Backpressure Meets Taxes: Faithful Data Collection in Stochastic Mobile Phone Sensing Systems

Transcription

1 Backpressure Meets Taxes: Fathful Data Collecton n Stochastc Moble Phone Sensng Systems Shusen Yang Imperal College Lodon Emal: s.yang9@mperal.ac.uk Usman Adeel Imperal College London Emal: u.adeel9@mperal.ac.uk Jule McCann Imperal College London Emal: j.mccann@mperal.ac.uk Abstract The use of sensor-enabled smart phones s consdered to be a promsng soluton to large-scale urban data collecton. In current approaches to moble phone sensng systems (MPSS), phones drectly transmt ther sensor readngs through cellular rados to the server. However, ths smple soluton suffers from not only sgnfcant costs n terms of energy and moble data usage, but also produces heavy traffc loads on bandwdth-lmted cellular networks. To address ths ssue, ths paper nvestgates cost-effectve data collecton solutons for MPSS usng hybrd cellular and opportunstc short-range communcatons. We frst develop an adaptve and dstrbute algorthm OptMPSS to maxmze phone user fnancal rewards accountng for ther costs across the MPSS. To ncentvze phone users to partcpate, whle not subvertng the behavor of OptMPSS, we then propose BMT, the frst algorthm that merges stochastc Lyapunov optmzaton wth mechansm desgn theory. We show that our proven ncentve compatble approaches acheve an asymptotcally optmal gross proft for all phone users. Experments wth Androd phones and trace-drven smulatons verfy our theoretcal analyss and demonstrate that our approach manages to mprove the system performance sgnfcantly (around 1%) whle confrmng that our system acheves ncentve compatblty, ndvdual ratonalty, and server proftablty. I. INTRODUCTION Ubqutous sensor-rch smartphones are begnnng to play an ncreasngly mportant role n the evoluton of the urban Internet of Thngs (IoTs), whch brdge the dgtal space to the physcal world at a socetal scale. Ther powerful computng and communcaton capactes, huge market prolferaton, and nherent moblty makes Moble Phone Sensng Systems (MPSS) [1] a much more flexble and cost-effectve sensng soluton compared wth tradtonal statc sensor networks. In turn ths has motvated the desgn of novel sensng applcatons [1], [2], coverng urban envronmental montorng [3], smart transportaton [4], and safety [5]. Most of current MPSSs transmt moble sensor data to the server through cellular networks. When MPSS becomes popular, ths smple soluton wll suffer from not only sgnfcant battery [6], [7] and 3G/4G fnancal costs [8] to the phone users, but also wll produce heavy traffc load on the underlyng bandwdth-lmted cellular networks, especally for MPSS applcatons that requre contnuous sensng wth fne granularty (e.g. [9]). Besdes the expensve cellular communcatons, current smartphones are beng equpped wth more and more shortrange wreless technologes such as WF, WF drect, and Bluetooth 4., whch enable opportunstc phone-to-phone and phone-to-server communcatons (e.g. through WF routers). Due to ther low energy and fnancal costs, t s promsng to explot the potental of short-range communcatons n MPSSs, especally for delay-tolerant moble sensng applcatons [7]. For nstance, wthout usng ts own cellular rado, a phone can report ts sensor data to the server, through another proxmty phone wth a cheaper cellular cost (e.g. unlmted moble data) or when t passes a free WF router. However, to buld such a MPSS wth hybrd cellular and short-range communcatons, the followng research ssues must be addressed: Networkng Issues. It s a challenge to perform the sensng and opportunstc mult-hop data transmsson tasks that are adaptve to the tme-varyng and potentally unpredctable network states, ncludng fluctuatng wreless channel qualty; ntermttent connectvty caused by phone user movement; heterogeneous transmsson and sensng costs across moble phones; 3G/4G moble data costs; and the opportunstc avalablty of nearby free Internet access ponts. Economc Issues. To encourage the phone users to partcpate the MPSS, they should be properly rewarded to cover sensng and transmsson costs [1] [12]. In addton, the self-nterest phone users may try to maxmze ther benefts strategcally by msreportng ther local state parameters. For nstance, n order to prolong battery lfetme, a phone user may hde that she s connected to a free WF router to avod relayng other nearby phone data to the server. Ths would result n sgnfcant performance degradaton of the system. Therefore, ncentvzaton s a key ssue for MPSS wth ths new networkng paradgm, whch s much more challengng compared to pure cellular networks. A. Our Approach In ths paper, we present theoretcal and practcal studes to address above two ssues. Our contrbutons are summarzed as follows: 1. We formulate a fnte-horzon stochastc optmzaton problem for contnuous data collecton n MPSS usng hybrd cellular and opportunstc short-range communcatons. The objectve of the formulated problem s to maxmze the global gross proft,.e. the total fnancal rewards of all phone users after costs ncurred by performng the sensng and transmsson tasks are deducted. 2. We develop a lghtweght jont sensng rate control and dynamc routng algorthm, OptMPSS to solves the data

