Enabling Crowd-Sourced Mobile Internet Access

Transcription

1 Enablng Crowd-Sourced Moble Internet Access George Iosfds, Ln Gao, Janwe Huang, and Leandros Tassulas Dept. of Informaton Engneerng, The Chnese Unversty of Hong Kong, Hong Kong Dept. of Electrcal and Computer Engneerng, Unversty of Thessaly, and CERTH, Greece Abstract Crowd-sourced moble Internet access servces enable moble users to connect wth each other and share ther Internet connectons. Ths s a promsng soluton for addressng users ncreasng needs for ubqutous connectvty and allevatng network congeston. The success of such servces heavly depends on users wllngness to contrbute ther resources. In ths paper, we consder a general model for such servces, and desgn a dstrbuted ncentve mechansm for encouragng users partcpaton. Ths barganng based scheme ensures that the contrbuton of user resources, n terms of Internet access bandwdths and battery energy, and the allocaton of servce capacty, measured n the delvered moble data, are Pareto effcent and proportonally far. The numercal results verfy that the servce always mproves users performance and that these benefts depend on the dversty of the users resources. I. INTRODUCTION Motvaton. As the global moble data traffc ncreases rapdly [1] and the cellular networks get congested much more frequently [2], t s mportant to desgn more flexble and nnovatve mechansms to offer ubqutous Internet connectvty to users by fully utlzng the resources of heterogeneous networks. In ths context, user provded connectvty (UPC) servces [3] offer a low cost soluton for allevatng network congeston and satsfyng users communcaton needs. One of the frst UPC servces was FON [4], a communty-based WF Internet access scheme, where roamng FON users can access Internet through the home WF connectons of other nearby FON users. Several novel UPC schemes that leverage the capabltes of user-owned equpment to operate as moble hotspots have also emerged recently, such as the ones by Karma [5] and Open Garden [6]. The award wnnng Open Garden soluton 1 enables moble devces to connect through Bluetooth or WF drect lnks n order to share ther Internet connectons. More specfcally, the Open Garden moble software creates a mesh network, where each user (devce) may act as a clent node (consumng data), a relay node (relayng data to other nodes), or a gateway node (connectng the mesh overlay wth the Internet through a WF or a cellular connecton). An example of the Open Garden operaton s depcted n Fg. 1. Each user can concurrently The work of L. Gao and J. Huang was supported by the General Research Funds (Project Number CUHK , CUHK 41271, and CUHK ) establshed under the Unversty Grant Commttee of the Hong Kong Specal Admnstratve Regon, the Natonal Natural Scence Foundaton of Chna (Project Number ). The work of G. Iosfds and L. Tassulas was supported by the project SOFON whch s mplemented under the "ARISTEIA" Acton of the "OPERATIONAL PROGRAMME EDUCATION AND LIFELONG LEARNING" and s co-funded by the European Socal Fund (ESF) and Natonal Resources. 1 On May 212, Open Garden won the Most Innovatve Startup Award at the TechCrunch Dsrupt Conference. Fg. 1. An example of users nteractons n the crowd-sourced moble Internet access servce. Left: concurrent downloadng from two gateways. Rght: multhop connecton to Internet. consume data from multple gateways (channel bondng [6]), over multple and possbly mult-hop paths, and serve as a relay or even a gateway for others. The software dentfes the best Internet connectons, wth the goal to ncrease the amount of data the partcpatng users can consume. In a nutshell, Open Garden consttutes a crowd-sourced Internet access servce, where users contrbute resources n terms of Internet connectons and battery energy. The key beneft s to turn the negatve externalty of network congeston to the postve network effect, by explotng the dversty of connectons and demands of dfferent users. However, the success of ths servce depends on the wllngness of users to jon the servce and contrbute ther resources. Clearly, a user wth a low battery energy level and a fast Internet connecton, may not be wllng to partcpate and serve other users. Therefore, t s of paramount mportance to desgn a proper ncentve mechansm for nducng user partcpatons, a mechansm that s currently mssng from Open Garden. Motvated by the Open Garden software, n ths paper we propose a general model for the crowd-sourced moble Internet access servce, and desgn an ncentve mechansm to guarantee ts successful operaton. Such an ncentve scheme not only encourages moble users to collaborate, but also leads to a proper data transmsson and routng polcy that balances effcency and farness. The effcency s quantfed n terms of the aggregate throughput, and can be maxmzed by havng users wth the hghest Internet connecton capactes serve as gateways, wth other users servng as relays f necessary. The farness crteron, on the other hand, concerns the relatonshp among data delvery, resource contrbuton, and economc gans/losses of each user. If a user experences excessve unfar consumpton of her resources by others, she wll probably leave the servce and hence deterorate the performance experenced by other users. Nevertheless, the desgn of ths mechansm s very challengng. Frst of all, there s often no central entty controllng /14/$ IEEE /14/$ IEEE 451

