD, Darmou, and MIT. parcpans and a e parcpans eep em carged. Te daa se we use comes from an expermen a lased 16 days. Te races from e Realy Mnng projec [4] nclude drec Blueoo sgngs, recorded every 3 seconds by eac parcpan s cell pone. 2.2 Defnons We are neresed n ow e caracerscs of ransfer opporunes mpac daa forwardng decsons. In s paper, we focus on ow ofen suc opporunes occur, bu no n er duraon. We decded no o analyze ow muc daa can be ranspored durng a ransfer opporuny because s srongly depends on e wreless ecnology used. Laer n our analyss (see Secon 3), we wll assume a all conacs las a sngle me slo and we wll address wo exreme cases correspondng o a lower and upper bounds of e amoun of daa a could be ransferred n eac connecon opporuny. We defne e nerconac me as e me elapsed beween wo successve conac perods for a gven par of devces. Inerconac me caracerzes e frequency w wc daa can be ransferred beween newored devces; as rarely been suded n e leraure. Two remars mus be made w regard o s defnon Frs, e nerconac me s compued once a e end of eac conac perod, a e me nerval beween e end of s conac and e begnnng of e nex conac w e same devce. 3 An alernave opon would be o compue e remanng nerconac me seen a any me for eac par of devces, s e me aes afer before ese devces mee agan (a formal defnon s gven n Secon 3). Inerconac me and remanng nerconac me ave dfferen dsrbuons, wc are relaed, for a renewal process, va a classcal resul nown as e wang me paradox (see [5, p. 147]). A smlar relaon olds for saonary processes n e eory of Palm Calculus (see [6, p. 15]). We coose o sudy e frs defnon of nerconac me seen a e end of a conac perod as e second gves oo muc weg o large nerconac mes. In oer words, e defnon we ave cosen s e mos conservave one n e presence of large values. 3. Noe a we dd no nclude e me beween e begnnng of e expermen and e frs conac for a par, nor e me beween e las conac of a par and e end of e expermen. Second, e nerconac me dsrbuon s nfluenced by e expermen s duraon and s granulary (.e., e me elapsed beween wo successve scannngs for e same devce). Inerconac mes a las more an e duraon of e expermen canno be observed, and nerconac mes close o e duraon are less lely o be observed. In a smlar way, we canno observe e nerconac mes a las less an e granulary of measuremen (wc ranges from wo o fve mnues for dfferen expermens). Anoer measure of e frequency of ransfer opporunes a could be consdered s e ner-any-conac me,.e., for a gven devce, e me elapsed beween wo successve conacs w any oer devce. Ts measure s very muc dependen on e densy of wreless devces durng e expermen as caracerzes me a devces spend wou meeng any oer devce. Ts measure was suded for mos of ese daa ses n [1]. We do no presen furer resuls ere. 2.3 Inerconac Tme Caracerzaon We sudy e emprcal dsrbuon of e nerconac mes obaned for all expermens sown n Fg. 1 and Fg. 2. For all plos, an emprcal dsrbuon of e nerconac mes was frs compued separaely for eac par of devces a me a leas wce. I s ard o sudy e caracerscs of e dsrbuons for all pars ndvdually because ere are many suc dsrbuons and some of em may only nclude a few observed values. Ts s wy we follow a wosep approac Frs, we presen e dsrbuon obaned wen all pars dsrbuons are combned, eac w an equal weg, n a dsrbuon a we call e aggregaed dsrbuon. Second, we use a paramerc model movaed by s frs par and esmae e parameer of e ndvdual dsrbuon for eac par. 2.3.1 Aggregaed Dsrbuon Fg. 1 presens e aggregaed dsrbuon for dfferen daa ses. All plos sow e complemenary cumulave dsrbuon funcon usng a log-log scale. For Moe expermens, () ndcaes a e daa se sown s obaned usng nernal conacs only, wle (e) ndcaes a e daa se sown ncludes only exernal conacs. For e frs wo Moe expermens (labeled

CHAINTREAU ET AL. IMPACT OF HUMAN MOBILITY ON OPPORTUNISTIC FORWARDING ALGORITHMS 69 Fg. 2. Moe-based expermen a INFOCOM (a) Quanle-quanle plo of a comparson beween e aggregaed dsrbuon of e nerconac me and ree paramerc models, (b) esmaon of e eavy al ndex of e power law appled separaely for eac par, and (c) summary of e resuls obaned n all daa ses. Cambrdge and Hong Kong), we presen only one case ere (correspondng, respecvely, o nernal and exernal conacs). Tey are sown n Fg. 1a, wc also ncludes e dsrbuon obaned among pars of expermenal devces n e race from e Unversy of Torono. Dsrbuons belongng o e Moe-based expermen a INFOCOM are sown n Fg. 1b, were dsrbuons assocaed wnernal and exernal conacs ave been ploed separaely for comparson. Fg. 1c presens e dsrbuon of nerconac me compued usng races from oer expermens an ours. Le us frs noe a, alougnerconac mes are sor n mos cases, e occurrence of large nerconac mes s far from neglgble In e ree Moe-based expermens, 17 o 3 percen of nerconac mes are greaer an one our, and 3 o 7 percen of all nerconac mes are greaer an one day. In e Torono daa ses, 14 percen of nerconac mes las more an a day and 8 percen more an a wee. Tese large nerconac mes are even more frequen n e races colleced a UCSD, Darmou, and MIT, e mos exreme case beng e MIT race usng Blueoo sgngs, were up o 6 percen of e nerconac mes observed are above 1 day. Te varaon beween daa ses s sgnfcan. I can be expeced gven e dversy of communcaon ecnologes and populaon suded, as well as e mpac of expermenal condons (granulary, duraon). Bu, ere are also common properes a we now dscuss n more deal. We now concenrae on e regon beween 1 mnues and 1 day. In s regon, all daa ses exb e same caracerscs Te CCDF s slowly varyng and s lower bounded by e CCDF of a power law dsrbuon, wc may, n some cases, be a close approxmaon. Ts conradcs e exponenal decay of e al, wc caracerzes e mos common mobly models found n e leraure (see Secon 4), and we prove n e nex secon a s can ave a sgnfcan mpac on e performance of opporunsc neworng algorms. To jusfy e above clam, we suded e quanlequanle plo comparson beween e emprcal dsrbuon found and ree paramerc models (exponenal, lognormal, and power law). An example s sown n Fg. 2a for e dsrbuon based on nernal conacs durng e INFOCOM expermen. All paramerc models ave been se o ae e same medan value as e emprcal dsrbuon. We also normalze e power law o f e granulary ¼ 12 seconds and e log-normal dsrbuon suc a e logarm of bo e emprcal varable and e model ave e same varance. No surprsngly, we observe a e ree models devae sgnfcanly from e emprcal fndngs for values above one day. As expeced, e exponenal dsrbuon s very far from e emprcal one and e quanle for e log-normal dsrbuon devaes from e emprcal case by a nonneglgble facor. Te power law dsrbuon, n conras, remans close o e emprcal one for values of up o 18 ours, and seems o be e mos approprae model o apply. In oer daa ses, e power law may somemes no mac e emprcal fndngs, as well as n s example, bu among ese ree models, s always e one closes o e emprcal dsrbuon. For values above one day, we expec models w addonal parameers (e.g., followng a Webull dsrbuon) o mprove e mac w e emprcal dsrbuon, bu a s beyond e scope of s paper. Te mos noable dfference we observe beween daa ses s a e f w a power law s beer for e daa ses a conan e larges number of pons, suc as n Fg. 1b and Fg. 1c. We also observe a e slope of e power law a s a lower bound on e range [1 mnues; 1 day] s dfferen beween daa ses Ts s.6 for e Moe expermens a Cambrdge and Hong Kong, as well as for e Torono daa se,.35 for e Moe-based expermen a INFOCOM, and.2 for e races colleced a UCSD, Darmou, and MIT. In all cases, s below 1. Te value of s slope, wcs also called e eavy al ndex, s crcal for e performance of opporunsc forwardng algorms (see e analyss n Secon 3), and we dscuss furer below. Fg. 1b sows a e dsrbuon s almos uncanged f one consders nernal or exernal conacs. Te same observaon was made for oer Moe expermens [1], excep for e expermen conduced n Hong Kong, were, as expeced, very few nernal conacs were logged. Some varaons of e eavy al ndex ave been observed dependng on e me of e day [1].