2 collecton problem n a fully dstrbuted and therefore scalable way. We prove that OptMPSS s an asymptotcally optmal soluton to the formulated problem. 3. We propose a fully dstrbuted mechansm, Backpressure Meet Taxes (BMT), to ncentvze phone users to fathfully mplement OptMPSS, by mposng taxes or provdng subsdes for each phone user, dependng on her mpact on the rest of phone users n the MPSS. We prove that BMT manages to acheve asymptotc ncentve compatblty [13]. To our knowledge, BMT s the frst approach that ntegratng algorthmc mechansm desgn theory [14], [15] to the stochastc Lynapunov optmzaton framework [16]. Besdes MPSS, ths method developed for BMT also has a great potental to be apples to other stochastc dstrbuted systems wth self-nterest and strategc users. 4. Through experments wth WF-drect-enabled Androd devces and extensve smulatons wth real human moblty trace [17], we demonstrate that system performance can be sgnfcantly mproved by explotng low-cost short-range communcatons, n terms of global socal profts and phone users costs. Evaluaton results also show that each phone user can always get a postve net proft (.e. gross proft plus subsdes or mnus taxes) and the server never ncurs a defct (.e. the server always obtan a postve proft). Furthermore, each phone user cannot ncrease her net proft mprovement by lyng about her prvate parameters. These results demonstrate that BMT can acheve ndvdual ratonalty, server proftablty, and ncentve compatblty (fathful mplementaton) n practce. B. Related Work Recently, several ncentve-based mechansms have been proposed for MPSS [1] [12], [18]. [11] develops platformcentrc and user-centrc schemes based on a Stackelbergy game and aucton theory respectvely. [12] proposes a mechansm based on a Bayesan game to mnmze partcpaton costs whle ensurng certan servce qualtes, by determnng the level of user partcpaton (.e. sensng rate). However, all of these schemes focus on MPSS wth pure cellular rados only, whch cannot be drectly used n MPSS wth hybrd cellular and mult-hop short-range communcatons. The explosve growth of cellular traffc has motvated an ncrease n research nto cellular traffc offload usng other forms of opportunstc connectvty, ncludng WF [19] [21] and Bluetooth [22]. However, none of these focus on MPSS. EffSense [7], consders MPSS wth the same hybrd wreless networks as us. However, ths heurstc-based scheme does not provde any performance guarantees, and does not consder ncentvsaton for the strategc and self-nterest phone users. Stochastc Lyapunov optmzaton [16], [23] [26] provdes elegant and powerful theoretcal tools to derve backpressure style cross-layer network optmzaton and control algorthms. Due to ther adaptveness to network dynamcs, several backpressure rate control and routng schemes [23] [25] have been proposed for opportunstc moble networks. However, Fg. 1. An llustratve example of a MPSS wth hybrd cellular and short-range communcatons, consstng of 4 phones and a server. agan none of them focus on MPSS nor do they account for ncentvsaton and the strategc behavors of phone users. Mechansm desgn [14], [15] s concerned wth how to make a global decson wth desrable propertes n systems consstng of strategc self-nterest ndvduals who have prvate nformaton. Recent theoretcal work [13], [27] on dstrbuted Vckrey-Clarke-Groves (VCG) mechansms enables the fathful mplementaton of algorthms producng desred outcomes (such as dual decomposton and average consensus) n a dstrbuted way. However, these approaches focus on determnstc rather than stochastc systems. Our work combnes threads of all the above works n a novel way. C. Paper Organzaton The next secton presents the system model and desgn objectves. Secton III descrbes the OptMPSS algorthm. Mechansm desgn models are establshed n Secton IV. Secton V presents the BMT algorthm, then Secton VI dscusses the performance evaluaton. Fnally, we conclude the paper n Secton VII. II. SYSTEM MODEL AND OBJECTIVES As shown n Fg. 1, we consder a MPSS that conssts of a server S and a set of moble phones N collectng urban sensng data. The MPSS operates durng a fnte tme horzon (e.g. a week) wth dscrete tme slots t = {1, 2,..., t end }, t end < +. Every phone can communcate wth the server S through 3G/ 4G cellular rados, or through the low-cost WF when t passes a WF router (slots 1-3 n Fg. 1). In addton, phones n mmedate proxmty can communcate wth each other, usng short-range communcatons such as WF drect (slot 2) and Bluetooth 4. (slot 3). A. Sensng and Communcaton Models At each tme slot t, each phone produces r (t) r max sensor data packets, where the fnte sensng rate upper bound r max s defned by the specfc moble sensng applcaton. Let µ,j (t) be the channel capacty from a phone N to a phone j N or to the server j = S

