IEEE/ACM TRANSACTIONS ON NETWORKING 1 Efﬁcient and Fair

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IEEE/ACM TRANSACTIONS ON NETWORKING 1

Efficient and Fair CollaborativeMobile Internet Access

George Iosifidis, Lin Gao, Senior Member, IEEE, Jianwei Huang, Fellow, IEEE,and Leandros Tassiulas, Fellow, IEEE

Abstract— The surging global mobile data traffic challenges theeconomic viability of cellular networks and calls for innovativesolutions to reduce the network congestion and improve userexperience. In this context, user-provided networks (UPNs),where mobile users share their Internet access by exploitingtheir diverse network resources and needs, turn out to bevery promising. Heterogeneous users with advanced handhelddevices can form connections in a distributed fashion and unleashdormant network resources at the network edge. However, thesuccess of such services heavily depends on users’ willingness tocontribute their resources, such as network access and devicebattery energy. In this paper, we introduce a general frameworkfor UPN services and design a bargaining-based distributedincentive mechanism to ensure users’ participation. The proposedmechanism determines the resources that each user shouldcontribute in order to maximize the aggregate data rate inUPN, and fairly allocate the benefit among the users. Thenumerical results verify that the service can always improveusers’ performance, and such improvement increases with thediversity of the users’ resources. Quantitatively, it can reach anaverage 30% increase of the total served traffic for a typicalscenario even with only six mobile users.

Index Terms— Network economics, network optimization, nashbargaining, fog computing, user-provided networks.

I. INTRODUCTION

A. Background and Motivation

ACCORDING to several recent industry reports [2], [3],mobile data is expected to increase with an annual growth

rate of 60% in the next several years, reaching 25 exabytes permonth in 2020. This surging traffic places an unprecedentedstrain on cellular networks, which need to substantially expandtheir capacities. However, it is clear that the traditional capac-ity increase strategies of mobile network operators (MNOs),such as acquiring more spectrum or deploying additional

Manuscript received July 20, 2015; revised June 24, 2016; acceptedNovember 13, 2016; approved by IEEE/ACM TRANSACTIONS ON NET-WORKING Editor S. Chong. This work was supported in part by the GeneralResearch Funds under the University Grant Committee of the Hong KongSpecial Administrative Region, China, under Project CUHK 14202814 andProject 14206315 and in part by the National Science Foundation, USA,under Grant CNS 1527090. This work was presented at the IEEE INFOCOM2014 [1].

G. Iosifidis is with the School of Computer Science and Statistics, TrinityCollege Dublin, The University of Dublin, and also with the Research CentreCONNECT, Dublin 2, Ireland (e-mail: [email protected]).

L. Gao is with the College of Electronic and Information Engineering,Harbin Institute of Technology, The University Town of Shenzen, Shenzen518055, China (e-mail: [email protected]).

J. Huang is with the Department of Information Engineering, The ChineseUniversity of Hong Kong, Hong Kong (e-mail: [email protected]).

L. Tassiulas is with the Department of Electrical Engineering and theInstitute for Network Science, Yale University, New Haven, CT 06520 USA(e-mail: [email protected]).

Digital Object Identifier 10.1109/TNET.2016.2638939

network infrastructure, are often time-consuming, costly, andeventually inadequate to accommodate the traffic growth.Therefore, MNOs often end up offering services of lowquality [4], or charging their subscribers very expensive usage-based fees [5]. This means that a large number of mobile usersdo not have access to the low-cost and high-speed mobileInternet, and hence there are significant user dissatisfactionsand frequent user churns. This leads to the growing consensusthat more disruptive methods and forward-looking solutionsare needed to resolve the growing gap between data supplyand demand.

At the same time, recent technological advancements haveresulted in sophisticated user handheld equipments, such assmartphones with Wi-Fi (802.11) and Bluetooth (802.15.1)interfaces, 4G chipsets supporting cellular connections up to150Mbps [6], and high-end processors that can execute com-plicated networking tasks. However, the conventional approachof using these devices as simple transceivers, which arecompletely controlled by the cellular base stations to serveonly the needs of their owners, does not fully exploit theircommunication and computational capabilities. Clearly, thesedevices can also offer communication services to nearby users,by acting as mobile Wi-Fi hotspots or relays. In other words,it is to transform users to local micro-operators, serving eachother’s needs. This leads to the so-called user-provided net-works (UPNs) [7]–[10] which constitute a promising solutionfor alleviating network congestion, reducing network accesscosts, and improving the user satisfaction by enabling networkcontrol at the edge of the network.