61 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 6, NO. 6, JUNE 27 2.3.2 Indvdual Dsrbuons for Eac Par So far, we ave suded e aggregaed dsrbuon were all pars ave been combned ogeer, and we found a can be approxmaed by a power law for values up o 1 day. In s secon, we assume a s clam can be made ndvdually for all pars, aloug e parameer of s power law, also called e eavy al ndex, may be dfferen among em. Ts approac allows us o sudy e eerogeney beween pars va a sngle parameer; some of ese resuls also measure e accuracy of e above assumpon for eac par. Esmaor for e Heavy Tal Index. Le us consder a par of nodes. Te sample of e nerconac mes observed for s par wll be denoed by X 1 ;...;X n, s order sascs by X ð1þ... X ðnþ, and s medan value by m. All mes wll be gven n seconds. If we assume a s sample follows a power law w granulary 12 s and eavy al ndex, we ave IP½X xš ¼ðx=12Þ, suc a an esmaor of based on e sample s medan m s gven by ¼ lnð2þ lnðmþ lnð12þ More generally, one can consder all order sascs X ðþ a f n e range [1 mnues; 1 day] and esmae based on eac of em. Ts creaes a collecon of esmaors for e value of as follows lnðnþ lnðn Þ lnðx ðþ Þ lnð12þ 6 X ðþ 86;4; <n We denoe by and, respecvely, e mnmum and maxmum value n s se above. Ts s equvalen o plong e emprcal CCDF for s sample n a log-log scale and boundng s CCDF from above and below by wo srag lnes a go roug probably 1 a me value 12 s. Te slopes of ese lnes would be equal, respecvely, o and. In conras o, ese wo esmaors are no cenered around e value of, and ey do no converge o s value wen e sample becomes large. Tey raer serve e purpose of a eursc analyss; ey caracerze some bounds a are verfed by eac par. Noe also a, nuvely, e dfference ndcaes ow e condonal dsrbuon of e sample n s range dffers from a pure power law. In Fg. 2b, we plo e values of and e nerval ½; Š for all pars of Moes durng e expermen conduced a INFOCOM. One can expec a e eavy al ndex aes dfferen values among pars, as some parcpans are more lely o mee ofen an oers. We nally raned all pars accordng o er value for n e decreasng order. Aloug we ave compued ese values for all pars, we only draw e nerval ½; Š for 1 pars cosen arbrarly accordng o er ran (one every 14) n order o eep e fgure readable. As sown n Fg. 2b, esmaons of for dfferen pars may ndeed vary beween.5 and 1. Beween ese wo exreme values, wc are very rarely observed, esmaes for almos all pars le beween.1 and.7 dependng on e esmaor. Noe a all esmaes of are smaller an 1; e only excepons are e upper esmae for ree pars (.e., less an.2 percen of pars n s case). Te medan-based esmae les n [.2 ;.4] for Fg. 3. Correlaon coeffcens for e sequence of nerconac mes (a) for all pars of Moes n e INFOCOM daa se and (b) for all pars of devces n e MIT GSM daa se. alf of e pars and e lower esmaes (respecvely, e upper esmae) les n [.14 ;.32] (respecvely, [.32 ;.5]) agan for alf of e pars. Tese resuls ave ree major mplcaons Frs, e eerogeney among pars mples dfferen possble values for, wc are cenered around e value already observed wen sudyng e aggregae dsrbuon (.e.,.33). Second, e dfference beween e medan esmaor and e eursc bounds we defned above remans wn 25 excep n a few cases. Las, e upper esmae almos never goes above 1, wc esablses a e nerconac me dsrbuon for eac par s lower bounded n s range by a power law w a eavy al ndex smaller an 1. Te same resuls ave been obaned for oer daa ses, and ey are summarzed n Fg. 2c. For eac daa se ndcaed, we sow e dsrbuon of values obaned among pars for e ree esmaors defned above. Eac esmaor sands for one box-plo From lef o rg, ; ; ; e c par ndcaes e values found n 5 percen of e pars and e n par conans e regon were 9 percen of e pars are found. In e Hong Kong and Darmou daa ses, were conacs are sparser, nerconac me samples for eac par conans fewer values. As a consequence, e dfference beween esmaors can grow sgnfcanly. We even observe a goes slgly beyond 1 for 1 percen of e pars n Hong Kong daa se, aloug s could be an arfac of our conservave esmae. Correlaon. We sudy e auocorrelaon coeffcens o see ow e value of e nerconac me may depend on e prevous values for e same par. Te resuls are sown n Fg. 3 for all order up o 5. Snce e nerconac me dsrbuon usually as no fne varance, we compued e correlaon coeffcen on e values of e logarm of e nerconac mes. Noe a, snce a correlaon coeffcen was compued for eac par, we presen for all orders e average value we observed among all pars, as well as e nerval conanng 5 percen and 9 percen of e cenered values (respecvely, n e c box and e n bar). In e INFOCOM daa se, e varaon of e coeffcen among pars s que mporan, aloug mos pars reman reasonably noncorrelaed (e c box always remans less an 3 away from zero). Overall, we observe a slgly negave correlaon over all pars on average, wc reduces as grows. Correlaon coeffcens are smaller wen e daa se s large (as seen, for example, n e MIT

CHAINTREAU ET AL. IMPACT OF HUMAN MOBILITY ON OPPORTUNISTIC FORWARDING ALGORITHMS 611 GSM race sown ere, as well as for all oer long races). Ts ends o ndcae a ese coeffcen pars would be closer o zero f e Moe expermen could be done w a longer duraon, and a e sample of nerconac mes colleced for eac par was bgger. Based on e above resuls, we assume n e nex secon a e nerconac me dsrbuon follows a power law for eac par. To smplfy e analyss, we assume, n addon, a e coeffcen s e same for all pars, a e sequence of nerconac mes s..d. (.e., correlaon coeffcens are null), and a ey are ndependen beween pars. Ts smplfcaon allows us o caracerze e performance of forwardng algorms que generally. Some of e resuls we presen can be exended o saonary ergodc sequences or correlaon beween pars, bu a s lef for fuure wor. 3 FORWARDING WITH POWER LAW-BASED OPPORTUNITIES We now analyze e mpac of our fndngs on e performance of a class of forwardng algorms. We frs defne our absrac model of e opporunsc beavor of moble users based on our expermenal observaons. 3.1 Assumpons and Forwardng Algorms 3.1.1 Conac Process Model We consder a sloed me ¼ ; 1;... For a gven par of devces ðd; d Þ, le us nroduce s conac process ðu ðd;d Þ Þ defned by U ðd;d Þ ¼ 1 f d and d are n conac durng slo ; oerwse For e par ðd; d Þ, we consder e sequence of e me slos T ðd;d Þ <T ðd;d Þ 1 <...<T ðd;d Þ <... a descrbes all e values of 2 IN suc a U ðd;d Þ ¼ 1. We do no nclude n s model e conac me represenng e duraon of eac conac, assumng a eac conac sars and ends durng e same me slo. Ts s jusfed ere by e fac a we are neresed n a model accounng for consequences of large values of e nerconac me. I was observed (see [1]) a e conac me dsrbuon may also be approxmaed by a power law, bu over a range a s muc smaller an e range for e nerconac me. Under s condon, e me ðd;d Þ ¼ T ðd;d Þ þ1 T ðd;d Þ for any d; d and s e nerconac me afer e conac of s par. We suppose n our model a as e same law as X, wc follows a power law w eavy al ndex > P½X Š ¼ for all ¼ 1; 2;... Noe a X s no bounded bu s fne almos surely. I may easly be seen a X as a fne mean f and only f >1. In addon, we assume a e conac process ðu ðd;d Þ Þ of eac node par ðd; d Þ s a renewal process and a conac processes assocaed w dfferen pars are ndependen. In oer words, e nerconac mes n e sequence ð ðd;d Þ Þ are..d., for all ðd; d Þ, and sequences belongng o dfferen pars are ndependen. ð1þ We come bac o ese assumpons laer n Secon 5. Noe a ese assumpons are sared explcly or mplcly by mos of e analyses of currenly proposed mobly models. Ts s because s ypcally very dffcul o analyze models were dependence may arse beween dfferen devces or beween successve evens occurrng w one or more devces. Even f we do no explcly model e conac me (eac conac lass one me slo), we need o ae no consderaon e fac a a conac may las long enoug o ransm a sgnfcan amoun of daa. We en nroduce wo suaons. e sor conac case, were only one daa un can be sen beween e wo devces durng eac conac, and. e long conac case, were we assume a all queues n e wo devces can be compleely emped durng eac conac. Tese wo cases represen lower and upper bounds for e evaluaon of bandwd. Te number of daa uns ransmed n a conac (weer sor or long) s defned as a daa bundle. 4 Te long and e sor case dffer from a queung sandpon. In e long conac case, as soon as a daa un as arrved n a node, can be sen o all oer nodes a are me. In e sor conac case, only one daa un s sen a once and, erefore, daa can accumulae n e memory of a relayng devce. Noe a our model does no ae no accoun explc geograpcal locaons or movemen of devces; raer, drecly descrbes e processes of conacs beween devces. Te resuls of s secon exend o any mobly model wc creaes ndependen conac processes for all pars of devces a follow s same law. For any par of devces ðd; d Þ, le us nroduce e remanng nerconac me observed a me slo Isan neger denoed by R ðd;d Þ and defned as n o R ðd;d Þ ¼ mn and U ðd;d Þ ¼ 1 As e conacs for eac par are supposed o follow a renewal process, R ðd;d Þ s a omogeneous Marov Can. As sown n Appendx A, s recurren and ergodc f and only f >1. 3.1.2 Forwardng Algorms We are neresed n a general class of forwardng algorms, wc all rely on oer devces o ac as relays, carryng daa beween a source devce and a desnaon devce a mg no be conemporaneously conneced. Tese relay devces are cosen purely based on conac opporunsm and no usng any sored nformaon a descrbes e curren sae of e newor. Te only nformaon used n forwardng s e deny of e desnaon so a a devce nows wen mees e desnaon for a bundle. We call suc algorms oblvous as ey could be n realy que complex and, as we wll see, very effcen n some cases. 4. In DTN sandards, a bundle usually denoes a large objec w a collecon of daa uns.