3 at slot t,.e. the maxmum (nteger) number of data packets that can be successfully transmtted from to j durng slot t. It can be seen that µ,j (t) may vary sgnfcantly over the tme slots, due to the stochastc phone user movement and wreless channel qualtes. In practce, all possble channel capactes (.e. µ,j (t),, j, t) must have an fnte upper bound µ max, determned by the fnte data rate of the wreless transcevers. Each phone mantans a tme-varyng temporary neghbor table N (t), consstng of the server S (f currently connected) and the phones n proxmty at slot t: N (t) := {j : j N {S}, µ,j (t) > } (1) In practce, N (t) can be establshed by usng neghbor dscovery schemes such as [28]. Denote f,j (t) µ,j (t) as the amount of forwarded data from phone to ts current neghbor j N (t) at slot t. We use a vector x (t) = (r (t), f,j (t), j N (t)) (2) to represent the sensng and data forwardng actons of a phone N at slot t. B. Queue Dynamcs Each phone mantans a data queue wth sze Q (t) to store the sensng data collected by tself and receved from other phones. Consderng sensng and data forwardng dynamcs, the queue backlog of each phone updates as follows: Q (t + 1) = Q (t) f out (t) + + r (t) + f n (t) (3) where for any real number a, the operator a + = a f a > ; a + = otherwse. f out (t) = j N (t) f,j(t), and f n (t) = j N (t) f j,(t) represent the total numbers of outgong and ncomng packets of phone at slot t respectvely. It s worth notng that the queue backlog of the server S s always zero,.e. Q S (t) =, t, snce t s the destnaton of all sensor data packets. C. Costs of Phones At each slot t, each phone ncurs costs due to sensng and data transmsson. Let p s (t) > be the per packet sensng prce of phone at slot t. Therefore, the sensng cost of phone at slot t s p s (t)r (t). In practce, the sensng prce p s (t) depends on both MPSS applcaton requrements, and the avalable resources that phone has at tme t such as remanng battery energy. Denote p t,j (t) as the per packet transmsson prce for phone to send a sensor data packet to a temporary neghbor j. If j s the server S, then p t,j (t) depends on fnancal cellular costs, the avalablty of a nearby WF router, and the remanng battery level of phone. Specfcally, prce p t,j (t) are normally sgnfcantly smaller when sends data to the server through WF than through cellular rados. If j s another phone, the transmsson prce p t,j (t) manly depends on battery concerns of the users of phones and j. We can see that the data transmsson prce s hghly dynamc and heterogeneous across dfferent wreless transmsson lnks. It s worth notng that although sensng and transmsson prces are nfluenced by varous practcal aspects, they can be all normalzed to monetary values (e.g. US dollar or credts per packet), estmated by each phone user herself rather then the server. The detaled estmaton n practce s out of the scope of ths paper, but our BMT scheme can guarantee that fathful estmaton s the best strategy for each self-nterest phone user. For a gven slot t, the total cost of each phone N can be computed as where the vector cost (t) = p (t)x (t) (4) p (t) = (p s (t), p t,j(t), j N (t) (5) characterzes the prce profle of phone at slot t. D. Revenue and Gross Proft Maxmzaton Durng the complete tme horzon, the server obtans totally t end N v (r ) amount of monetary revenue (.e. global socal revenue), by sellng the collected moble sensng date to externa MPSSl users. Here, r represents the average sensng rate of phone over the tme horzon [1, t end ], and the revenue functon v (r ) can be any concave (ncludes lnear), dfferentable, and non-decreasng functon of r. The revenue functon may dffer across moble phones, dependng on specfc sensng applcatons and the Qualty of Informaton (QoI) of sensor data produced by each phone [12], [29]. Therefore, v (r ) ndcates the tme-average contrbuton level of phone to the MPSS. At slot t end, the server computes v (r ) and makes a payment αt end v (r ) to each phone (shown n Fg. 1), where the system parameter < α 1 s the percentage of the global socal revenue t end N v (r ) that s allocated to all phones. As a result, the tme-average gross proft of each phone user s gven by: φ = αv (r ) cost, N (6) where cost s the tme-average of cost (t) over tme horzon 1 t t end. We call the tme-average aggregated gross proft of all moble phones N φ, as the global gross proft. The MPSS ams to maxmze the global gross proft by solvng the followng fnte-horzon stochastc problem: f out maxmze x (t), N s.t. Φ = N φ (7) r (t) < r max, N 1 t t end (8) f,j (t) µ,j (t), N, j N (t), 1 t t end (9) r + f n f out =, N (1) where f n and f out are the tme-averages of f n (t) and (t) over tme horzon 1 t t end respectvely. Constrant (1) states the flow conservaton law,.e. the average