One of the first UPN services is FON [11], a community-based Wi-Fi Internet access scheme, where roaming FONusers can access the Internet through the home Wi-Fi connec-tions of other nearby FON users. Different from FON whichutilizes fixed user equipments (Wi-Fi access points), there isan emerging trend of mobile UPNs, which focus on leveragingthe capabilities of handheld mobile devices [12]–[14]. Forexample, Open Garden [13] offers a mobile software whichenables mobile devices to connect with each other throughWi-Fi direct [15] or Bluetooth [16], and share their Internetconnections. This solution creates a mesh network, where eachuser (device) may act as a client node (consuming data), arelay (relaying data to other nodes), or a gateway (connectingthe mesh overlay with Internet), as illustrated in Figure 1.

In a nutshell, mobile UPN services aim to crowdsourceInternet access by allowing users to collaboratively consumetheir Internet connections and battery energy. The key idea isto turn the negative externality of network congestion to thepositive network effect, by exploiting the diversity of resources

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2 IEEE/ACM TRANSACTIONS ON NETWORKING

Fig. 1. An example of users interactions in UPNs. Each user can concurrentlyconsume data from multiple gateways, over multiple and possibly multi-hoppaths, and serve as a relay or even a gateway for others. Left: concurrentdownloading from two gateways. Right: multi-hop connection to Internet.

and demands of different users. Recent measurement-basedstudies [17] have revealed the large benefits of these sharingmechanisms. However, the success of such services heavilydepends on (i) the willingness of users to join the serviceand contribute their resources, and (ii) the efficient allocationof the aggregated capacity. Clearly, a user with low batteryenergy and fast Internet connection may not be willing to serveother users, unless this improves her satisfaction level. There-fore, it is important to design a resource sharing mechanismfor properly incentivizing user participation.

Such an incentive mechanism (currently missing from [13]and similar services) should encourage users to collaborate,and lead to a proper data transmission and routing scheme thatbalances efficiency and fairness. The efficiency is quantified interms of the aggregate throughput which can be maximized byhaving users with the highest Internet connection capacitiesserve as gateways, and by properly scheduling the traffic toavoid heavy interferences among users. The fairness criterion,on the other hand, concerns the relationship among datadelivery, resource contribution, and economic gains/losses ofeach user. If a user experiences excessive unfair consumptionof her resources she will probably leave the service and hencedeteriorate the performance experienced by other users.

Nevertheless, the design of this mechanism is very chal-lenging. First of all, there is often no central entity controllingsuch a wireless mesh network with devices belonging toheterogeneous physical networks, and each user only hasinformation regarding her own needs and resources. Therefore,the proposed scheme has to be distributed. Moreover, thefairness criterion should consider that users have differentneeds and may contribute different resources with differentcosts. At the same time, this criterion should take into accountthat a user will participate in the service only if she expectsto improve over her standalone performance, i.e., the one sheachieves when acting independently.

B. Methodology and ContributionsWe introduce a detailed framework for the UPN service,

which is modeled as a multi-hop, multi-path mesh network thatmanages multiple unicast sessions between the Internet anddifferent users. Each device may have one or more networkinterface cards (NICs), which enable it to transmit/receiveover one or more frequency channels. Each user is parameter-ized by her Internet connection capacity (through cellular orWi-Fi connections), her available battery energy, the monetary

cost for downloading and uploading data (based on the user’spricing scheme or data plan), and her relaying capabilities.Finally, we employ user-specific utility and cost functions toaccount for the communication needs and energy consumptionaversion, respectively, that may vary across users.

We use game theory, and specifically the Nash bargainingsolution (NBS) concept [18], to determine the efficient and faircontribution of the user resources and allocation of the servicecapacity to each user. The NBS yields an outcome which isPareto efficient and fair [19], and hence is self-enforcing, i.e.,acceptable by all users. A particularly important feature ofthe NBS rule is that it takes into account the disagreementperformance of each player, i.e., the utility she perceives whenan agreement is not reached. This means that the NBS ensuresthat each user participating in the UPN service will receive aperformance at least as good as her standalone performance.

We further introduce a virtual currency system to facilitatethe users’ cooperation and address the inherent incentive issue.Such a system allows the users to cooperate not only by directservice exchanges (e.g., relaying data for each other) but alsoby using this currency to pay for the services that they receive(e.g., exchange currency with relayed data). This encouragesusers to participate and serve other users so as to collectcurrency, even if they currently do not have communicationneeds (but can use the currency later when they have needs).Similarly, it enables users with poor Internet connections toutilize the service by paying other users. Clearly, this virtualcurrency system addresses the problem of double coincidenceof needs [20], therefore increases the number of users who areable to cooperate with each other.