612 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 6, NO. 6, JUNE 27 Te followng wo algorms provde bounds for e class of algorm descrbed above. Wa-and-forward Te source was unl s nex drec conac w e desnaon o communcae.. Floodng A devce forwards all s receved daa o any devce wc encouners, eepng a copy for self. Te frs algorm uses mnmal resources bu can ncur very long delays and does no ae full advanage of e ad oc newor capacy. Te second algorm, nally proposed n [7], delvers daa w e mnmum possble laency bu does no scale well n erms of bandwd, sorage, and baery usage. In beween ese wo exreme algorms, ere s a wole range of algorms a dffer n e number of relays used o maxmze e cance of reacng e desnaon w a delay as small as possble wle avodng floodng. Te mos mporan reasons no o flood are o mnmze memory requremens and relaed power consumpon n relay devces and o delee e baclog of prevously relayed messages a are sll wang o be delvered and could be oudaed. A number of sraeges, based on me-ous, buffer managemen, lm on e number of ops, and/or duplcae copes, ave been proposed [7], [8], [9] o mnmze replcaon and baclog. 3.2 Analyss of e Two-Hop Relayng Algorm Havng descrbed e class of oblvous algorms we are consderng n s wor, we now nroduce e wo-op relayng algorm [1] and evaluae s performance for e model of power law nerconac mes a we ave descrbed. Resuls are generalzed o all oblvous algorms n e followng secon. 3.2.1 Descrpon Te wo-op relayng algorm was nroduced by Grossglauser and Tse n [1]. Ts forwardng algorm operaes as follows Wen a source as a bundle o send o a desnaon, forwards once o e frs devce a mees. Ts frs devce s eer a relay devce or e desnaon self. If s e desnaon, e bundle s delvered n one op; oerwse, e devce acs as a relay and sores e bundle n a queue correspondng o s desnaon. Bundles from s queue wll be delvered wen e relay devce mees e desnaon. Bundles for e same desnaon are delvered by a relay devce n a frs-comefrs-served order. As queung may occur n e devces a ac as relays, n e sor conac case, e forwardng process of bundles sen by e source o a relay needs o be of lower nensy an e bundles sen by s relay o e desnaon. Ts s e case n e mplemenaon proposed n [1] and we mae e same assumpon below. We coose s algorm o sar our sudy of e mpac of power law nerconac mes on opporunsc forwardng for e followng ree reasons. In e sor conac case, s algorm was sown [1] o maxmze e capacy of dense moble ad oc newors under e condon a devces locaons are..d., dsrbued unformly n a bounded regon.. Te mobly process of e devces s an mporan parameer. Grossglauser and Tse [1] assumed a eac node moves a eac me slo o an..d. poson, wcmples a e nerconac me s geomercally dsrbued. Ts resul olds more generally for any Marovan evoluon (suc as a random wal) defned on a fne doman. I as also been sown wen devces move accordng o e random way-pon mobly model (see e analyss of Secon 3 n [11]).. Grossglauser and Tse [1] and Sarma and Mazumdar [11] ave sown a daa experences a fne expeced delay under ese condons. 3.2.2 Analyss We consder N moble devces wc ransm daa accordng o e wo-op relayng algorm descrbed above. Insead of e mobly model used n [1], we assume a conacs beween devces follow e model a we ave nroduced n e begnnng of s secon. To ensure sably n e relay s queung mecansm, we assume a e source s s no sauraed Bundles are creaed a s durng a sequence of me slos, denoed by ð ðsþ Þ 2 Z. Te same assumpon s made for e long conac case, aloug sably of e queue occupancy s no an ssue n s conex as e queue s emped afer eac conac w e desnaon. We ave e followng resul, wcs a consequence from e regenerave eorem (or Sm s formula) Teorem 1. For a par of source-desnaon devces ðs; dþ, le ðsþ be e me wen e bundle s creaed a s o be sen o d and le ðdþ be e me wen s delvered o d. Leng D ¼ ðdþ ðsþ, we ave, sarng from any nal condon 1. If <2, lm!1 IE½D Š¼þ1. 2. If >2 and we assume a all conacs are long, lm!1 IE½D Š¼ D <þ1 and we ave R D 2 R; were R ¼ 1 2 þ IE½X2 Š 2 IE½XŠ 3. If >2 and we assume a all conacs are sor, wen eac source sends daa o a unque and dsnc desnaon w rae < N 1, en e delay of a 2IE½XŠ bundle as fne expecaon. Proof. We sudy frs e case of long conacs, were any amoun of nformaon may be excanged wen a conac occurs beween wo devces. We analyzed ere a sngle source-desnaon par. Te wo-op relayng sraegy uses mulple roues o ranspor bundles belongng o s par because any oer conaced devce may ac as a relay. Ts bundle s ransmed o e frs relay a s me by s afer me ðsþ. Leng r be s relay, we ave r ¼ argmn r 6¼sR ðs;r Þ, and ðsþ s ransmsson occurs a me ðrþ ¼ ðsþ þ mn r 6¼s R ðs;r Þ. ðsþ Te bundle s en delvered o desnaon d a me ; ðdþ ¼ ðrþ þ R ðr;dþ. We can rewre ðrþ D ¼ ðdþ ðsþ ¼ mn r6¼s Rðs;rÞ ðsþ þ R ðr;dþ ð2þ ðrþ

CHAINTREAU ET AL. IMPACT OF HUMAN MOBILITY ON OPPORTUNISTIC FORWARDING ALGORITHMS 613 Le us frs esabls e posve resul from Teorem 1.2 a e wo-op relayng sraegy aceves a delay w fne mean f >2. Provng Teorem 1.2. In s case, IE½X 2 Š s fne and IE X T ðd;dþ 1 1 ¼T ðd;d Þ R ðd;d Þ ¼ IE½XðX þ 1Þ=2Š < 1; for any par ðd; d Þ of devces. By Sm s formula (see (5) n e Appendx), we ave lm!1 IE R ðd;d Þ ¼ IE½X2 ŠþIE½XŠ 2IE½XŠ Te process ðmn r6¼s R ðs;rþ Þ s aen as a mnmum of a fne number of ndependen processes, correspondng o pars fðs; rþjr 6¼ sg, wc all ave e same law. Hence, lm IE mn!1 r6¼s Rðs;rÞ r6¼s Rðs;rÞ ðsþ IE½X2 ŠþIE½XŠ 2IE½XŠ Lemma 2 can en be appled o s process, w ð ðsþ Þ, wcs ndependen from ; s proves lm IE mn IE½X2 ŠþIE½XŠ!1 2IE½XŠ If we consder e collecon of random varables ððr ðr;dþ Þ Þ r6¼s, e condon n Lemma 2.1 s me. As ð ðrþ Þ and ðr Þ depend only on ð ðsþ Þ and conacs processes belongng o oer pars an fðr; dþjr 6¼ sg, ey are ndependen from e collecon above, and we ave lm!1 IE R ðr;dþ ¼ 1 þ IE½X2 Š ðrþ 2IE½XŠ Usng (2), we ave R ðr;dþ ðrþ ence, 1 2 1 þ IE½X2 Š IE½XŠ D ¼ mn r6¼s Rðs;rÞ ðsþ þ R ðr;dþ ; ðrþ lm IE½D Š 1 þ IE½X2 Š!1 IE½XŠ Noe a s resul olds f e law of X s replaced by any law a adms a fne second momen. Provng Teorem 1.1 for 1 <<2. As >1, Sm s Formula (5) olds n s case for any funcon f verfyng e negrably condon. Le r denoe any devce dfferen from s. For convenence, le us denoe X 1 ¼ T ðr;dþ 1 T ðr;dþ. Ten, we ave, for any A a may be cosen arbrarly large, AðA þ 1Þ II fx1 Ag 