4 total ncomng and outgong data rate should be equal for each phone. Ths constrant also ensures that the server wll know the average sensng rate r for each phone N at slot t end. Secton III wll develop OptMPSS, an optmal dstrbuted soluton to problem (7)-(1). However, because each phone owner s only nterested n maxmzng her own proft φ rather than the global gross proft of the system Φ, the optmal soluton to problem (7)-(1) cannot be mplemented wthout proper ncentvzaton mechansm that encourages phone owners to apply the OptMPSS. All varables regardng the ncentvzaton mechansm such as net proft wll be defned n Secton IV. E. Objectve The objectve of ths paper s to develop an algorthm that can acheve the followng desred propertes: 1. Global Gross Proft Optmalty. The algorthm should be the optmal soluton to problem (7)-(1). 2. Adaptveness. The algorthm should be adaptve to all possble dynamc network states, ncludng tme-varyng and heterogeneous sensng and transmsson cost across phones; wreless lnk qualtes; and network connectvty (e.g. ncludng extremely dense networks where all phones can always communcate wth each other, to extremely sparse networks where short-range communcaton s rare or not avalable). 3. No Predcton Requrement. The desred algorthm s based on the current system state only, and does not requre the predcton of any future MPSS nformaton. 4. Dstrbuted and Real-tme Operatons. The computatonal and communcaton overheads of the algorthm should be lghtweght for real-tme operatons of each phone. 5. Indvdual Ratonalty. Each partcpatng phone user should obtan a non-negatve net proft, whch s formally defned n Equaton (18). 6. Server Proftablty. The server S should not ncur a defct, whch means a non-negatve server proft (formally defned n Equaton (19)) should be acheved. 7. Incentve Compatblty. Adoptng the acton suggested by the proposed algorthm should be the best strategy for each phone user, regardless others actons. An mportant corollary of ncentve compatblty s that usng hybrd cellular and (opportunstc) short-range communcatons wll always result n a same or ncreased net proft for each phone, compared wth usng the cellular communcatons alone. III. THE OPTMPSS ALGORITHM In ths secton, we develop an fully dstrbuted algorthm, OptMPSS to optmze global gross proft (7), by controllng the acton x (t) of each phone N at every slot 1 t t end : ts sensng rate r (t) and the data forwardng rate f,j (t) to each of ts temporary neghbors j N (t). Intally, n ths secton, we assume that all phone users are wllng to truthfully mplement the OptMPSS algorthm. We wll relax ths assumpton n later sectons. A. Dstrbuted Operatons of OptMPSS At each slot 1 t t end, each phone N operates as follows: 1. Sensng Rate Control. Phone sets ts sensng rate r (t) as r (t) = mn(r max, αv 1 ( Q (t) + V p s (t) )) (11) V where v 1 () represents the nverse functon of revenue functon v () s frst dervatve, and V > s a system parameter defned by the server. 2. Opportunstc Routng and Data forwardng. Phone computes a weght w,j (t) for each temporary neghbors j N (t) as w,j (t) = (Q (t) Q j (t))µ,j (t) V p t,j(t) (12) Based on w,j (t), sets the forwardng rate f,j (t) for each of ts temporary neghbor j N (t) as: { µ,j (t) f w,j (t) > f,j (t) = (13) otherwse Remark 1. Snce every node N requres only the nformaton of ts temporary neghbors n N x (t), OptMPSS algorthm s fully dstrbuted. In addton, OptMPSS requres current knowledge of the network only for slot t and does not requre any future knowledge after slot t. At each slot, each phone broadcasts a one-hop beacon message to communcate ts queue backlog to ts current temporary neghbors and performs smple arthmetc calculatons. Therefore, the per slot per node communcaton of OptMPSS s O(1) wth respect to the network sze N. B. Asymptotcal Optmalty To prove the optmalty of OptMPSS, We dvde the tme horzon of the MPSS, 1 t t end, nto K successve frames wth sze T slots (.e. t end = KT ). We assume that there exsts