We propose an algorithm that computes the NBS in adistributed fashion, thus enabling the decentralized imple-mentation of the resource sharing mechanism. This is highlynon-trivial mathematically, since the respective optimizationproblem has both a coupled constraint set and a coupled objec-tive function. The obtained solution determines the amount ofeach resource (Internet access capacity, wireless bandwidth,and battery energy) that each user should contribute, theamount of data that she will be served in return, and thevirtual currency transfers. Moreover, it describes how this willbe achieved, i.e., how much traffic will be conveyed overeach link, which channels will be used for the users’ com-munications, and which Internet connections will be utilized.Such a holistic methodology enables more than two users tocollaborate over multihop paths, and therefore outperformsprior bilateral-only cooperation schemes. Besides, this jointdesign and coordination of the users can mitigate interferenceamong users through proper channel reallocations, as shownin Figure 2.

Additionally, the proposed service model goes beyond typ-ical self-organized networks or device-to-device communica-tions, as it is capable of connecting multiple heterogeneousInternet access networks. In particular, it can offload cellu-lar traffic to Wi-Fi networks [21] or onload Wi-Fi trafficto cellular networks [22]. These scenarios are illustsratedin Figure 3. The optimal strategy depends on congestionlevels of the Internet connections and the data access costs.More interestingly, these decisions are made by users in a


IOSIFIDIS et al.: EFFICIENT AND FAIR COLLABORATIVE MOBILE INTERNET ACCESS 3

Fig. 2. The proposed service can be used to mitigate interference by properchannel assignments. In this example, both access points transmit in the samechannel (with a frequency f1), hence close-by users (1 and 2) will interferewith each other if they directly communicate with the access points (dashedarrow for user 2). The UPN service can exploit the two NICs of user 3 (who isfurther away from user 1) for relaying the traffic of user 2 through a differentchannel, thus reducing the interference for user 1.

distributed fashion and without the intervention of networkoperators.

To this end, the main technical contributions are as follows:

• Analytical Model: We introduce a general mobile UPNservice that incorporates users’ communication needs,monetary costs, and energy consumption, which are thekey factors affecting users’ servicing decisions.

• Incentive Provision & Service Allocation Mechanism:We design a resource sharing mechanism based on theNash bargaining solution, that induces users’ participa-tions through fair allocation of the contributed resources.It is Pareto efficient and takes into account users’ stand-alone performances. These aspects are very crucial tomaintain a good performance of the service.

• Distributed Algorithm: We propose a distributed algo-rithm, which combines the concepts of consistency pric-ing [23] and primal-dual Lagrange relaxation [24], andachieves the unique NBS. This enables the decentralizedimplementation of the service, without requiring centralcoordination or additional infrastructure.

• Intelligence-at-the-edge: We discuss how the service canaccount for interference and congestion effects, by takingintelligent (at-the-edge) channel assignment, routing, andflow control decisions. We explain how the service canbe used both for mobile data offloading and onloading,adapting on the congestion levels of the different net-works as well as the Internet access costs.

• Performance Evaluation: We evaluate the performance ofthe service for various system parameters and scenarios.We find that the benefits increase as users become moreheterogeneous (diverse) in terms of their needs andresources, increasing on average by at least 30% theamount of served data in a typical scenario with 6 users.

The rest of the paper is organized as follows. Section IIintroduces the system model. Section III analyzes the userdecisions and provides the problem statement. In Section IV,we present the Nash bargaining formulation, and in Section Vwe provide the algorithm for its distributed solution.We present numerical results in Section VI. Finally, we analyzerelated works in Section VII, and conclude in Section VIII.

Fig. 3. The proposed service can be used to offload cellular traffic to Wi-Fiaccess points (left), or onload Wi-Fi traffic to cellular networks (right). Theoffloading decisions depend mainly on the data usage (and energy) costincurred by the users, while the onloading decisions depend on the congestionof Wi-Fi APs. Here the dashed arrow means the data downloading choicebefore collaboration, and the solid arrow means the data downloading choiceafter collaboration.

II. MODEL

A. Basics of the UPN Model

Network Graph: We consider a set of mobile usersI = {1, 2, . . . , I}, who are interested in providing a crowd-sourced Internet access service (hereafter referred to as ser-vice) to each other for a time period T (e.g., several minutes).The users create a mesh network that is described by adirected graph G = (I, E ,B). Here, E denotes the set ofcommunication links that can carry data between the nodes(or, users), and B denotes the set of “interference links”. If alink (i, j) ∈ E , then node i can transmit data to j. If a link(i, j) ∈ B, then nodes i and j are not in communication rangebut still their concurrent transmissions (independent of theirtransmission destinations) interfere with each other.1 This ispossible since in 802.11 the carrier sense range is larger thanthe transmission range [25].