2 452 Fg. 2. The servce can be used to offload cellular traffc to WF access ponts (AP), or onload WF traffc to cellular networks (downloadng scenaro). The offloadng decsons depend manly on the data usage (and energy) cost ncurred by the users (user-ntated offloadng), whle the onloadng decsons depend on the congeston of WF APs. such a wreless mesh network wth devces belongng to heterogeneous physcal networks, and each user only has nformaton regardng her own needs and resources. Therefore, the proposed scheme has to be dstrbuted. Moreover, the farness crteron should be carefully selected, so as to consder the fact that users have dfferent needs and may contrbute dfferent resources wth dfferent costs. Also, a user wll partcpate n the servce, only f she expects to mprove her performance compared to the one when actng ndependently (n standalone mode). Clearly, the ncentve mechansm should also take nto account ths standalone performance. Contrbutons. We ntroduce a new analytcal framework for the UPC servce, whch s modeled as a mult-hop, mult-path mesh network that manages multple uncast sessons from the Internet towards dfferent users. Each user s parameterzed by her Internet connecton capacty, energy resources (e.g., battery level), monetary cost for downloadng data (dependng on the user s data plan), and her relayng capabltes. Users may have dfferent communcaton needs, whch are captured by dfferent utlty functons. We employ game theory and specfcally the Nash barganng soluton (NBS) concept [7] to characterze the effcent and far contrbuton of the user resources and allocaton of the servce capacty to each user. The NBS yelds an outcome whch s Pareto effcent and proportonally far [8], and s selfenforcng and acceptable by all users. Our proposed algorthm can compute the NBS of the system n a dstrbuted fashon, thus enablng a decentralzed mplementaton of the ncentve mechansm. Achevng ths s hghly non-trval mathematcally, snce the correspondng system optmzaton problem has both a coupled constrant set and a coupled objectve functon. Moreover, we ntroduce a vrtual currency system whch facltates the cooperaton of users. Namely, users can cooperate not only by drect servce exchange (e.g., relayng data for each other), but also by usng ths vrtual currency to pay for the servces they receve (e.g., exchange vrtual money wth relayng data). Addtonally, t encourages users who currently do not have communcaton needs, to partcpate and serve other users so as to collect vrtual money (that can use later when they have needs). Smlarly, t enables users wth poor Internet connectons to utlze the servce by payng other users. Clearly, ths system ncreases the number of users who are wllng to partcpate n the servce and are able to cooperate wth each other. Fnally, we dscuss the mpact of network congeston on the servce. Interestngly, through the cooperaton of users, ths servce can offload cellular traffc to WF networks [9], or onload WF traffc to cellular networks [1]. These scenaros are depcted n Fg. 2. The optmal strategy s determned by the NBS, and depends on congeston levels of users Internet connectons (whch determne the effectve capacty experenced by users), and the data plans of the users (.e., the cost of cellular access). Our man techncal contrbutons are as follows: Servce Modelng. We ntroduce a general crowd-sourced moble Internet access servce model that ncorporates users communcaton needs, monetary costs, and energy consumpton costs, whch are the key factors affectng users partcpaton and servcng decsons. Incentve Mechansm. We desgn an ncentve mechansm, based on the Nash barganng soluton (NBS), that nduces users partcpaton through far allocaton of the contrbuted resources. Ths s very crucal to mantan a good performance of the servce. Dstrbuted Implementaton. We propose a dstrbuted algorthm, whch combnes the concepts of consstency prcng [11] and prmal-dual Lagrange relaxaton [12], and acheves the unque NBS. Ths enables the decentralzed mplementaton of the servce wthout requrng central coordnaton or addtonal nfrastructure. Applcaton Scenaros. We dscuss how the servce can account for nterference and congeston effects, and how t can be for used for moble data offloadng and onloadng. Performance Evaluaton. We evaluate the performance of the servce for varous system parameters and offloadng/onloadng scenaros. We fnd that the servce benefts ncrease as users become more heterogeneous (dverse) n terms of ther needs and avalable resources. The rest of the paper s organzed as follows. Sec. II ntroduces the system model and the Nash Barganng problem formulaton. In Sec. III we present the ncentve mechansm for the servce, and n Sec. IV we provde the algorthm for ts dstrbuted mplementaton. We present numercal results n Sec. V. Fnally, we analyze related works n Sec. VI, and conclude n Sec. VII. II. SYSTEM MODEL AND PROBLEM STATEMENT A. System Model We consder a set of moble users I = {1, 2,...,I}, who are nterested n provdng a crowd-sourced Internet access servce (hereafter referred to as servce) to each other for a certan tme perod. The users can communcate wth each other by formng a mesh network G = (I, E), where E s the set of drected lnks connectng them through WF Drect [13] or Bluetooth technology (IEEE ). Some users may not be able to communcate drectly, e.g., due to dstance or ncompatblty of ther wreless nterfaces. We focus on the downloadng operaton of the system,.e., when users download data from the Internet and relay t to