an deal algorthm operatng at the frst slot of each frame t = (k 1)T + 1, 1 k K, whch can obtan full nformaton regardng the dynamcs of the MPSS for future T slots (whch s mpossble n practce). Based on future knowledge, the deal algorthm solves problem (7)-(1) over each frame [(k 1)T + 1, kt ], 1 k K rather than the whole horzon [1, t end ]. Note that when T = t end, the deal algorthm becomes the optmal soluton of the orgnal problem (7)-(1). Let Φ deal (k, T ) denote the optmal global gross proft computed by the deal algorthm over each frame 1 k K. Theorem 1. The tme-average global gross proft computed by OptMPSS satsfes: Φ OptMP SS 1 K Φ deal (k, T ) MT (14) K V k=1 where M = N (r max + µ max ) 2 /2 s a constant value. Proof. Theorem 1 can be proved by usng sample-path based

5 Lyapunov optmzaton theory. Due to page lmts, we present the detals ths proof n appendx ( Inequalty (14) shows that parameter V can be set as large as desred to force M T/V to be arbtrarly small. Specfcally, Theorem 1 also demonstrates that when T = t end, the optmal average global gross proft can be asymptotcally acheved by OptMPSS, as V. We can see that OptMPSS manages to attan the desred propertes 1 4, lsted n Subsecton II-E. We wll dscuss how to acheve the other propertes n later sectons. IV. MECHANISM DESIGN FOR FAITHFUL MPSS A key property of MPSS s that all parameters local to each phone are prvate and not observable to other phones and the server. Consequently, ths provde the phone users wth the opportunty to subvert the system by mscommuncatng ther local parameters. In ths secton, we brefly dscuss algorthmc mechansm desgn [15], whch studes fathful mplementaton of an ntended algorthm n a system wth a center and a set of ndvduals wth prvate parameters. MPSS can be vewed as such a system where the center s a server S and the ndvduals are moble phones, and we am to desgn a mechansm to fathfully mplement the ntended OptMPSS algorthm. A. Centralzed Mechansm Desgn Although we focus on dstrbuted mechansm desgn, for readablty, we frst dscuss drect revelaton (centralzed) mechansms [27] n the context of MPSS. 1) Effcent Socal Decson: For each phone, defne ts prvate type (parameters) as θ = (p (t), µ,j (t), j N (t), 1 t t end ) Θ where Θ represents the set of all possble types θ. Denote the prvate types of all phones as θ = (θ 1,..., θ N (t)) (Θ 1,... Θ N ) = Θ, where the type space Θ represents the set of all possble θ. Let x(θ) represent the jont rate control and routng decsons of the MPSS durng the whole tme horzon 1 t t end. x = (x (t), N, 1 t t end ) = (r (t), f,j (t), N, j N (t), 1 t t end ) X where X represents the set of all possble rate control and routng decsons. It s easy to see that the gross proft of each phone φ, N depends on ts prvate type θ and the decson x. Therefore, we can rewrte φ as φ (x, θ ). In mechansm theory, The functon x : Θ X s called a socal decson. Defnton 1 [Effcent Socal Decson] A decson x opt s sad to be effcent f φ (x, θ ) (15) N φ (x opt, θ ) N for all θ Θ and for all x X. Accordng to Theorem 1, t can be seen that the sensng rate control and routng decsons made by OptMPSS s the effcent socal decson when V. In order to make an effcent socal decson x( θ) n a centralzed way, each phone s asked to report ts type, denoted as θ, θ = ( p (t), µ,j (t), j N (t), 1 t t end ) Θ to the server S, where θ Θ represents the reported types of all phones. Snce each phone user exhbts strategc behavors n realty, he or she may be untruthful and report a type value θ that s dfferent from the real type (.e. θ θ ), n order to derve an alternatve socal decson x ( θ) that results n a better gross proft φ (x ( θ), θ ) > φ (x opt, θ ). 2) Tax, Subsdy, Net Proft, and Server Proft: In order to make an effcent socal decson, server S ntroduces a monetary transfer functon λ : Θ R N λ( θ) = (λ 1 ( θ),..., λ N ( θ)) (16) to encourage the phone users to report ther true types. Based on the announcement of a phone s type θ (t), the functon λ ( θ ), where ths s negatve ths represents a tax that s mposed on phone, or where postve a subsdy s pad to. The combned socal decson and monetary transfer functon (x( θ), λ( θ)) s referred to as the socal choce functon [14]: g : Θ X R N (17) As a result, the net proft of each phone user s defned as u (θ, x( θ), λ ( θ)) = φ (x( θ), θ ) + λ ( θ) (18) In our MPSS model, the tme-average server proft u S can be formally defned as u S = (1 α) v (r ) λ ( θ) (19) N N 3) VCG Mechansms: A drect revelaton mechansm s defned as (g, Θ), wth a strategy (type) space Θ and socal choce functon g. A mechansm defnes a non-cooperatve game wth ncomplete nformaton as each phone has no knowledge of the types of other phones. Defnton 2 [Incentve Compatblty] A drect revelaton mechansm g(θ) s domnant strategy ncentve compatble, f the reported θ (t) s a domnant strategy for each phone N : u (g(θ, θ ), θ ) u (g( θ, θ ), θ ), θ, θ, θ θ, where θ (t) represents the types of all other phones j N {}. In ths case we say the socal choce functon s mplemented n ex-post Nash equlbra. The Vckrey-Clarke-Groves (VCG) mechansm s wellknown for the desred property of ncentve compatblty [14]. The socal decson rule of the VCG mechansm s gven by x vcg ( θ) = arg max x( θ) X φ (x( θ), θ ) (2) N