We assume that the graph is connected, i.e., any two nodescan communicate (e.g., for exchanging control messages)through a (possibly multi-hop) path along the communicationlinks. We also define the sets

In(i) = {j : (j, i) ∈ E}, Out(i) = {j : (i, j) ∈ E}, (1)

for the upstream and the downstream one-hop neighbors ofnode i, respectively. Similarly, we introduce the extended setsIne(i) and Oute(i) that include the interference links as well,e.g., Ine(i) = {j : (i, j) ∈ E ∪ B}. Finally, we define the setof neighbors for i, N (i) = In(i) ∪Out(i) and the respectiveextended neighbor set N e(i) = Ine(i) ∪Oute(i).

Channels: Each node can access the Internet using multipleInternet connections simultaneously, for example through bothcellular and Wi-Fi connections. This is consistent with therecent technology development (e.g., see [27], [28]). Ourmodel also allows the more restricted case where each gatewaynode can only use the best of her multiple Internet connections.

There is a set F of unlicensed channels (Bluetooth orWi-Fi) available for each direct link among the users.2

1The interference link is based on [25] and is consistent with the typicalinterference range approach: an interference link exists among two nodeswhenever one is within the interference range of the other. For simplicity, weassume a symmetric relationship.

2Note that the Wi-Fi Internet access channel is determined by the Wi-FiAP instead of by users participating in the UPN. Hence, it may or may notcoincide with one of the orthogonal channels in F . For the more generalmodel, we assume that this channel is one of the elements in set F .



For example, in the IEEE 802.11 family of standards [15],there are 3 orthogonal channels in the 2.4GHz band and12 channels in the 5GHz band. Each communication link canutilize any one (and only one) of these channels f ∈ Fat any given time. Note that set F does not include thelicensed cellular channel which we denote as c. Each nodei ∈ I has ki network interface cards (NICs) which allowthe concurrent utilization of up to ki different channels on ki

communication links connected to this node. This includes thespecial case of ki = 1, where a node has only one Wi-FI NIC(besides her capability of accessing the Internet through thecellular channel c). Similarly to [25] and [26], we assume thatthe devices can change channels very fast without significantoverheads (e.g., in energy consumption).

Link Capacities and Commodities: We denote with Cci

and Cfi the Internet access capacity for user i ∈ I when

she employs her cellular connection c, or Wi-Fi connectionchoosing channel f ∈ F , respectively. Also, let Cf

ij ≥ 0denote the capacity of link (i, j) ∈ E when choosing channelf ∈ F assuming no other interference links are active atthe same time. In general, we allow to have Cf1

ij �= Cf2ij

for f1, f2 ∈ F , so as to take into account possible channeldiversity. We assume that the users are nomadic (not veryfast moving), and the time period length much larger thanthe channel coherent time. This means that we can useproper coding techniques to deal with the fast small scalefading, therefore the link capacities are considered constantduring T .

B. Network Constraints, Routing and Internet Access

In order to simplify the presentation, we will focus on thescenario where users download data from the Internet. Ouranalysis can be easily extended for the uploading scenario withmore complicated notations. During period T , each user canhave more than one roles if needed: she can be a client node(consuming data), a relay node (routing data to/from otherusers), and/or a gateway node (downloading data from theInternet). Therefore, there exist at most |I| data commoditiesin the UPN, where each commodity n ∈ I corresponds toa (potentially multi-hop) unicast session originating from theInternet (e.g., a content server) and ending at a user n ∈ I.

Scheduling and Network Constraints: We assume that thetime period T = {1, 2, . . . , T} is divided in T equal lengthtime slots t = 1, 2, . . . , T , with each slot having a normalizedlength of 1. In each slot, every node i ∈ I can potentiallyupdate her strategy and decide whether she is going to useany of her outgoing links to transmit data, or receive datafrom her upstream neighbors, or access the Internet throughthe cellular or a Wi-Fi network. If the node has multiple NICs,she can choose multiple choices at the same time. Namely,we use the binary variable xf

ij [t] ∈ {0, 1} to denote nodei’s decision of whether transmitting data (of any commodity)to node j ∈ Out(i) during slot t in channel f . We furtheruse binary variables yc

i [t] ∈ {0, 1} and yfi [t] ∈ {0, 1} to

denote user i’s decisions of whether downloading data fromthe Internet during t, through the cellular connection or theWi-Fi channel f ∈ F , respectively.