3 453 each other 2. There are I data commodtes n the system, where each commodty (n) corresponds to a (potentally multhop) uncast sesson orgnatng from the Internet (e.g., a web/content server) and endng at a user n I. In every perod, each user can serve one or more roles as follows: she can be a clent node (consumng data), a relay node (routng data to other users), and/or a gateway node (downloadng data from Internet). Specfcally, let C be the data amounts (n bytes) that can be transferred over lnk (, j) E durng the current perod. Let C be the amount of data that user I can download (as a gateway) from the Internet through a cellular or a WF connecton. For smplcty, we assume that each gateway only downloads data from the Internet usng her best Internet connecton. Clearly, wreless channel condtons may be affected by factors such as fadng and shadowng and hence can be tme-varyng. Hence we wll consder a tme perod length that s large enough comparng wth the small-scale channel fluctuatons such as fast fadng, but small enough comparng wth the large-scale channel fluctuatons such as shadowng. Each user I has a maxmum energy budget of E unts (joules) that can be spent durng the current tme perod. The user consumes energy durng ether downloadng or relayng data. Let e s > be the energy that user consumes when she sends one byte to user j (over lnk (, j) E). Also, e r > s the energy that user j consumes for recevng one byte from user. Fnally, e > s the energy consumpton when node downloads one byte from the Internet. Typcally, energy consumpton s hgher wth cellular than wth WF connectons [15]. Downloadng data can nduce certan monetary cost to the gateway users, dependng on the type of Internet connecton and prcng scheme (data plan). Let p be the prce that each user pays for each byte that she downloads (for herself or other users) from the Internet 3. Each user perceves certan satsfacton (utlty) for consumng data (not ncludng relayng for other users). We ntroduce the utlty functon U ( ) for user, whch s a postve, ncreasng, and concave functon of the total bytes she drectly downloads and receves from her neghbors. The concavty of the utlty functon models the user s dmnshng margnal satsfacton of addtonal data consumpton. Dfferent users may have dfferent utlty functons [16], [17]. For example, the utlty of a user browsng the web s ntally proportonal to the amount of data that she downloads, and saturates after the maxmum ntended data (or, equvalently tme sesson) has been reached. Each user downloads data to satsfy her own communcaton needs and/or the needs of other users. Let y (n) be the data (bytes) that user downloads from Internet for user n I. We also defne the data amount (n bytes) of commodty (n) that user delvers (routes) to her one-hop neghbor user j. The operaton of the system can be descrbed by the downloadng matrx y =(y (n) : I,n I), 2 For the uploadng scenaro there are slght changes, e.g., the amount of energy consumpton s hgher and uplnk capactes are smaller [14], whch however do not affect the desgn of our mechansm. 3 For the tme perod of users nteracton, and for the gven value of C, I, prce p s assumed fxed. and the routng matrx x =( : (, j) E,n I). These varables characterze the total amount of data of all commodtes that are downloaded or routed by each user over each lnk, durng the current tme perod. The routng and downloadng decsons should satsfy the flow balance equatons + y (n) =,, n I, n, (1) j In() where In() = ( j :(j, ) E ) and Out() = ( j :(, j) E ) are the sets of upstream and downstream one-hop neghbors of user, respectvely. Clearly, t holds x () =,, j Out(). Moreover, each lnk (, j) cannot support more data than ts maxmum capacty. Hence: C, (, j) E, y (n) C, I. (2) e s Fnally, the total consumed energy e, I s: e = + e r + e j In() y (n). Clearly, we need to have e E. For moble devces, battery energy s an mportant concern [18], and dfferent users may have dfferent energy consumpton preferences. For example, some users may be wllng to consume almost ther entre energy budgets for the current tme perod, whle others may prefer a lower energy consumpton. Thus, for each user we ntroduce an energy consumpton cost functon V ( ), whch s strctly convex, postve, and ncreasng n e. Its value goes to nfnty when the energy budget of the user s depleted. A functon that satsfes these requrements s, for example, V (e ) = δ /(E e ), where δ [, 1] s a normalzaton parameter ndcatng user s senstvty n energy consumpton. B. Problem Statement Let J G ( ) denote the payoff that user receves when she partcpates n the crowd-sourced Internet access servce (superscrpt G stands for Open Garden). More specfcally, J G ( () (x, x, y )=U y + x () ) p y (n) V (e ), j In() where y = ( y (n) : n I ) s the downloadng vector of user, x = ( : j Out(), ) s the vector of her routng decsons, and x = ( : j In(), ) the routng decsons of her upstream neghbors (delverng data to ). As y () ncreases, user s utlty ncreases, as well as her monetary cost and energy cost. Hence the overall payoff J G may not ncrease. On the other hand, the payoff J G monotoncally decreases wth the amount of data that user downloads for other users n I,n, and routes to her downstream neghbors j Out(), due to the ncrease n the monetary and energy cost. Clearly, the user wll have no ncentve to perform these tasks unless she s compensated. Moreover, we also need to consder the user payoff when she operates n standalone mode. Notce that a ratonal user wll jon the servce only f ths wll mprove her payoff. In the standalone operaton, each user does not receve or delver data to her neghbors ( =, j Out(), =