6 and the monetary transfer functon of each phone N s: λ vcg ( θ ) = φ j (x vcg ( θ), θ j ) max φ j (x, θ j ) x X j } {{ } (a) j } {{ } (b) (21) where the term (a) corresponds to the gross proft of all phones excludng (.e. all phones n N {}) when an effcent socal decson has been made, and term (b) represents the maxmum global gross proft achevable for all phones n N {}, wthout s presence n the MPSS. Therefore, the monetary transfer λ vcg ( θ ) represents the mpact (ether loss or ncrease) n value that s mposed on all other ndvduals (.e. margnal socal mpact) due to the socal decson that has been updated resultng from s presence n the MPSSs. B. Dstrbuted Mechansm Desgn A dstrbuted mechansm dm = (h, Π, A) [13], [27] defnes an outcome (.e. decson and taxng) functon h = (h x, h λ ), a feasble strategy space Π = (Π 1... Π N ) (.e. all possble sensng rate control and routng strateges n our MPSS model), and ntended dstrbuted algorthm (.e. strategy) A = (A 1,..., A N ), such as our OptMPSS algorthm. A strategy s = (s 1,..., s N ) Π s a mappng from type space to dstrbuted actons ncludng message transmsson and computaton. The socal choce functon can be vewed as g = h s(θ) = (x, λ). Fg. 2 llustrates the relatonshp between drected and dstrbuted mechansms. Fg. 2. The relatons between drect and dstrbuted mechansms. Defnton 3 [Fathful Implementaton]. A dstrbuted mechansm dm = (h, Π, A) s an fathful mplementaton of the socal choce functon g = h A(θ) X R N, when the ntended dstrbuted algorthm (.e. strateges for phones) A = (A 1,..., A N ) s an ex post Nash equlbrum. u (h(a (θ ), A (θ ), θ ) u (h(a (θ ), A (θ ), θ ) for all N, A A, θ, θ. In ths case, the dstrbuted mechansm dm = (h, Π, A) s also sad to be ncentve compatble. In our MPSS model, the ntended dstrbuted algorthm A s OptMPSS. Due to the asymptotcal optmalty of our OptMPSS, we defne the asymptotc ncentve compatblty as follows: Defnton 4 [Asymptotc Incentve Compatblty]. A dstrbuted mechansm dm = (h, Π, A) s asymptotcally ncentve compatble, f u (h(a (θ ), A - (θ - ), θ ) u (h(a (θ ), A - (θ - ), θ ) ε(v ) for all N, A A, θ, θ -, where ε(v ) > and ε(v ) as V. V. THE BMT ALGORITHM By applyng dstrbuted mechansm desgn to OptMPSS, we develop BMT, an on-lne and fully dstrbuted algorthm that calculates the margnal socal mpact (for computng the VCG tax) of each phone. n parallel wth the operatons of OptMPSS. A. Dstrbuted Operatons of BMT Durng the complete tme horzon 1 t t end, the BMT algorthm operates as follows: 1. Intalzaton. At begnnng of slot t = 1. The server: S broadcasts the set N, revenue functon αv (), and system parameters V and r max to each phone N. Moble phones: Besdes storng ts data queue holdng data, each phone ntalzes a vrtual queue length (a non-negatve nteger number) Q (t) for each of all other phones j N, j, where Q (t) means the queue length of phone wthout phone j s presence. The ntal lengths of all vrtual queues are set as zero. 2. At each slot 1 t t end Dstrbuted Sensng and Routng. Each phone N adopts the OptMPSS algorthm for optmal dstrbuted sensng and data forwardng. Dstrbuted Margnal Socal Impact Computaton. In parallel, each phone N computes the vrtual sensng rate (t) and the vrtual cost cost (t) for each of all other phones j N, j based on the correspondng vrtual r queue length Q and r (t), (t) = mn(r max, αv 1 cost (t) = p s (t)r (t) + ( Q where the vrtual forwardng rate s f,k (t) = k N (t), k j { µ,k (t) f w,k (t) > otherwse (t) + p s (t) )) (22) V f,k ct,k(t) (23) where for each k N (t), k j, the vrtual weght s w,k (24) (t) = (Q (t) Q k (t))µ,k(t) V p t,k(t) (25) The vrtual queue lengths Q (t), j N {} are updated as Q (t + 1) = Q (t) f,k (t) + + r (t) + k N (t) k N (t) f k, (t)