2 T ðr;dþ 1 X 1 ¼T ðr;dþ mnðr ðr;dþ ;AÞA X 1 Tese varables are posve; ey all ave a fne expecaon by comparson w e rg erm. Ts proves e negrably condon requred n (5) for e funcon fðxþ ¼mnðx; AÞ; ence, we oban lm IE mnðrðr;dþ!1 ;AÞ AðAþ1Þ 2 IP½X 1 AŠ A2 A IE½X 1 Š 2IE½X 1 Š As s nequaly olds for arbrary large A and <2, we ave lm!1 IE½R ðr;dþ Š¼þ1. Te collecon of processes ððr ðr;dþ Þ Þ r6¼s verfes e condon n Lemma 2.2. As ð ðrþ Þ and ðr Þ are ndependen of s collecon, we can erefore deduce a lm IE!1 Rðr ;dþ ¼þ1; ence; lm IE½D ðrþ Š¼þ1!1 Provng Teorem 1.1 for 1. In s case, for any devce r, e Marov can defnng ðr ðr;dþ Þ 1 s recurren null, so a Orey s eorem (see [5, p. 131]) mples ¼ ¼ for all lm!1 IP Rðr;dÞ In parcular, for any A, IP Rðr;dÞ <A lm!1 ¼ and lm IP R ðr;dþ!1 A ¼ 1 We ave IE½R ðr;dþ ŠA IP½R ðr;dþ AŠ. As a consequence, and because e resul olds for any arbrary A, we ave lm!1 IE½R ðr;dþ Š¼þ1. Ts olds for any devce r. Anoer applcaon of Lemma 2 w Condon 2 allows us o prove lm!1 IE½R ðr;dþ Š¼þ1. ðrþ Te sor-conac case. Te resul n Teorem 1.1 follows from e long-conac case, as e delay n e sor conac case s always larger. Te proof of Teorem 1.3 s a lle more complex, bu follows from classcal resuls on Palm Calculus n dscree me and random wals. I may be found n Appendx B. u To summarze, we ave denfed wo regons were e beavor of e wo-op relayng algorm would dffer under e power law nerconac me assumpon Wen s greaer an 2, e algorm converges o a fne expeced delay as n e case of an exponenal decay. Wen s smaller an 2, e wo-op forwardng algorm does no converge o a fne expeced delay, as e delay a can be expeced, sarng from any nal condon, grows wou bound w me. Ts remans rue even for e long conac case, were daa excange s unlmed durng conacs, and queung n relay devces erefore as no mpac on e delay experenced. In oer words, e regon >2 may be oug of as e sably regon of e wo-op relayng algorm. 3.3 Generalzaon In s secon, we caracerze e sably regon (defned as e values of for wc an algorm aceves a bounded delay) for e general class of oblvous algorms. We conduc e followng proofs n e long conac case only. We furer assume, wen >1 and, erefore, a a seady sae exss, a e sysem as reaced s

614 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 6, NO. 6, JUNE 27 saonary beavor; oerwse, wen 1, we sar from any nal condon. We generalze e wo-op relayng algorm as follows Insead of sendng a sngle copy of a gven daa un o a unque relay, e source wll send m copes of eac daa un one o eac of e frs m relays a mees. As we ave assumed a e conac processes belongng o ese relays are ndependen, e source may ereby reduce e oal ransmsson delay by ncreasng s probably o pc a relay w a small delay o e desnaon among e m relays o wc as forwarded e message. Ts observaon s made rgorous n e followng lemma Lemma 1. Le ðr ðd1;d 1 Þ Þ ;...; ðr ðd m;d m Þ Þ be e remanng nerconac mes for m dfferen pars of devces ðd ;d Þ 1m. We suppose a ey ave reaced er seady sae. If we suppose a m>1 and 1 þ 1 m <<2, en IE R ðd 1;d 1 Þ ¼...¼ IE R ðdm;d m Þ ¼þ1and IE mn R ðd1;d 1 Þ ;...;R ðd m;d m Þ < 1 Proof. As >1, Lemma 3.2 olds A unque saonary dsrbuon exss for e produc can R ðd 1;d 1 Þ ;...;R ðdm;d m Þ gven as e produc of e saonary dsrbuon for eac componen. Hence, IP mn R ðd1;d 1 Þ ;...;R ðd m;d m Þ > ¼ IP R ðd1;d 1 Þ m > 1 m ð þ 1Þ mð 1Þ c 1 ð 1Þ Te expecaon of e mnmum s erefore fne as soon as m ð 1Þ < 1 or, equvalenly, >1 þ 1 m. u Ts resul sows a, for smaller an 2, e expeced me o mee e desnaon s nfne. However, e expeced me for e desnaon o mee a group of m devces may ave a fne expeced value, provded a >1 and a m s large enoug. Ts observaon s e ey componen n e nex resul, wc proves a usng a wo-op relayng sraegy w m relays s suffcen o exend e sably regon o any value of >1. Ts eorem also proves a e case <1, wcs observed n mos daa ses, s of que a dfferen naure, as even unlmed floodng does no aceve a bounded delay. We commen on s dfference furer n Secon 5. Teorem 2. Le us consder a source desnaon par ðs; dþ and ðsþ ;ðdþ ;D defned as n Teorem 1. We assume a all conacs are long. 1. If >2, ere exss a forwardng algorm usng only one copy of e daa, w a fne expeced delay, suc a, sarng from any nal condon, lm!1 IE½D Š¼ D <þ1. 2. If 1 <<2, m 2 IN s cosen suc a >1 þ 1 m, and e newor conans a leas N 2m devces, ere exss an algorm usng m relay devces suc a, n seady sae, IE½D Š¼ D <þ1. 3. If 1, for a newor conanng a fne number of devces and any forwardng algorm, ncludng floodng, we ave, sarng from any nal condon, lm!1 IE½D Š¼þ1. Proof. Provng Teorem 2.1. Ts proof s jus a remnder of e resul of Teorem 1. Te wo-op relayng algorm may be cosen and aceves a fne expeced delay. Provng Teorem 2.2. Le us assume a >1 þ 1=m and N 2m, were m 2 IN. Te forwardng algorm a we consder n s case s a wo-op relayng algorm usng m dfferen relays. Sep 1. A bundle s creaed a me n e source (denoed as devce s). I s frs ransmed o e m frs devces a are me. We esmae frs e me wen eac of ese m relays are all conaced and ave receved e bundle. Le us consder e collecon of remanng ner-conac me w all e oer devces ðr ðs;rþ Þ r6¼s. Ts collecon conans N 1 varables. If we consder a verson of s collecon, sored for eac me, n e ncreasng order, e me o conac m dfferen devces a me s e m value of s sored sequence. Corollary 2, wcs a smple varaon of Lemma 1 sown n Appendx C, ells a s varable s of fne expeced value f >1 þ 1=ðN 1 m þ 1Þ. Ts las assumpon s auomacally verfed as N 1 m þ 1 ¼ N m m by assumpon. Sep 2. A me, a copy of e bundle s presen n eac of e m relays a we denoe r 1 ;...;r m. We now consder e vecor ðr ðr1;dþ ;...;Rðrm;dÞ Þ wc descrbes e mes needed for eac of ese relays o ge n conac w e desnaon. Te me leng elapsed unl e pace s delvered o e desnaon s aen as e mnmum of s values. An applcaon of Lemma 1 ells us a s me as a fne expeced value. As a consequence, e overall delay, from e me of creaon of e bundle n e source o e delvery a e desnaon, s e sum of wo varables w fne expecaons. I s ence of fne expeced value. Provng Teorem 2.3. Le us consder, n s case, for a source s and any oer devce r n e newor, e remanng me R ðs;rþ a me unl e nex conac. As <1, all of ese sequences of random varables are rreducble null recurren Marov cans. By Orey s eorem ([5, p. 131]), we en ave a lm IP½R ðs;rþ ¼ Š ¼ for all wen ends o nfny. In parcular, for any arbrary large A, we ave lm IP½R ðd;d Þ AŠ ¼, so a " IP mn r6¼s Rðs;rÞ A ¼ IP \ n o # R ðs;rþ A!!1 1 r6¼s Consequenly, IE½mn r6¼s R ðs;rþ Š dverges for large. As a consequence, sarng from any nal condon, e me for a source o reac any oer devce s of nfne expecaon as mes ncrease. No forwardng algorm, no maer ow redundan, can en ranspor a pace wn a fne expeced delay usng only opporunsc conacs beween devces. u