4 454, j In(), n I ) nor she downloads data for any other user ( y (n) =, n ). Here the optmal downloadng strategy can be obtaned by smply solvng the followng Standalone Operaton Problem (SOP): ( ()) max U y y () p y () ( ()) V y (3) C Ths problem has a strctly concave objectve, and a compact and convex non-empty constrant set. Hence t has a unque soluton, denoted as J s where s stands for Stand-alone. Ths wll serve n the sequel as the performance benchmark for the comparson purpose. We are nterested n desgnng an ncentve mechansm that determnes whch users should contrbute how much resources (connectvty and/or battery energy), so as to maxmze the servce capacty (amount of data delvered wthn the current perod). Accordngly, t should decde how ths servce capacty wll be shared by the dfferent users and how users should be compensated. These two tasks should be jontly desgned so as to satsfy the farness crteron. There are two mportant notes here. Frst, a user beng served by another user, may not be able to drectly return the favor n the current perod by offerng smlar relayng or downloadng servces. Hence, a resourceful user may be reluctant to help other less resourceful users. Second, some users may not have communcaton needs n a certan tme perod, and therefore may not be wllng to partcpate n the servce. Ths, n turn, may deterorate the overall servce performance. In order to address both ssues, we ntroduce a vrtual currency system, smlar to the one for peer-to-peer or ad hoc networks [19], where users need to pay for recevng servces. Ths enables the cooperaton of users, even f they cannot drectly exchange routng or downloadng servces, and encourages users to partcpate even f they currently have no communcaton needs themselves. As we wll see n Sec. III, such a vrtual currency exchange system allows users to share benefts of cooperaton, n a flexble fashon, and acheve a good system operaton pont through a barganng process. Formally, the problem can be defned as follows: Key Research Problem: Gven the graph G =(I, E), the capacty constrants, the energy consumpton parameters, the prcng parameters, and the utlty functons of the users, fnd the downloadng, routng and payment decsons of the users, whch ensure the far and effcent performance of the crowdsourced Internet access servce. III. THE COOPERATIVE SERVICING GAME In ths secton, we frst explan how the vrtual currency system works, and then formulate the operaton of the servce as an I -person Nash barganng problem based on the vrtual currency system. Vrtual Currency. The currency system allows one-hop neghborng users to exchange (vrtual) money for the servces they offer to each other. Specfcally, let z (n) denote the prce pad by user to j, for the data of commodty (n) that s delvered over lnk (j, ) E. Smlarly, z (n) denotes the payment by user j Out() to user for data commodty (n). We defne the matrces z = ( z (n) : j In(),n I ), and, z = ( z (n) : j Out(), ) for each user I. At the begnnng of the perod, each user has a budget D, and s rewarded wth an addtonal amount γ>of vrtual money for her partcpaton n the current perod. Ths latter parameter s determned by the system, and t s the same for each user. However, γ s very small compared to the vrtual money a user receves when she serve others. As t wll become clear n the sequel, ths parameter ensures that partcpaton n the servce s benefcal even for users who wll not serve others, or receve servce by others. At the end of the tme perod, user s vrtual currency s: ( H (z, z )=β D +γ+ z (n) z (n) ), j In() where parameter β > captures how mportant the vrtual money s for user,.e., reflects her expectaton for explotng the vrtual currency n the future. In game theoretc terms, β can be consdered as the dscount rate for each user. For example, a user that does not ntent to partcpate n the servce later, does not value the vrtual currency much, and the correspondng β wll be close to. The lnear form of H (z, z ) mples that users are rsk neutral [8]. Of course, after ntroducng the vrtual currency system, the payoff of each user becomes the sum of J G and the normalzed currency H ( ). Barganng Problem. The users are self-nterested, and only partcpate n the crowd-sourced connectvty servce f ths ensures hgher payoffs for them. In ths work, we desgn the mechansm to acheve the Nash barganng soluton, whch has the followng desrable propertes regardng the users payoffs [2]: () Pareto optmal, () proportonally far, and () consders the standalone performance of each user. The last pont s especally mportant, as a farness rule based on drect resource allocaton only, e.g., an equal energy or bandwdth sharng scheme, may fal to ncentvze all users to jon the servce. We defne an I -person barganng game and solve t usng the NBS [7]. Due to the ntroducton of vrtual currency, ths s a game of transferrable utltes [8], whch means that the produced welfare (servce capacty and vrtual money) can be dvded n an arbtrary fashon among the users (through vrtual currency transfers). Based on the Open Garden servce archtecture [6], we assume that when a user jons the servce she may cooperates wth any of the other nearby users,.e., there s no opton for selectng wth whom to cooperate (no subgroups creaton) 4. Hence, ths s a pure barganng problem. Next we formally ntroduce the Nash barganng soluton. Consder the barganng game G = I, A, {u }, where I {1, 2,...,I} s the player set, and A A 1 A 2... A I s the strategy space where A s the set of strateges (actons) avalable to player. The payoff of each player, u ( ), depends on the strategy profle of all players, a =(a 1,a 2,...,a I ), wth a A. The NBS for ths game s [8]: 4 Ths assumpton holds also for other UPC servces, e.g. FON [4]. A coaltonal game theoretc analyss s requred n case formaton of subgroups s possble. However, t can be shown that also n ths case the grand coalton wll be formed snce there s no cost for usng the servce and hence the game s superaddtve [8] (ths does not hold for FON).