7 The average vrtual sensng rates and vrtual costs for all j =, j N are updated as r = (r + (t 1)r )/t cost = (cost + (t 1)cost )/t 3. At slot t = tend. Each phone reports the average vrtual sensng rates r and vrtual cost cost for all j N, j = to the server. The server The server can compute the VCG tax λvcg = (αvj (r j ) costj ) j N {} (αvj (rj ) costj ) Fg. 3. Experment Prototype Illustraton. j N {} of each phone N. Fnally, the server makes a payment b of tend (αv (r ) + λvcg (θ )) to phone. From a global vew of pont, the BMT algorthm runs n total one real and N vrtual OptMPSS algorthms n parallel durng the tme horzon of the MPSS: the real OptMPSS algorthm makes the actual sensng rate and routng decsons at each slot, whle N vrtual OptMPSS algorthms smulate N vrtual margnal socetes wth absence of each phone N to compute the fnal tax or subsdy for each phone n a fully dstrbuted way. Remark 2. It worth notng that the N 1 vrtual queue lengths mantaned n each phone are nteger numbers rather than real data packet queues, whch results n neglgble storage overheads for moble phones (e.g. only several KB storage overhead for a MPSS wth thousands of phones wth several GB RAMs). In addton, BMT requres each node to transmt O( N ) bytes of nformaton (ts real and mantaned vrtual queue backlogs) to ts current neghbors only, whle also performng O( N ) smple arthmetc calculatons. Ths s stll realstc for today s smart phones usng short-range rados such as WF drect that can acheve up to 25Mbps data transmsson rate. Due to ts dstrbuted operatons and lght overheads, BMT has a great potental to be appled n large-scale MPSS. s asymptotcally effcent. Proof. Snce the dstrbuted socal decson (e.g. sensng rate control and routng decsons) made by BMT s the same as that of OptMPSS, ths Lemma obvously holds when ε(v ) = M T /V and frame sze T = tend, accordng to Theorem 1. Theorem 2. BMT acheves asymptotc ncentve compatblty. Proof. We prove Theorem 2 by contradcton. Consder a dstrbuted mechansm dm = (h, Π, Abmt ), where Abmt = bmt (Abmt 1,..., A N ) s the dstrbuted strategy of each phone allocated by BMT algorthm. Suppose that BMT s not asymptotcally ncentve compatble,.e. N, A = Abmt such that (θ ), Abmt u (h(abmt (θ ), θ ) + ε(v ) (θ ), Abmt =(a) φ (hx (Abmt (θ )), θ ) =(b) N N for all θ Θ and for all A Π, where ε(v ) > and ε(v ) as V. Lemma 1. The socal decson made by BMT algorthm, xbmt +hλ (Abmt (θ ), Abmt (θ )) + ε(v ) (θ ), Abmt φ (hx (Abmt (θ )), θ ) N max < φj + ε(v ) j = φ (hx (A (θ ), Abmt (θ ), θ ) max N B. Asymptotc Incentve Compatblty In ths subsecton, we prove that BMT acheves asymptotc ncentve compatblty. We frst ntroduce a new defnton and a supportung lemma. Defnton 5 [Asymptotcally Effcent Socal Decson] For a dstrbuted mechansm dm = (h, Π, A), a socal decson hx (θ) made by the suggested algorthm A s sad to be asymptotcally effcent f φ (hx A(θ), θ ) φ (hx A (θ), θ ) ε(v ) φj j = = u (hx (A (θ ), Abmt (θ ), θ ) (26) where equaltes (a) and (b) follow the defntons of net proft and VCG tax respectvely. It can be seen that nequalty (26) mples that φ (hx Abmt (θ), θ ) < φ (hx A (θ), θ ) ε(v ) N N bmt where A = (Abmt 1,..., A,..., A N ). Ths contradcts the asymptotcally socal effcency of BMT,.e. Lemma 1. VI. E VALUATION In ths secton, we evaluate the performance of the BMT algorthm va both prototype experments and smulatons

8 global gross proft hybrd hybrd cheatng 3G only scenaros (a) ndvdual gross proft 4 2 no cheatng cheatng A B C nodes (b) ndvdual net proft cheatng no cheatng A B C nodes Fg. 4. Experment results: (a) tme-average global gross profts for the three experments. (b) and (c) shows the mpact of devce A s cheatng acton on the tme-average ndvdual gross and net profts of every devce respectvely. usng real human moblty traces. A. Experments Based on Androd Devce We mplemented the BMT algorthm n Androd OS 4.3, and developed an applcaton called BMT App. We constructed a proof-of-concept MPSS wth three WF-drect enabled Androd devces (.e. a Nexus 5 phone and two Nexus 7 tablets) and a server mplemented n NODE.JS ( as shown n Fg.3. The duraton of a slot was set as two seconds and the duraton of each experment was 1 mnutes. At the each slot, the BMT App run a dscovery phase to update the temporary neghbor table (e.g. the server and nearby devces), and then performed the sensng, routng, and margnal socal mpact computaton tasks as defned by the BMT algorthm. Each devce was held by a researcher moved around our lab. We use the revenue functon v (r ) = 4 ln(1 + r ) for each N, and set the system parameters V = 1 and α =.5. We use WF drect as the short-range rados. The channel capactes of all wreless rados are set at 25 packets per slot. The sensng prces and transmsson prces (n credts per data packet) for the data sent by WF drect were set as.1, for all three Androd devces A, B, and C. The 3G transmsson prces of A, B and C were set as.1, 1, and 1.5 respectvely 1. As shown n Fg.4 (a), the tme-average global gross proft of MPSS usng hybrd 3G and WF drect communcatons s approxmately twce of that usng 3G rados