CHAINTREAU ET AL. IMPACT OF HUMAN MOBILITY ON OPPORTUNISTIC FORWARDING ALGORITHMS 615 Noe. By comparson, e resul n Teorem 2.3 apples o any case a ncludes sor conacs as well as long conacs. Generally, a newor conanng N devces adms forwardng algorms a aceve a bounded expeced delay for any >1 þ 1 bn=2c. One example of ose s floodng (a may use up o N 2 relays); a s no e only one, as a forwardng algorm usng only bn=2c relays s suffcen. 3.4 Summary A s sage, we ave esablsed e followng resuls for e class of oblvous forwardng algorms defned n Secon 3.1 n e long conac case. For >2, any algorm from e class we consdered aceves a delay w fne mean.. If 1 <<2, e wo-op relayng algorm, nroduced n [1], s no sable n e sense a e delay ncurred as an nfne expecaon. I s, owever, sll possble o desgn an oblvous forwardng algorm a aceves a delay w fne mean. Ts requres a m duplcae copes of e daa are produced and forwarded, were m mus be greaer an 1 1 and e newor mus conan a leas 2 1 devces.. If <1, none of ese algorms, ncludng floodng, can aceve a ransmsson delay w a fne expecaon. In oer words, we ave caracerzed e performance of all ese algorms n e face of exreme condons (.e., eavy aled nerconac mes). Te las case, were <1, corresponds o e mos exreme suaon, and e resul we provde n s case seems a frs unsasfacory None of e algorms we ave nroduced can guaranee a fne expeced delay. To mae e maer worse, s case, were <1, seems o be ypcal of e nerconac me dsrbuon n e [1 mnues; 1 day] range for all e scenaros we ave prevously suded emprcally. Ts mples overall a e expeced delay for all e scenaros we ave dscussed before sould be a leas of e order of one day. Noe a s was sown for any forwardng algorms used and, even wen queung delay n relay devces are negleced. In fac, s s a negave resul, and we come bac o nerpre and dscuss s mplcaons n Secon 5. 4 RELATED WORK Our opporunsc communcaon model s relaed o bo Delay-Toleran Neworng and Moble Ad Hoc Neworng. 5 Researc wors on MANET, DTN, and, more recenly, Poce Swced Newors [12] confrm e mporance of e problem we address, as several proposons were made o use moble devces as relays for daa ranspor. Suc an approac as been used o enable communcaon were no conemporaneous pa may be found [7], o effcenly gaer nformaon n a newor of low power sensors [13], [14], [15], and o mprove e spaal reuse of dense MANET [1], [11]. All ose wors ave proved a e mobly model used as a srong mpac on e performance of e algorms ey use. 5. www.dnrg.org and www.ef.org/ml.carers/mane-carer.ml. We dd no fnd any prevous wor sudyng e caracerscs of nerconac me for users of porable wreless devces. However, we ave denfed relaed wor n e area of modelng and forwardng algorms. A common propery of e mos common mobly models s a e al of e nerconac me dsrbuon decays exponenally. In oer words, for ese models, e nerconac me s lg aled Ts s e case for..d. locaon of devces n a bounded regon (as assumed n [1]) or, more generally, for any random wal defned on a fne regon usng a comparson argumen. I s also e case for e popular random way-pon model as demonsraed n e Secon 3 of [11]. Ts fac s commonly used n e analyss of moble newors o esmae e delay of a sceme. I was sown recenly a devces movng accordng o a Brownan moon n a bounded regon exb eavy aled nerconac me w a fne varance (correspondng n our analyss o e case >2) (see [16] and e assocaed ecncal repor). Te mos relevan wor s e algorm proposed by Grossglauser and Tse n [1], furer analyzed by Sarma and Mazumdar n [11]. Te wo-op relay forwardng algorm was nally nroduced o sudy ow e mobly of devces mpacs e capacy of e newor. Our wor sars from very dfferen assumpons. Mos noably, we do no model e bandwd lmaon due o nerference, as we focus only on e delay nduced by mobly. However, some of e resuls a we sow could be used o caracerze e delay obaned n suc conexs. 5 CONCLUSION We ave analyzed several newor scenaros for opporunsc daa ransfer among moble devces carred by umans usng eg expermenal daa ses. For all daa ses, we observe a e nerconac me beween wo devces can be approxmaed by a power law n e [1 mnues; 1 day] range. We prove n a smple model e followng major resuls Power law condons may be addressed w fne expeced delay by oblvous forwardng algorms as long as e eavy al ndex of e power law s greaer an 1. Wen e eavy al ndex s smaller an 1, e expeced delay canno be bounded for any forwardng algorm of a ype, even wen one gnores e queung occurrng n eac relay devce. We ave measured a eavy al ndex smaller an 1 n all daa ses. As a consequence, e expeced delay s a leas of e order of one day. Tese observaons brng new praccal recommendaons o evaluae e performance of forwardng algorms. Mos of e mobly models commonly used oday are caracerzed by a lg aled nerconac me dsrbuon for any par of nodes. Ts propery as been used n e pas o esmae e delay n ese newors. Our emprcal fndngs of nerconac me dsrbuons, n conras, are well-approxmaed by a power law for values up o one day. Some mobly models can, n eory, be modfed o accoun for s las propery; s may be a fuure researc drecon. Anoer complemenary drecon, wcs cosen n s paper, s o drecly model opporunes beween devces nsead of er geograpcal locaons. Ts approac as e advanage a can be drecly compared w a growng ses of real-lfe connecvy