5 455 Defnton 1 (Nash Barganng Soluton NBS). A strategy profle a = (a 1,a 2,...,a I ) s an NBS, f t solves the followng problem: max Π I(u (a) u d ) a A (4) s.t. u (a) u d, I where u d s the dsagreement pont of player,.e., her payoff when an agreement s not reached. In the sequel, we use the equvalent formulaton where the product of terms n (4) s substtuted by the sum of respectve logarthmc terms [2]. Hence, we derve the NBS by solvng the Barganng Optmzaton Problem (BOP): log ( J G (x, x, y )+H (z, z ) J s ) β D max x,y,z s.t. I j In() + y (n) = z (n) j In(),, n I, n, (5) C, (, j) E (6) y (n) C, I (7) z (n) D + γ, I (8) J G (x, x, y )+H (z, z ) J s + β D, I (9), y (n), z (n) K,, j, n I (1) where the dsagreement pont for each user s the sum of the standalone performance J s she can acheve, and the normalzed vrtual currency β D she has at the begnnng of the perod. Eq. (5), (6), and (7) are the flow balance and lnk capacty constrants respectvely (defned n Sec. II). Eq. (8) states that users cannot have a vrtual currency defct, and (9) s the feasblty (ndvdual-ratonalty) constrant, ndcatng that each user wll agree to cooperate only f ths does not make her payoff worse. Fnally, notce that each payment decson z (n) s also upper bounded by the total avalable vrtual currency at the system K = I (D + γ). The BOP problem has always a non-empty feasble regon. Therefore, due to constrant (9), there s no user of whom the payoff wll decrease by partcpatng n the servce. Ths, n turn, mples that all users are ncentvzed to jon the servce n each tme perod. Techncally, ths s ensured due to the vrtual currency system and specfcally the rewardng parameter γ. In partcular, the followng lemma holds. Lemma 1. The BOP problem has a unque optmal soluton. Proof. The objectve functon s strctly concave snce t s a composton of (strctly) concave functons. Addtonally, the constrant set s compact, convex and non-empty. Notce that constrant (9) can be always strctly satsfed by some soluton pont. For example, each user can choose not to route any traffc,.e., = =,, j, n I, and only download data for herself. Ths way, she acheves her standalone performance, but stll mproves her payoff due to the partcpaton reward γ. Ths also ensures that the logarthmc arguments are non-zero. Therefore, the problem has always a unque soluton (x, y, z ) [12]. We can derve the soluton of the BOP problem by solvng the necessary and suffcent KKT condtons [12]. Ths wll yeld the effcent and far downloadng and routng polcy, as well as the necessary vrtual currency transfers among the users. Based on the system parameters,.e., the users connecton capactes, battery energy, and prcng plans, the servce can offload data to WF networks or even onload data to cellular networks. However, n all these cases, the crtcal queston s whether we can fnd ths soluton n a dstrbuted fashon. Ths wll enable the dstrbuted executon of the ncentve mechansm, whch s a prerequste for crowd-sourced moble Internet access servces. IV. DISTRIBUTED ALGORITHM DESIGN FOR BOP The dffcultes to solve the BOP problem n a decentralzed fashon are twofold. Frst, the decson varables of dfferent users are coupled n the constrants. That s, the routng decsons of each user should take nto account the capacty constrants of her neghborng nodes. Second, there s couplng n the objectve functons. Namely, the logarthmc component of the BOP objectve that corresponds to each user s dependent on the decson varables of her neghbors. We address these ssues by ntroducng new auxlary local varables for each user and consstency constrants for each par of neghborng users (for the coupled objectves) [11]. The transformed problem then has couplng only n the constrants, and can be solved usng a prmal-dual Lagrange decomposton method [11]. Let us focus on user I, whose payoff and vrtual currency functons depend on her own decsons (x, y, z ) and the decsons x, and z of her one-hop upstream and downstream neghbors, j In() and j Out(), respectvely. To deal wth ths couplng, we ntroduce the matrces of auxlary varables ξ = ( ξ (n) :j In(),n I ), and σ = ( σ (n) : j Out(),n I ), and the respectve component-wse equalty constrants: =, I,j In(),, (11) = z (n), I,,. (12) ξ (n) σ (n) Ths means that each user can ndependently determne her downloadng, routng, and payment varables, subject to the (teratve) coordnaton wth her one-hop neghbors about ther (common) routng and payment decsons (through the auxlary varables). Accordngly, we can group the varables per user so that each user only needs to take local decsons. Specfcally, we relax constrants (5), (8), (11), and (12), and ntroduce the respectve Lagrange multplers λ =(λ (n) :, n I), ρ =(ρ : I), τ = ( τ (n) :, n I,j In() ), and π = ( π (n) :, n I,j Out() ). Then, we