These decisions are subject to certain constraints. The firstcondition that should be satisfied is the link-channel constraint:for each link (i, j) ∈ E and each Wi-Fi Internet link, only onechannel can be employed in each slot t at most, i.e.,

∑

f∈Fxf

ij [t] ≤ 1, ∀ (i, j) ∈ E , ∀ t ∈ T , (2)

∑

f∈Fyf

i [t] ≤ 1, ∀ i ∈ I, ∀ t ∈ T . (3)

Second, the data amounts that each node i ∈ I can sendor receive from her neighbors or from Internet, in all theavailable channels, are constrained by the total number ofher network interface cards. Therefore, the following nodeconstraint should hold for every node i ∈ I and slot t ∈ T :

∑

f∈F

⎛

⎝yfi [t] +

∑

k∈In(i)

xfki[t] +

∑

j∈Out(i)

xfij [t]

⎞

⎠ ≤ ki, (4)

which does not include the cellular transmissions since theyuse a different NIC.

Moreover, the transmissions of the different nodes arecoupled due to interference. In particular, based on the protocolinterference model [25], [29], we assume that a transmissionover link (i, j) ∈ E in t is successful only if all nodes that areconnected to i or j through an interference or communicationlink are idle, i.e., do not transmit or receive data during t.To facilitate modeling, we define the set of all interfering links:

I(i, j) = {(c, b), (a, c) : c ∈ N e(i) ∪ N e(j),b ∈ Out(c), a ∈ In(c)}, ∀(i, j) ∈ E .

Therefore we have the set of interference constraints:

xfij [t] +

∑

(k,m)∈I(i,j)

xfkm[t] +

∑

k∈N e(i)∪N e(j)

yfk [t] ≤ 1, ∀(i, j) ∈ E , t ∈ T , f ∈ F (5)

Equation sets (2)-(5) constitute the sufficient and necessaryconditions for a feasible channel assignment and schedulingin the UPN during T . However, the above binary variablesrender any scheduling optimization problem highly complexsince they require - as it will be explained below - thesolution of challenging discrete non-linear optimization prob-lems. To address this issue, we employ a continuous-timeapproximation for modeling the operation of the UPN. Thisyields the one-off servicing policy the nodes decide at thebeginning of each period T . Nevertheless, since this policyis based on the detailed slot-by-slot analysis, it enables thedesign of near-optimal solutions as it will become clear next.

Routing and Internet Access Decisions: Specifically, wefollow the analysis (among others) of [25], [26], and [30], andrelax the above discrete decision variables by employing theaverage data rates over each link in every channel. In detail,we use yc

i (n) ≥ 0 and yfi (n) ≥ 0 to denote user i’s

average downloading rate (from the Internet) for commodityn ∈ I, over the cellular connection or the Wi-Fi channel



f ∈ F , respectively. Specifically, we define:

∑

n∈Iyf

i (n) = Cfi

T∑

t=1

yfi [t]/T , ∀ i ∈ I, f ∈ F , (6)

∑

n∈Iyc

i (n) = Cci

T∑

t=1

yci [t]/T , ∀ i ∈ I, (7)

where notice that we sum over all commodities.Also, we denote xf

ij(n) ≥ 0 as user i’s average rate ofrouting data of commodity n to her one-hop downstreamneighbor j, using channel f ∈ F . These routing decisionsare determined by the scheduling decisions:

∑

n∈Ixf

ij(n) = Cfij

T∑

t=1

xfij [t]/T, , ∀(i, j) ∈ E , f ∈ F (8)

Using the above definitions we can describe the operation ofthe UPN with the routing matrix x =

(

xfij(n) ≥ 0 : (i, j) ∈

E , n ∈ I, n �= i, f ∈ F)

, and the Internet access matrixy =

(

yfi (n), yc

i (n) ≥ 0 : i ∈ I, n ∈ I, f ∈ F)

. Thesematrices comprise also the channel and commodity selectiondecisions.