616 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 6, NO. 6, JUNE 27 races, now publcly avalable. We beleve a s s a praccal soluon, a leas for some of e ssues o be addressed n opporunsc neworng. More generally, our resuls are dealng w e feasbly of forwardng n opporunsc newors and er consequence requres furer aenon. A leas ree dfferen drecons may be followed. Frs, mg be a reasonng w an expeced value of delay s no suable, snce e possble occurrence of a long delay s unavodable wenever a forwardng algorm s used. Applcaons for suc newors sould erefore be desgned o cope w s aspec of opporunsc communcaon.. Second, noe a we dd no model e general case were conac processes for a par of nodes are eerogeneous or conan sgnfcan correlaon. I s sll possble a a fne expeced delay exss n a more complex model a accuraely reproduces e sascal properes of our daa ses. Ts drecon s appealng bu requres e removal of one of e modelng assumpons a we ave made and wc are common for mos of e resuls currenly nown n s area. I also necessaes e desgn of a forwardng algorm a dfferenaes beween nodes; some scemes of a ype ave been only recenly proposed [17], [18], [19].. Trd, one can nvesgae ow o add connecon opporunes n a moble newor usng specal devces or paral nfrasrucure a could, n some cases, be already avalable. We are currenly worng on performng more uman mobly expermens usng dfferen ype of devces, and dverse socologcal groups, n order o follow e drecons we menon above. One of our long erm goals s o sudy e properes of e acual raffc creaed by users n an opporunsc daa newor. APPENDIX A PRELIMINARY RESULTS A.1 Independen Composon and Lm Expecaon Lemma 2. Le ððf ðþ Þ 2IN Þ 2I be a fne collecon of sequences of real valued random varables verfyng lm!1 IE½F ðþ Š¼l, were l 2 IR [ fþ1g and 1. 8; ; IE½F ðþ Š2IR and l 2 IR or 2. 8; ; IE½F ðþ Š2IR [ fþ1g and l ¼þ1 Le ð Þ 2IN and ð Þ 2IN be wo IN valued processes, ndependen from F, suc a lm!1 ¼þ1as We en ave lm!1 IE½F ðþ Š¼l. Proof. Le us frs develop e followng expecaon IE F ðþ ¼ X X X jip ¼ ; ¼ ; F ðþ ¼ j 2I j ¼ X X X jip ½ ¼ ŠIP ½ ¼ ŠIP F ðþ ¼ j ð3þ 2I j ¼ X X IP ½ ¼ ŠIP ½ ¼ ŠIE F ðþ 2I If we suppose Lemma 2.1, we ave l<þ1 and 8" >; 9T s > T ¼) IE F ðþ l < " 2 If M ¼ sup 2I;T IE F ðþ l, ere exss K suc a >K¼) IP ½ TŠ 1 " 2 M and, ence, IE F ðþ l can be bounded from above by X X IP½ ¼ ŠIP½ ¼ Š IE F ðþ l 2I X IP½ ¼ Š M X IP½ ¼ Š 2I T þ X! IP½ ¼ Š IE F ðþ l >T X IP½ ¼ Š ð"=2 þ "=2Þ " 2I If we suppose Lemma 2.2, we ave l ¼þ1and 8A >; 9T;ð >T¼) IE F ðþ 2 ða þ 1ÞÞ Le M ¼ sup 2I;T max IE F ðþ ;. 9K suc a >K¼) IP½ TŠ maxð1=2; 1 1=M Þ; and IE F ð Þ ¼ X X IP½ ¼ ŠIP½ ¼ ŠIE F ðþ 2I X IP½ ¼ Š M X IP½ ¼ Š 2I T þ X! IP½ ¼ ŠIE F ðþ >T X IP½ ¼ Š 1 þ 1 ð2ða þ 1ÞÞ A 2 2I A.2 Remanng Inerconac Because e conac process ðu ðd;d Þ Þ s a renewal process, e sequence ðr ðd;d Þ Þ of negers s a Homogeneous Marov Can n IN suc a ( R ðd;d Þ þ1 ¼ Þ Rðd;d 1 f R ðd;d Þ > ; R ðd;d Þ þ1 ¼ 1 w prob IP½X ¼ Š f ð4þ Þ Rðd;d ¼ Ts Marov Can s clearly rreducble and aperodc as IP½X ¼ 1 > Š and s recurren as X s almos surely fne. Te followng lemma caracerzes s properes, wc depend on e value of based on classcal resuls from e eory of Marov cans. Lemma 3. For any devces d; d ;e;e suc a ðd; d Þ 6¼ ðe; e Þ, we ave 1. If >1, ðr ðd;d Þ Þ s ergodc. 2. If >1, e can ðr ðd;d Þ ;R ðe;e Þ Þ s ergodc and adms e followng saonary dsrbuon ð; jþ ¼ ð þ 1Þ ðj þ 1Þ ðc 1 Þ 2 ; were c 1 ¼ X ð þ 1Þ

CHAINTREAU ET AL. IMPACT OF HUMAN MOBILITY ON OPPORTUNISTIC FORWARDING ALGORITHMS 617 suc a we ave n seady sae ð þ 2Þ ð 1Þ c 1 ð 1Þ IP R ðd;d Þ > ð þ 1Þ ð 1Þ c 1 ð 1Þ 3. If 1, ðr ðd;d Þ Þ s recurren null. Proof. Le us nroduce re, e me for Rðd; d Þ o reurn n e sae. From e srucure of e Marov can (4), sarng from sae, we can easly deduce a IE ½re Š¼IE½XŠ. If>1, we ave IE½XŠ < þ1, provng Lemma 3.1, and f 1, we ave IE½XŠ ¼þ1, provng Lemma 3.3. By Lemma 3.1, we now a e Marov can Rðd; d Þ s recurren posve; ence, adms a saonary dsrbuon. I s easy o cec, from s regenerave srucure, a s gven by ðþ ¼c 1 ð þ 1Þ, were c 1 ¼ 1= P ð þ 1Þ. Te same resul olds for Rðe; e Þ. As ese wo Marov Cans are ndependen, one can en cec easly a e produc Marov can ðrðd; d Þ;Rðe; e ÞÞ, wcs rreducble and aperodc, adms a saonary dsrbuon gven by e produc of e measure. I s ence ergodc. In seady sae, we ave IP R ðd;d Þ > ¼ X ðþ ¼ 1 X ðj þ 1Þ c j> 1 j> As e funcon x 7! ðx þ 1Þ s nonncreasng, we ave Z 1 us þ 1Þ þ1ðx dx X ðj þ 1Þ j> ð þ 2Þ ð 1Þ 1 X ðj þ 1Þ j> Z 1 ðx þ 1Þ dx; ð þ 2Þ ð 1Þ ; 1 wc complees e proof for Lemma 3.2. u Sm s formula for >1. For any devces d and d, e process ðr ðd;d Þ Þ s regenerave w respec o e delayed renewal sequence ðt ðd;d Þ Þ. If we assume >1, we ave IE½XŠ < þ1; ence, e nereven of e sequence ðt ðd;d Þ Þ adms a fne mean. We now, n s case (see [5, p. 148]), a IE P T ðd;d Þ 1 1 lm IE f Þ ¼T ðd;d Þ f R ðd;d Þ!1 Rðd;d ¼ IE T ðd;d Þ 1 T ðd;d Þ 2 T ðd;d for any f verfyng IE X Þ 1 1 3 ð5þ 6 f Þ 4 7 Rðd;d 5 < 1 APPENDIX B ¼T ðd;d Þ QUEUING WITH A PROCESS OF SERVICE INSTANT In consras w classcal queung sysems, e nodes of a moble newor only serve bundles from a gven queue wen ey are n conac w e correspondng desnaon. In s secon, we exend some well-nown resuls on queues o andle s consran. Le us consder a queue recevng cusomers accordng o a pon process a ¼fa j 2 Zg, a may be served only a some servce nsan, wc follow a process s ¼fs m j m 2 Zg. We mae e followng assumpons. A cusomer arrvng a me jons e queue and can be served sarng from þ 1.. A eac servce nsan, one cusomer from e queue s served, excep f e queue s empy. Hence, s sysem beaves as f e me slo were dvded n wo pars In e frs alf of e me slo, a cusomer from e queue s served f e slo s a servce nsan; n e second alf, new cusomers jon e queue. Le us nroduce QðÞ, e number of cusomers presen afer e frs alf of me slo s compleed. Te process Q follows e recurson QðÞ ¼maxð;Qð 1ÞþN a ð 1Þ N s ðþþ; ð6þ were N a (respecvely, N s ) denoes e counng measure assocaed w e pon process a (respecvely, s). B.1 Saonary, Lle s Law Resuls are sown n e saonary ergodc framewor (see [6]). We assume ere a s a measurable mappng!, wc preserves e probably measure (.e., IP ¼ IP) and s ergodc (all nvaran evens ave probably or 1). A pon process s called saonary w respec o f s counng measure verfes Nðð!Þ;CÞ¼Nð!; C þ Þ, were C Z and! 2. We defne s nensy as IE½NðÞŠ. Te nex resul follows closely e proof of e sably regme for a sngle server queue (see [6, pp. 83-87]). I sows a, under a smple sably condon, e sysem adms a seady sae a s saonary n a srong sense (compable w e sf ). Te expeced delay of a cusomer roug s sysem s en gven by a generalzed Lle Formula. Noaon. Followng e usual convenon of Palm calculus (ere, n dscree me), we denoe by IP a e probably measure IP under e condon a pon process a as a pon n ¼. We number cusomer w e convenon a cusomer ¼ denoes e las cusomer a arrved srcly before 1. We denoe by V e sojourn me of cusomer. Lemma 4. If a; s are wo saonary pon processes w respec o, w respecve nenses ; suc a <, 1. Tere exss an nal condon, Q<1 ~ as, suc a e queue process verfes QðÞ ~ ¼ Q ~. 2. In s saonary regme, IE a ½ ~V Š¼1 þ 1 IE½ QŠ. ~ 3. If e queue sars empy, lm sup!1 IE ½V Š 1 þ 1 IE½ QŠ ~ Proof. We defne e sequence of varables ndexed by T ~Q ½TŠ ¼ max ð N að ;...; 1Þ N s ð þ 1;...; ÞÞ T Clearly, s sequence s posve, nondecreasng, and verfes ~Q ½T þ1š ¼ max ; Q ~ ½T Š þ N a ðþ N s ð1þ ð7þ