6 456 defne the (partal) Lagrangan: L = ( ( log J G (x, ξ, y )+H (z, σ ) J s ) β D I + λ (n) ( + y (n) ) j In() + τ (n) (ξ (n) ) j In() π (n) (σ(n) z (n) ) + ( ρ j In() z (n) D z (n) )), whch s separable n user-specfc components L ( ), I. In each teraton t, the user maxmzes the Lagrange functon n terms of the prmal varables, and uses the obtaned values to update the dual varables. More specfcally, each user I, n each teraton, solves the followng problem to optmze her prmal varables: ( ) max L x, ξ, y, z, σ (13) x,y,z,ξ,σ s.t. C, (, j) E, y (n) C (14) J G (x, ξ, y )+H (z, σ ) J s β D > (15),y(n),ξ (n),σ(n), z (n) K, n I,j N (16) where N = In() Out(), and the objectve L ( ) s: L =log ( J G (x, ξ, y )+H (z, σ ) J s ) β D + ( (n) λ y (n) ( (n) λ λ (n) )) j ρ z (n) + ρ j z (n) + j In() j In() [ ( (n) x τ (n) π (n) ) σ(n) + j In() τ (n) ξ (n) π (n) ] z(n). The user then uses the prmal varables to calculate the gradents and update the dual varables [12]: λ (n)(t+1) = λ (n)(t) + s (t)( τ (n)(t+1) π (n)(t+1) ρ (t+1) = τ (n)(t) = π (n)(t) = [ ρ +s (t)( (t) + s (t) + s (t) ( j In() j In() ) (ξ (n)(t) (σ (n)(t) (t) z (n)(t) (t) ) ) z (n)(t) + y (n)(t) z (n)(t) (2) where [ ] + denotes the projecton onto the non-negatve orthant and s (t) s a properly selected step durng teraton t [12]. Fnally, each user passes the updated dual varables to her one-hop neghbors, who wll use them to optmze the prmal varables n the next teraton. The Algorthm s executed n a synchronous fashon, whch requres a common clock of all users and a small delay for Algorthm 1: Dstrbuted Soluton of BOP output: x, y, z 1 t ; 2 Set x (), y (), z (), ξ (), σ (), λ (), τ (), π (), ρ (), ɛ; 3 conv_flag ; # ntalze the convergence flag 4 whle conv_flag = do 5 t t +1; 6 for =1:I do, y (t), z (t), n I\{}, to; 7 Solve (13) - (16) to get x (t) 8 Send (t) 9 Send z (n)(t), n I\{}, toj In(); 1 for j =1:I, n =1:I do 11 Calculate λ (n)(t+1) (17) - (2); end 12 Send λ (n)(t+1) j In(); 13 Send ρ (t+1) j Out(); end 14 f λ (n)(t+1) and π (n)(t+1) τ (n)(t+1),ρ (t+1), ξ (t), σ (t),τ (n)(t+1),π (n)(t+1) usng,τ (n)(t+1), n I\{}, to and π (n)(t+1), n I\{}, to λ (n)(t) <ɛand ρ (t+1) ρ (t) π (n)(t) <ɛand <ɛ ; τ (n)(t) <ɛ, n I,j Out() then conv_flag 1; end end message passng (crculaton of the dual and prmal varables). Ths s a reasonable assumpton for small-scale crowd-sourced connectvty networks n a small neghborhood. The complete algorthm s summarzed n Algorthm 1 and provably converges to the optmal soluton. Lemma 2. Algorthm 1 converges to the optmal soluton (x, y, z ) of the BOP problem, under properly chosen step szes s (t) for each teraton t. Proof. BOP has a strctly concave objectve and a closed, non-empty and convex constrant set. Thus, Algorthm 1 (17) converges to optmal soluton [12] f () the step sequence s (t), t =1, 2,..., s properly selected, and () the gradents (18) used n (17)-(2), are bounded. Consder user, and we see that,y(n),n I,j Out() are bounded by (14), (19) ξ (n),n I,j Out() are also bounded due to the energy )] + ) D cost functon, and z (n),n I,j Out() are postve and upper bounded by K. Hence, f we employ a dmnshng step sze, e.g. s (t) = (1 + m)/(t + m) wth m, then the convergence s guaranteed [11], [12]. Notce that each user passes messages for each commodty n I, only to her one-hop neghbors. Hence, the message passng overhead of the algorthm s O( dn 2 ), where d s the average degree of the graph G. However, we expect that the number of users n the group wll be small (due to the

7 457 need to be n proxmty), hence even a complexty of O(N 3 ) (assumng a fully connected graph) s affordable. V. NUMERICAL STUDY We consder a basc system setup and demonstrate how the crowd-sourced connectvty servce performs n certan representatve scenaros. The system parameters follow related expermental studes [14], [15], [21], [22], [23]. More numercal results can be found n our techncal report [24]. Smulaton Setup. We consder a set of I = 6 users, randomly placed n a geographc area 5, and study ther nteractons for a tme perod of T = 12 seconds. The Internet access capacty of each user depends on whether she uses a cellular 4G, 3G, or a WF connecton. Moreover, n practce, the effectve capacty s affected by the network condtons such as nterference and congeston. Feld experments have measured the actual average speed to be Mbps for LTE, 4.12 Mbps for WF, and 1 Mbps for 3G networks [14], [21], [22]. We assume that users communcate wth each other usng WF Drect. The achevable rate among two users and j decreases wth ther Eucldan dstance d (n meters). In order to account for a representatve settng wth average nterference and channel condtons, we assume that two users separated by 1 meter acheve a communcaton speed of 64Mbps, and the speed drops to.1 Mbps when the dstance ncreases to 3 meters. The rate wll be zero when the dstance s larger than 3 meters. For wthn range transmssons, the maxmum amount C of data that can be transferred over each lnk (, j) satsfes C = T 1 log(1 +.9/d 2 ). For moble devces, the energy consumed by a data transfer s proportonal to the sze of the data and the transmsson power level [15]. Moreover, the energy consumpton s affected by other parameters, such as the channel condtons (e.g., due to packet retransmssons) and the transmsson rate [14], [23]. Typcally, the energy consumpton (per MByte) of WF transmssons s smaller compared to LTE transmssons, whch, n turn, s smaller than 3G transmssons. We consder here an average energy consumpton of e = 1J/MByte when user has a 3G Internet access connecton, e = 4.65J/MByte for an LTE connecton, and e =2.85J/MByte for a WF connecton [15], [23], [25]. For WF drect lnks, we assume that the energy consumpton per MByte ncreases wth the dstance (snce the achevable rate decreases wth the dstance), n the form of 6 e s =( d2 )Joules/Mbt. Every user Ihas a logarthmc utlty functon U = α log ( 1+y () + ) j In() x(), whch satsfes the prncple of dmnshng margnal returns [26]. Parameter α [, 1] captures the dfferent communcaton needs of the dfferent users. Also, the vrtual currency parameters β, I, are unformly dstrbuted n (, 1]. Fnally, the data usage prces depend on the country, the data plan of each user, and the servce provder. In a recent publcaton, ITU reports an average prce of.21$/mbt n US,.6$/Mbt n Chna, 5 We expect to see such small groups n practcal networks, snce each user should be n communcaton range wth at least one more user. 6 The parameters of e s have been selected so as to have es = e =2.85J/MByte when d =1. Total Payoff Independent Centralzed Barganed User ID Fg. 3. Comparson of centralzed, ndependent, and barganed soluton. System basc parameters are: {C } = {12.7,., 1., 1., 4.12, 2.1} Mbps, {e } = {.58,., 12.5, 12.5,.36,.36}Joule/Mbt, and {p } = {.2,,.8,.1,.,.