With the above continuous-time relaxation and substituting(6)-(8) to (2)-(5) we devise the necessary conditions for aschedule to be feasible. In detail, based on (4) we have thefollowing node-radio constraint set for the Wi-Fi NICs:

∑

k∈In(i)

∑

f∈F

∑

n∈I xfki(n)

Cfki

+∑

j∈Out(i)

∑

f∈F

∑

n∈I xfij(n)

Cfij

+∑

f∈F

∑

n∈I yfi (n)

Cfi

≤ ki, ∀ i ∈ I. (9)

Similarly, eq. (5) lead to the scheduling constraints:

∑

(k,m)∈I(i,j)

∑

n∈I xfkm(n)

Cfkm

+

∑

n∈I xfij(n)

Cfij

+

∑

k∈N e(i)∪N e(j)

∑

n∈I yfk (n)

Cfk

≤1, ∀ (i, j) ∈ E , ∀f ∈ F . (10)

Note that the last term includes the Internet access transmis-sions of both nodes i (as a neighbor of j) and j (as a neighborof i). Moreover, according to (2) and (3), the transmissions indifferent channels over each link are coupled:

∑

f∈F

∑

n∈N xfij(n)

Cfij

≤ 1, ∀(i, j) ∈ E , (11)

∑

f∈F

∑

n∈N yfi (n)

Cfi

≤ 1,∑

n∈Iyc

i (n) ≤ Cci , ∀ i ∈ I. (12)

Finally, the routing and Internet access variables shouldsatisfy the flow conservation constraints:

∑

j∈In(i)

∑

f∈Fxf

ji(n) + yci (n) +

∑

f∈Fyf

i (n) =

∑

j∈Out(i)

∑

f∈Fxf

ij(n), ∀ i, n ∈ I, n �= i. (13)

In other words, the data that node i ∈ I receives fromher upstream neighbors plus the data she downloads (overall channels) should be equal to the amount of data sheroutes to her downstream neighbors. This should hold for allcommodities except n = i that is consumed locally by i.

Using matrices x and y, we can determine the UPN opera-tion (based on the objective that we will define in the sequel),which is implementable (feasible) but not necessarily optimal.In other words, due to the continuous-time relaxation the aboveconstraints are necessary but not sufficient for optimality [25].On the other hand, we note that the proposed scheme isexpected to operate based on the 802.11 MAC protocol,which does not support synchronous operation and hencecannot apply the discrete-time solution (even if it was known).A detailed gap characterization between the theoretical perfor-mance of the proposed scheme and its implementation (e.g., bya practical protocol) will be part of our future work.

III. USERS DECISIONS AND PROBLEM STATEMENT

Data Consumption Utility: Each user i ∈ I has elasticneeds and perceives certain satisfaction for consuming data(not including relaying for other users). This is modeled bya utility function Ui(·) that depends on the aggregate averagerate ri, with which user i directly downloads and receives dataof commodity i from her neighbors, i.e.,

ri = yci (i) +

∑

f∈Fyf

i (i) +∑

j∈In(i)

∑

f∈Fxf

ji(i). (14)

Function Ui(·) is assumed to be positive, increasing, andstrictly concave. The concavity captures the user’s diminishingmarginal satisfaction of additional data consumption. Differentusers may have different utility functions [31], [33]. Forexample, the utility of a user who is streaming a video fileis initially proportional to the downloading rate, and saturatesafter the maximum available (encoding) rate has been reached.On the other hand, the utility of a user who is downloading afile increases strictly with the downloading rate.

Energy Expenditure Cost: Energy consumption is a majorconsideration for mobile users since their devices have oftenlimited energy resources [34]. Let ef,s

ij (joules/bytes) be theenergy that node i consumes when she sends one byte tonode j over link (i, j) ∈ E in channel f . Also, ef,r

ij denotesthe energy that node j consumes for receiving one byte fromnode i in f . Finally, ec

i and efi are the energy consumptions

when node i downloads one byte from the Internet, through herWi-Fi or cellular connection, respectively.

Providing analytical expressions for wireless transmissionenergy costs is particularly challenging (e.g., see seminalwork [37]), and is further perplexed in the case of handhelddevices. For example, the relation of power consumption withthroughput is affected by the method that is employed toincrease the latter [38]. Nevertheless, it is commonly agreedthat the energy consumption depends on the transmission timeand the volume of transmitted data, and therefore on the linkcapacity which in turn is shaped by the channel conditions. Tocapture qualitatively the above aspects and avoid delving intothe physical layer details, we follow here the measurement



studies [35], [36], which indicate that the power consumption(in mWatts) for transmitting (P f,s

ij ) and receiving (P f,rij ) over

link (i, j) ∈ E has a constant offset plus a term linearlydependent on the rate (hence depends also on channel f ):

P f,sij = δf,sCf

ij + θf,s, P f,rij = δf,rCf

ij + θf,r

Parameters δf,s, δf,r, θf,s, and θf,r are constants and dependon the technology choices (Wi-Fi, 3G, or LTE-A) [35], [36].Hence, the energy consumption of node i in link (i, j) is3:

∑

n∈I

∑

f∈Fef,s

ij xfij(n)T =

∑

n∈I

∑

f∈F

xfij(n)

Cfij

T(

δf,sCfij + θf,s

)

.