618 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 6, NO. 6, JUNE 27 I en adms an a.s. lm, denoed by Q, ~ verfyng ~Q ¼ max ; Q ~ þ N a ðþ N s ð1þ Ts lm may ae nfne values. Noe a, snce f Q ~ ¼1g s nvaran and s ergodc, en as probably 1 or. In oer words, eer s lm s a.s. nfne or s a.s. fne. We can rewre (7) as ~Q ½T þ1š ¼ Q ~ ½TŠ mn Q ~ ½T Š ;N s ð1þ N a ðþ ; suc a IE mn Q ~ ½TŠ ;N s ð1þ N a ðþ ¼ IE Q ~ ½T Š Q ~ ½Tþ1Š ¼ IE ~ Q ½T Š ~ Q ½Tþ1Š By monoone convergence, we deduce IE½mn Q; ~ N s ð1þ N a ðþ Š Assumng a ~ Q s a.s. nfne, e mnmum above s en always gven by e second erm, wcmples a IE½N s ð1þ N a ðþš ¼. By e converse nducon, >¼) ~ Q<1 as; wc proves Lemma 4.1. Lemma 4.2 s an applcaon of e Campbell-Mece egaly 2 3 IE½ QŠ¼IE ~ 4 X II fa 1gII faþv 5 1g 2 Z ¼ X X II f 1g II fþv1g IP a ½V ¼ vš v> 2 Z ¼ X 1ÞIP v>ðv a ½V ¼ vš ¼ðIEðÞ a ½V Š 1Þ Le us denoe by S 1 ;S 2 ; e sequence of pons of e process a a belongs o f; 1; 2;...g. Tey may be seen as e resul of a random wal S n ¼ X 1 þ...þ X n, were varables ðx Þ are..d. and follow e nereven dsrbuon. Te above expecaon may be rewren IE maxð n S nþ ¼ IE maxð Y 1 þ...þ Y n Þ ; n> n> were Y ¼ 1 X. Noe a IE½ðY Þ 2 Š 2 < 1 and IE½Y Š <, provng by (8) a e above expecaon s fne. Nex, we prove a, for any <, IE maxð N s ð1;...;þþ ¼ IE max Sn n > n> ¼ IE maxð Z 1 þ...þ Z n Þ < 1 n> as Z ¼X 1, IE½Z Š<, and IE ðz þþ2 IE ðx Þ2 <1. To conclude, we coose suc as <<and we ave IE maxðn a ð1;...;þ N s ð1;...;þþ > ¼ IE maxðn a ð1;...; 1Þ þ N s ð1;...;þþ > IE maxðn a ð1;...;þ Þþmaxð N s ð1;...;þþ > Corollary 1. If a and s sasfy e condons of Lemma 5, > IE½ ~ QŠ < 1 and IE a ½ ~V Š < 1 Proof. Accordng o e proof of Lemma 4, u We ave a.s. V ~V, wc proves Lemma 4.3. B.2 Expeced Queue Leng Lemma 5. Assume a and s are wo renewal pon processes u ~Q ¼ maxðn a ð ;...; 1Þ N s ð þ 1;...; ÞÞ Te resul s en followng e above lemma. u. wnenses <,. suc a nereven dsrbuon F a as a fne mean, and. suc a e nereven dsrbuon F s as a fne varance. Ten, IE maxðn a ð1;...;þ N s ð1;...;þþ < 1 > Proof. We recall e classcal resul on random wals (see [2, p. 27]) For ðz Þ..d., IE½Z Š < ; IE½ðZ þþ2 Š < 1, we ave IE maxð Z 1 þ...þ Z Þ < 1 ð8þ Le us prove frs, for any >, IE maxðn a ð1;...;þ Þ < 1 > APPENDIX C PROOF OF THEOREM 1 IN THE SHORT-CONTACT CASE Le us summarze e resuls from e above secons In a queue w arrval a and servce nsan s, cusomers experenced a fne expeced delay f 1) a and s are renewal processes, 2) e sably condon s verfed, and 3) nerservce-nsan dsrbuon as a fne varance. Noe a Condons 2 and 3 are necessary. In e followng, we presen a sceme ensurng a all queues mplemened n e moble nodes verfy Condons 1, 2, and 3. I may be mproved a e cos of an addonal effor o weaen Assumpon 1. Eac source devces s manan a se of N 1 source queues correspondng o eac oer devce. We assume a bundles are creaed n eac of ese queues accordng o a renewal process wnensy < w p>. Wen anoer 1 p 2IE½XŠ

CHAINTREAU ET AL. IMPACT OF HUMAN MOBILITY ON OPPORTUNISTIC FORWARDING ALGORITHMS 619 devce d s me durng an odd me slo, a bundle from e queue assocaed w d s served, f s queue s no empy. Te devce d may be e desnaon for s, bu, oerwse, e bundle s enerng a relay queue (see below). For ecncal reasons, we also assume a, w a small probably p, aen ndependenly, an ndependen blocng occurs and no bundle a all s sen by e source durng s conac. All devces (ncludng all sources) manan, n addon, N 1 relay queues, eac one correspondng o a gven desnaon. Wen a bundle s receved durng an odd meslo (as descrbed above), s enerng e relay queue correspondng o s desnaon. If anoer devce d s me durng an even me slo, a bundle for desnaon d s sen, unless e correspondng queue s empy. Le us prove a bundles experence fne expeced delay n eac of ese queues. Eac source queue receves and serves bundles accordng o saonary processes a sasfy Condons 1, 2, and 3.. A relay queue sasfes Condons 2 and 3; unforunaely, e arrval process n s queue s no a renewal process. Nevereless, e same resul olds by a comparson. All arrval mes of a bundle n s relay queue are ncluded n a quassauraed renewal process (a ncludes all meeng mes w e source correspondng o e desnaon of e queue, wou ndependen blocng). Noe a e expeced delay n a relay queue s never larger an e expeced delay n e same queue w a quassauraed arrval process. One can cec easly a s las case verfes Condons 1, 2, and 3, provng a e expeced delay s fne n bo cases. We deduce a all sources can ransm o er desnaon a a rae smaller an ðn 1Þð1 pþ suc a 2IE½XŠ bundles experenced a fne expeced delay. As p may be cosen arbrarly, e same resul olds for any rae smaller an N 1. 2IE½XŠ C.1 Proof of Corollary of Lemma 1 For any real numbers ðx 1 ;...;x m Þ and m, le us denoe by ordð; ðx 1 ;...;x m ÞÞ e elemen of e sequence afer s reordered n e ncreasng order. In parcular, ordð1; ðx 1 ;...;x m ÞÞ ¼ mnðx 1 ;...;x m Þ. We ave Corollary 2. Le R ðd1;d 1 Þ ;...; Rðd m;d m Þ be e remanng nerconac mes for m dfferen pars of devces ðd ;d Þ 1 1m. We suppose a >1 þ m jþ1, en IE ord j; R ðd1;d 1 Þ ;...;R ðd m;d m Þ < 1 Proof. Le M j ¼ ord j; R ðd1;d 1 Þ ;...;R ðd m;d m Þ. n o IP½M j >nš¼ip # R ðd;d Þ >n m j þ 1 Ts s e probably a a leas m j þ 1 evens occur on a collecon of m varables. Noe a all ese evens are ndependen, and eac of em occurs w e same probably p ðnþ1þ ð 1Þ c 1 ð 1Þ. As a consequence, e above probably may be rewren as X m ¼m jþ1 X p ð1 pþ m m p m jþ1 m ¼m jþ1 Ts proves a, for c 2 ¼ 1 c 1 ð 1Þ P m ¼m jþ1 m m ; IP½M j >nšc 2 ðn þ 1Þ ðm jþ1þð 1Þ ; wcmples a IE½M j Š < 1 as soon as 1 >1 þ m j þ 1 ACKNOWLEDGMENTS Te auors would le o graefully acnowledge Dave Koz and Trsan Henderson a Darmou College, Geoff Voeler a e Unversy of