} $/Mbt. The aggregate total payoff mprovement of the barganed soluton (compared to the ndependent soluton) s approxmately 1%. and.2$/mbt n UK [27]. We select the prces accordng to these fndngs, and we set p =for users who have an unlmted cellular data plan or usng WF connectons. Numercal Results. Frst, we consder a settng where user 1 has an LTE connecton, user 2 does not have any Internet access, users 3 and 4 have 3G connectons, and users 5 and 6 have WF connectons. The Internet access capacty, energy, and prce values for all users are shown n the capton of Fg. 3. For smplcty, all other system parameters have been set equal for all users. In ths experment, we compare the barganed payoff J G for each user (under the barganng soluton), wth the ndependent payoff J s that she acheves n the standalone operaton. We also compute the user s centralzed payoff J c that corresponds to a benchmark case where the system maxmzes the aggregate welfare. For each case, we plot the total payoff whch has also accounted for the vrtual currency beneft. The results represent the average obtaned over 1 experments for dfferent user locatons and hence user dstances 7. We observe that the barganed soluton always mproves upon the ndependent payoff. However, a centralzed soluton mght lead to a lower total payoff for some user comparng wth the ndependent soluton. Ths llustrates the far allocaton of the proposed barganed soluton. The performance benefts of the crowd-sourced servce depend on the dversty of the users s resources. In Fg. 4 we nvestgate ths aspect regardng the dfference of Internet capactes among users. Namely, we assume that 2 users have hgh Internet access capactes, whle the other 4 have equal but much lower Internet access capactes. We run the experment 3 tmes and average the results for dfferent user locatons and dstances. We calculate the aggregate downloaded data n a sngle perod, when users partcpate n the servce and when they operate n standalone mode. All the other system parameters are equal for all users and reman unchanged across the dfferent experments. We see that as users become less dverse (.e., the 4 users capacty ncreases) the gap of total downloaded data for the barganed soluton (compared to the standalone soluton) decreases from 29.36% to almost %. Smlar results hold when users are dverse n terms of ther energy consumpton [24]. Ths reveals that the servce benefts are larger for users wth dfferent Internet 7 Specfcally, users are placed n the [, 1m] [, 1m] plane randomly, wth a unform dstrbuton.

8 458 Total Data Consumpton (MByte) Independent Barganed Value of k (Mbps) Fg. 4. Servce performance for users wth dverse Internet access capactes. C 1 = C 2 = 12.7 Mbps, C 3 = C 4 = C 5 = C 6 = k Mbps. Internet access prces are dentcal and equal to p =.1. Smlarly, energy consumpton for downloadng s e =.158 for each user. Results are averaged over 3 runs wth unformly dstrbuted user locatons n [, 1m] [, 1m]. Onloaded Data (MBx1) Offloaded Data (MBx1) Normalzed Energy consumpton (Joules/1KBytes) Cellular Usage Prcng (dollars per 1MBytes) Fg. 5. Upper subfgure (Onloadng): 4G capacty (1 Mbps) s 5 tmes larger than the WF capacty (2 Mbps), moble data prce s p =.1 $/Mbt, and the 4G lnk energy consumpton 3-tmes larger than the WF lnk energy consumpton (e =2.85 J/MB). Lower subfgure (Offloadng): 4G capacty (4 Mbps) s twce the WF capacty, and data usage prce ncreases. access capactes and/or energy consumpton parameters. In Fg. 5 we smulate the offloadng - onloadng scenaro llustrated n Fg. 2. Onloadng becomes an attractve opton when WF lnks are congested and cellular access s of a low cost for each user. The upper subfgure n Fg. 5 shows that the amount of onloaded data decreases when the energy consumpton (e ) of the cellular user for delverng data to the WF user ncreases. On the other hand, offloadng becomes attractve when the WF connecton s resourceful. The lower subfgure n Fg. 5 shows that the amount of offloaded data ncreases wth the prce per byte pad by the 4G user. Interestngly, after a certan pont (about cellular prcng equal to.44 n the fgure), the offloadng data amount slghtly decreases and then remans constant despte the further cellular prce ncrease. Ths s due to the farness crteron mposed by the proposed mechansm, whch compares the standalone performance of each user. In partcular, as the data prce ncreases, the cost of the 4G user for offloadng more traffc ncreases sgnfcantly, and hence t cannot be compensated wth the vrtual currency payment by the WF user (due to the total vrtual currency constrant). Therefore, the 4G user does not delver any more data to the WF user. Next, we study the mpact of the energy parameters on the onloadng - offloadng decsons for the system n Fg. 2. As- Offloaded Data (Mbytes) Rato of Downloadng Energy Consumpton e /e 1 2 Fg. 6. Offloadng - onloadng decsons based on the energy consumpton raton e 1 /e 2 for the 4G user (user 1) and the WF user (user 2). Cellular data usage s free of charge, and 4G capacty s twce the WF capacty (2Mbps). sume that both users have zero data usage cost 8. Also, assume that the 4G user (user 1) has an Internet access connecton wth a capacty twce as the capacty of the WF user (2Mbps) (user 2). In Fg. 6 we plot the amount of offloaded data (negatve values represent onloadng decsons) versus the rato of the energy consumpton of the two users, e 1 /e 2. We observe that when ths energy cost rato s between (approxmately) 1.5 and 2.5, there s nether offloaded nor onloaded data,.e., each user serves her own traffc needs. However, when the cellular lnk becomes more expensve n terms of energy consumpton, the WF user begns to serve and delver data for the 4G user. The amount of offloaded data ncreases as the rato ncreases, but follows a concave curve due to the mposed farness rule (as t would be unfar for the WF user to delver too much traffc for the cellular user). On the other hand, when the cellular lnk has almost equal or lower energy consumpton than the WF connecton (e.g., due to nterference n the WF channels), our scheme wll onload data from the WF lnk to the cellular lnk. Notce that when the rato of the energy consumpton s 1, the proposed scheme wll onload traffc snce the cellular connecton has a hgher capacty. VI. RELATED WORK One man example of UPC servces s the WF communty network, where resdental users share ther WF connectons wth roamng users [4], [28]. The key challenges for these servces nclude securty ssues 9 [29] and ncentve ssues of user partcpaton [3]. One popular approach for addressng the ncentve ssues s to desgn recprocty schemes (reputaton-based or credt-based), whch deter free rdng by rewardng the users who contrbute more resources. References [19], [31], and [32] studed smlar mechansms for other classes of autonomous networks, such as peer-to-peer (P2P) or ad hoc networks. However, these results are not drectly applcable to our model, snce the proposed mechansms dd not account for users dfferent types of resources, or for ther moble data usage cost. Also, most users n our model can access the Internet wthout relyng on other users help, whle ths s typcally not the case for ad hoc networks. The characterzaton of such standalone operatons s crtcal n 8 Ths can be the case when, for example, the 4G user has an unlmted data plan. Smlar results and conclusons hold for the case the users have non-zero but equal data usage cost. 9 Recent technologcal advances, such as the HotSpot 2. protocol, address many of the ntal securty ssues n ths type of servces [33].

9 459 determnng whether a user wll agree to jon the servce or not. To address both challenges, we consder a utlty-based crteron and employ the Nash barganng soluton [7], [2]. UPC servces can be centralzed (as n FON), or decentralzed where users negotate drectly wth each other. For the centralzed case, [34] studed a prcng rule for nducng servce adopton, and [35] analyzed the prce competton among FON-lke operators and conventonal operators. For decentralzed servces, [17] and [16] performed game-theoretc analyss to predct the prces that users charge to each other. Also, n [36] a UPC model was consdered wth moble WF hotspots. Our scheme dffers n that each user can concurrently provde servce (as a gateway or a relay), and consume servce (as a clent), and the data transmssons to a sngle user can be mult-hop and mult-path. Besdes, moble users often have tght prcng constrants and are lmted by battery energy, both of whch affect ther decsons. Another cluster of lterature that s closely related to our work focuses on the ncentve schemes for wreless mesh networks [37] and cooperatve wreless networks [38]. However, these results often do not account for the users monetary cost due to moble data usage. Another unque aspect of our model s the nteractons between users from heterogeneous networks (cellular and WF). Hence the dstrbuted cooperaton of users may lead to ether offloadng cellular traffc to WF APs [9], or onloadng WF traffc to cellular networks [1] as was llustrated n Fg. 2. Such flexble cooperaton framework dffers from prevous offloadng-only archtectures [39]. VII. CONCLUSIONS UPC servces for moble Internet consttute a paradgm shft n wreless communcatons, whch many compare to the advent of P2P overlays for wred networks. In ths work, we proposed a dstrbuted ncentve mechansm for a crowdsourced moble Internet access servce, whch mproves the performance of the partcpatng users. The more dverse the needs and resources of the users are, the hgher the performance benefts of the servce s. There are many drectons for future work. Frst, we wll nvestgate the mpact of the vrtual currency parameters, such as the budget D and the reward γ, on the servce performance. There are several related studes for P2P systems, but we need to take nto account the specfc characterstcs of our new servces. Moreover, t would be exctng to study the mpact of ths ad hoc offloadng-onloadng servce on the cellular network congeston and operator s cost. Operators and users may have conflctng nterests, regardng the crowd-sourced servce, and t would be nterestng to try to reconcle them by properly extendng the ncentve mechansm. REFERENCES [1] Csco, Csco Vsual Networkng Index: Global Moble Data Traffc Forecast Update, , Whte Paper, February 213. [2] New York Tmes, Phones Overload AT&T Network, Angerng Customers, September 29. [3] R. Sofa, and P. 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