Note that the first term on the RHS captures the total time(within T ) used for transmitting data in f , and the secondterm of this product captures the power consumption on aparticular data rate. The energy consumption for a receiver canbe defined similarly. Finally, the total energy consumption bynode i is:

ei =∑

n∈I

∑

f∈Fef

i yfi (n)T +

∑

j∈Out(i)

∑

n∈I

∑

f∈Fef,s

ij xfij(n)T

+ eci

∑

n∈Iyc

i (n)T +∑

j∈In(i)

∑

n∈I

∑

f∈Fef,r

ji xfji(n)T. (15)

We assume that each node i ∈ I has a maximum energybudget of Ei ≥ 0 units (joules). This parameter can beexplicitly set by the user (e.g., through a proper user interfaceon the mobile app), or it may represent her actual residualbattery. Clearly, we need to have ei ≤ Ei for each node.Moreover, different users may have different energy consump-tion preferences. For example, some users may be willing toconsume almost their entire energy budgets, while others mayprefer a much more conservative energy consumption.

To capture the above user difference, we introduce foreach user i an energy cost (or, dissatisfaction) function Vi(·),which is positive, increasing, and strictly convex in ei. Itsvalue goes to infinity when the energy budget of the useris depleted. A function that satisfies these requirements is,for example, Vi(ei) = φi/(Ei − ei), where φi ∈ [0, 1] isa normalization parameter indicating user i’s sensitivity inenergy consumption. Finally, we wish to stress that there isan additional energy cost for the exchange of coordinationmessages (as it will be explained in Section V) and an energyconsumption due to ACK messages. The latter is a relativelysmall portion of the relayed traffic volume, and does not havea significant impact on the UPN operation [28].

Data Plan Cost: The impact of the remaining data planquota on users’ collaboration decisions are very crucial. Yet,the analysis of quota dynamics is very challenging [40],especially if the demand is elastic and dynamically decided(as here). In order to study this aspect in a tractable fashion,we characterize each user by a psychological price per unit ofcellular data, as a function of her remaining data quota.

3This formulation assumes that each time a link is employed, it can achieve itsmaximum capacity since the underlying scheduling scheme ensures a proper coordinationamong the interfering transmissions [32], [26]. If the scheduling is achieved withthe traditional CSMA/CA protocol, i.e., not a time-slotted system, then the energyconsumption will be higher due to collisions.

We assume that these psychological parameters remain fixedduring each time period, but they can change across differenttime periods so as to reflect the quota’s impact. Therefore, thedissatisfaction of each user i due to the consumption of herdata plan can be described by a convex function as follows:

Qi(yag,ci ) =

oi

Ai − yag,ci

(16)

where yag,ci =

∑

n∈I yci (n)T is the aggregate amount of data

that will be downloaded through her cellular link during T ,and Ai the available quota at the beginning of the period. Para-meter oi > 0 is the psychological price, which captures theuser aversion on the consumption of her data plan (includingthe impact of the actual cost per byte, the anticipation of futureneeds, and other such latent factors) and can vary both acrossusers and time periods. This model has the following desirableproperties. First, as the amount of consumed data approachesthe currently available quota, the psychological monetary costincreases very fast. Second, even if two users i and j have thesame quotas (Ai = Aj) and download equal amounts of data(yag,c

i = yag,cj ), they still might incur different costs due to

their preferences (oi �= oj).Payoff Function: In order to capture all the above aspects

that affect the users’ decisions, we introduce the payofffunction Ji(·) that user i receives when she participates inthe crowdsourced Internet access service. More specifically:

Ji(xi,xini ,yi) = Ui(ri) −Qi(y

ag,ci )

−∑

f∈Fpf

i

∑

n∈Iyf

i (n)T − Vi(ei),

where pfi ≥ 0 is the price for accessing Internet through Wi-Fi

channel f . Also, we have defined the matrices of downloadingand routing: yi = (yf

i (n), yci (n) : n ∈ I, f ∈ F), xi =

(xfij(n) : j ∈ Out(i), n ∈ I, f ∈ F), and xin

i = (xfji(n) :

j ∈ In(i), n ∈ I, f ∈ F).Note that the payoff Ji monotonically decreases with

the amount of data that user i downloads for other usersn ∈ I, n �= i, and routes to her downstream neighbors.Therefore, users are reluctant to execute these tasks withoutproper compensations. Furthermore, some users may not havecommunication needs in a certain time period, and thereforemay not be willing to participate in the UPN service. Toaddress these issues, it is necessary to use a payment mech-anism that will alter the payoff function of the users andpromote collaboration. We provide the details in Section IV.