Calforna, San Dego, Eyal de Lara and Jng Su a e Unversy of Torono, and e Realy Mnng projec a e Massacuses Insue of Tecnology for provdng er daa. Tey would also le o an Vncen Hummel and Ralp Klng a Inel for er suppor, Mar Crovella for s nsgful commens on er fndngs, Lauren Massoulé for s advce on some of e proofs, and e parcpans of e ree expermens ey conduced. Ts wor was parally funded by e Informaon Socey Tecnologes program of e European Commsson n e framewor of e FET-SAC HAGGLE projec (27918). REFERENCES [1] P. Hu, A. Canreau, J. Sco, R. Gass, J. Crowcrof, and C. Do, Poce Swced Newors and e Consequences of Human Mobly n Conference Envronmens, Proc. ACM SIGCOMM Frs Worsop Delay Toleran Neworng and Relaed Topcs, 25. [2] M. McNe and G.M. Voeler, Access and Mobly of Wreless PDA Users, ecncal repor, Dep. of Compuer Scence and Eng., Unv. of Calforna, San Dego, 24. [3] T. Henderson, D. Koz, and I. Abyzov, Te Cangng Usage of a Maure Campus-Wde Wreless Newor, Proc. MobCom 4, pp. 187-21, 24. [4] N. Eagle and A. Penland, Realy Mnng Sensng Complex Socal Sysems, J. Personal and Ubquous Compung, 25. [5] P. Bremaud, Marov Cans, Gbbs Feld, Mone Carlo Smulaon and Queues, frs ed. Sprnger-Verlag, 1999. [6] F. Baccell and P. Bremaud, Elemens of Queung Teory, second ed. Sprnger-Verlag, 23. [7] A. Vada and D. Becer, Epdemc Roung for Parally- Conneced Ad Hoc Newors, ecncal repor, Unv. of Calforna, San Dego, 2. [8] X. Cen and A. Murpy, Enablng Dsconneced Transve Communcaon n Moble Ad Hoc Newors, Proc. Worsop Prncples of Moble Compung, pp. 21-27, 21. [9] J.A. Davs, A.H. Fagg, and B.N. Levne, Wearable Compuers as Pace Transpor Mecansms n Hgly-Paroned Ad-Hoc Newors, Proc. Ff IEEE In l Symp. Wearable Compuers (ISWC 1), p. 141, 21. [1] M. Grossglauser and D. Tse, Mobly Increases e Capacy of Ad Hoc Wreless Newors, IEEE/ACM Trans. Neworng, vol. 1, no. 4, pp. 477-486, 22. [11] G. Sarma and R.R. Mazumdar, Delay and Capacy Trade-Off n Wreless Ad Hoc Newors w Random Way-Pon Mobly, preprn, Scool of Elecrcal and Compuer Eng., Purdue Unv., 25, p//mn.ecn.purdue.edu/lnx/paper/5.pdf. u

62 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 6, NO. 6, JUNE 27 [12] J. Sco, P. Hu, J. Crowcrof, and C. Do, Haggle A Neworng Arcecure Desgned around Moble Users, Proc. Trd IFIP Wreless on Demand Newor Sysems Conf., 26. [13] S. Jan, R.C. Sa, G. Borrello, W. Brunee, and S. Roy, Explong Mobly for Energy Effcen Daa Collecon n Sensor Newors, Proc. IEEE Symp. Modelng and Opmzaon n Moble, Ad Hoc, and Wreless Newors, 24. [14] P. Juang, H. O, Y. Wang, M. Maronos, L.S. Pe, and D. Rubensen, Energy-Effcen Compung for Wldlfe Tracng Desgn Tradeoffs and Early Experences w Zebrane, Proc. 1 In l Conf. Arcecural Suppor for Programmng Languages and Operang Sysems (ASPLOS-X), pp. 96-17, 22. [15] T. Small and Z.J. Haas, Te Sared Wreless Infosaon Model A New Ad Hoc Neworng Paradgm (or Were Tere Is a Wale, Tere Is a Way), Proc. MobHoc 3, pp. 233-244, 23. [16] X. Ln, G. Sarma, R.R. Mazumdar, and N.B. Sroff, Degenerae Delay-Capacy Tradeoffs n Ad-Hoc Newors w Brownan Mobly, IEEE/ACM Trans. Neworng, vol. 14, pp. 2777-2784, 26. [17] H. Dubos-Ferrere, M. Grossglauser, and M. Veerl, Age Maers Effcen Roue Dscovery n Moble Ad Hoc Newors Usng Encouner Ages, Proc. MobHoc 3, pp. 257-266, 23. [18] A. Lndgren, A. Dora, and O. Scelén, Probablsc Roung n Inermenly Conneced Newors, SIGMOBILE Moble Compung Comm. Rev., vol. 7, no. 3, pp. 19-2, 23. [19] J. Leguay, T. Fredman, and V. Conan, Evaluang Mobly Paern Space Roung for DTNs, Proc. INFOCOM, 26. [2] S. Asmussen, Appled Probably and Queues, second ed. Sprnger- Verlag, 23. Augusn Canreau joned e Tomson Pars Researc Lab n 26, soon afer recevng e PD degree n compuer scence and maemacs from Ecole Normale Supéreure de Pars. He wored prevously a INRIA under e supervson of Francos Baccell, and n collaboraon w Alcael Bell and IBM researc on e naure and e consequences of neracon beween TCP flows. He vsed Inel Researc Cambrdge for one year unl 25. Hs curren researcneress are n desgnng and analyzng algorms for opporunsc, wreless, and overlay newors. Crsope Do receved e PD degree n compuer scence from Insu Naonal Polyecnque de Grenoble n 1991. He was w INRIA Sopa-Anpols from Ocober 1993 o Sepember 1998, Sprn (Burlngame, Calforna) from Ocober 1998 o Aprl 23, and Inel Researc (Cambrdge, Uned Kngdom) from May 23 o Sepember 25. He joned Tomson n Ocober 25 o sar and manage e Pars Researc Lab (p//parslab.omson. ne). Dr. Do s fuure researc acves wll focus on communcaon servces and plaforms. He s a fellow of e ACM. Rcard Gass s a researc engneer a Inel Researcn e Psburg lable. Hs neress are n opporunsc communcaon, wreless newors, and vecular ad oc newors. He s also enrolled as a PD suden a e Unversy of Perre and Mare Cure n Pars. James Sco joned Mcrosof Researcn Cambrdge, Uned Kngdom, n January 27, and prevously wored a Inel Researcn Cambrdge, Uned Kngdom, for four years. He receved e PD degree from e Unversy of Cambrdge under Professor Andy Hopper. Hs researcneress are broad and nclude moble neworng and ubquous compung.. For more nformaon on s or any oer compung opc, please vs our Dgal Lbrary a www.compuer.org/publcaons/dlb. Pan Hu receved e bacelor s and Mpl degrees from e Elecrccal and Elecronc Engnnerng Deparmen a e Unversy of Hong Kong n 22 and 24, respecvely. He s currenly a PD suden n e Sysem Researc Group, Compuer Laboraory, Unversy of Cambrdge. He began wor on e PD degree n 24 and s expeced o graduae n fall 27. See s Web page a p//www.cl.cam.ac.u/ ~p315/. Jon Crowcrof s e Marcon Professor of Newored Sysems n e Compuer Laboraory of e Unversy of Cambrdge. Pror o a, e was professor of newored sysems n e Compuer Scence Deparmen a Unversy College London. He s a fellow of e ACM, e Brs Compuer Socey, e IEE, e Royal Academy of Engneerng, and e IEEE. He was a member of e IAB and was e general car for ACM SIGCOMM from 1995 o 1999. He s on e edoral eam for COMNET,and on e program commees for ACM SIGCOMM and IEEE INFOCOM. He as publsed fve boos, e laes of wcs Lnux TCP/IP Implemenaon (Wley, 21). Currenly, e s e Prncple Invesgaor for e CMI-funded Communcaons Researc Newor, wcs a 3M pound governmen/ndusry/academa muldscplnary collaboraon o auomae e successful exploaon of dsrupve communcaons ecnologes.