alone, whch demonstrates that sgnfcant performance mprovement can be acheved by usng hybrd cellular and short-range rado. In addton, we also evaluated the ncentve compatblty of BMT. Snce devce A had a much lower 3G prces than B and C, the routng decsons made by BMT would requre A to relay the sensor data packets collected by B and C (when A passed them) to the server, n order to maxmze the global gross proft. However, ths would result n an ndvdual gross profts reducton for A (due to the relayng cost), and therefore (the owner of) A may not want to fathfully adopt the dstrbuted routng actons suggested by BMT. To check 1 Ths mples that A may have an unlmted moble data budget, whle B and C may adopt a lmted monthly contract or pay as you go tarff rate. (c) packets per second profts scenaro 1 scenaro days (a) dynamc throughput global gross profts global net profts server profts scenaros (c) global profts packets per second ndvdual net proft 1 8 scenaro 1 scenaro days (b) average throughput no cheatng cheatng Fg. 5. Smulaton results of BMT node ID (d) ncentve compatblty whether BMT can avod ths, we mmc a qute ntutve cheatng behavor for A,.e. dsablng ts WF drect rado. Fg. 4 (b) shows that the ndvdual gross proft for each devce before and after A s cheatng acton. It can be seen that ths untruthful behavor can ndeed mprove A s ndvdual gross proft, but results n a sgnfcant degeneraton of global gross proft for the whole system, as shown n Fg. 4(a). As shown n Fg.4 (c), however, A eventually mssed the opportunty of obtanng approxmately 36% more net proft due to cheatng. Ths means that A would be better off relayng sensor data from other devces than msnformng the network. Ths demonstrates that n practce BMT can acheve the hghly desred ncentve compatblty property. In addton, the server proft and net proft of each devce and server proft were postve n all experments (These results are not plotted due to page lmts), whch demonstrates that BMT can acheve ndvdual ratonalty and server proftablty n practce. B. Trace-drven Smulatons To evaluate the practcal performance of BMT at scale, we establshed smulatons usng the real human trace collected from Infocom5 (41 nodes for 3 days) [17]. In all smulatons, each phone has both 3G, WF, and WF drect rados. When a phone meets a free WF router, t sends data through the WF rado rather than 3G. In each smulaton, a power-law dstrbuted random varable was assgned to each phone to smulate the heterogeneous free WF access probablty across phones, observed from real human moblty traces [3], [31]. The sensng and WF/Wf-drect transmsson prces for each phone were dynamcally set between and.1 for each slot (representng channel qualty varaton) at each slot, whle 3G transmsson prce of each phone was randomly set between.1 and.5 at the begnnng of each smulaton and remaned constant over slots. We set r max = 5 and the duraton of a

9 slot as one second. All other smulaton parameters were set the same as n the prototype experment represented earler. We agan run three smulatons: MPSS wth all wreless rados (scenaro 1), MPSS wthout WF drect (scenaro 2), and cheatng actons n MPSS wth all wreless rados (scenaro 3), where the users of phone 1 to 1 try to hde ther WF drect abltes. Fg. 5 (a) and (b) show the dynamc and tmeaverage throughput (.e. total sensng data packets produced by all phones at each slot) of MPSS respectvely, whch demonstrate that the BMT algorthm s adaptve to network dynamcs (e.g. moblty) and manages to converge to the tmeaverage optmal. In addton, Fgure 5 (c) and (d) demonstrate that usng mult-hop opportunstc short-range communcatons can sgnfcantly mprove network performance and BMT can acheve ncentve compatblty, ndvdual ratonalty, and server proftablty n practce. VII. CONCLUSION In ths paper we nvestgate a cost-effectve data collecton soluton to Moble Phone Sensng Systems (MPSS) that utlze hybrd cellular and opportunstc short-range wreless communcatons. We formulate a stochastc optmzaton problem for moble sensor data collecton, and develop OptMPSS, a scalable jont sensng rate control and routng algorthm to solve the formulated optmzaton problem n a fully dstrbuted and scalable way. In order to encourage phone users to fathfully apply the OptMPSS algorthm s control suggestons, we propose BMT, a jont networkng and taxng scheme, based on combng Lyapunov stochastc optmzaton and dstrbuted mechansm desgn theores. We prove that BMT acheves asymptotcal optmalty and ncentve compatblty. In order to evaluate the practcal performance of BMT, we developed BMT App, an Androd applcaton that mplements BMT algorthm for WF-drect-enabled devces. 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