Standalone Operation: Moreover, a rational user will jointhe service only if this will improve her payoff in comparisonto her standalone performance. In the standalone operation,each user i does not receive or deliver data to her neighbors,nor she downloads data for any other user. Therefore, theoptimal Internet access strategy can be obtained by solvingthe following Standalone Operation Problem (SOP):

maxyc

i (i),{yfi (i)}f∈F

Ui

(

yci (i) +

∑

f∈Fyf

i (i))

− pfi

∑

f∈Fyf

i (i)T

−Qi(yci ) − Vi

(

yci (i) +

∑

f∈Fyf

i (i))

(17)



TABLE I

BASIC NOTATIONS

s.t.∑

f∈F

yfi (i)

Cfi

≤ 1, 0 ≤ yci (i) ≤ Cc

i , (18)

where we have written both Ui(·) and Vi(·) as functions ofthe downloading decisions of user i. This problem has astrictly concave objective, and a compact and convex non-empty constraint set (under the assumption of at least onenon-zero Internet access capacity). Hence, it has a uniquesolution denoted as Js

i , where s stands for “standalone”. Thiswill serve in the sequel as the performance benchmark for thecomparison purpose benchmark for the comparison purpose.The notation is summarized in Table I.

Problem Statement: We are interested in designing aresource sharing mechanism that determines how muchresources each user should contribute, in terms of Internetaccess, relaying bandwidth, and battery energy, so as to max-imize the service capacity (amount of data delivered withinperiod T ). Accordingly, the mechanism should decide how thiscapacity will be shared by the users, and how they should becompensated for their contribution in terms of money transfers.These tasks should be jointly designed to satisfy the agreedfairness criterion. Formally, the problem is defined as follows:

UPN Collaboration and Servicing Problem: Given thegraph G = (I, E ,B), the capacity constraints, energy con-sumption parameters, pricing parameters, and the users’ util-ity functions, find the Internet access, routing and paymentdecisions of the users, which ensure the fair and efficientperformance of the crowdsourced Internet access service.

IV. THE COOPERATIVE SERVICING GAME

A. Virtual Currency System

In these cooperative systems, an important issue that maydeteriorate their performance is the problem of double coin-cidence of needs [20]. In the context of UPNs, this problemappears as follows. A user served by another user may not

be able to directly return the favor in the current period byoffering similar services. Therefore, users may not want to helpthose that cannot reciprocate. Clearly, this problem reduces thenumber of users who can potentially collaborate with eachother and impacts the UPN performance.

To address the above issue, we introduce a virtual currencysystem where users pay for the services they receive and arepaid when offering such services. This solution makes offeringservice more attractive even for users who do not currentlyhave communication needs. Since we aim at a decentralizedservice design, we assume that transactions are only possibleamong adjacent nodes (i.e., two nodes of the same link) insteadof between the final destination node and the gateway or theintermediate relays. Specifically, let zji(n) ≥ 0 denote thecurrency paid by user i to j, for the data of commodity n thatis delivered over link (j, i) ∈ E .

At the beginning of the current period, each user i has abudget Di ≥ 0, and is rewarded with an additional amountγ > 0 of virtual currency by the system for her participationin the current period. This value of γ is small, compared to thepayments exchanged among the nodes, and it is identical foreach user. However, γ is very important, as we explain in detailbelow, since it ensures that all users are willing to participatein the service even if they don’t eventually exchange Internetaccess and relaying services with the other users.

At the end of the period, user i’s virtual currency budget is:

Hi(zi, zouti ) = βi

(

Di + γ +∑

n∈I

∑

j∈Out(i)

zij(n)

−∑

n∈I

∑

j∈In(i)

zji(n))

,

where we have defined zi =(

zji(n) : j ∈ In(i), n ∈ I)

and zouti =

(

zij(n) : j ∈ Out(i), n ∈ I)

. Parameter βi > 0captures how important the virtual currency is for user i, i.e.,reflects her expectation for exploiting the virtual currency inthe future. Parameter βi can be considered as the discountrate for each user. For example, a user that does not intendto participate in the service later does not value the virtualcurrency much, and her corresponding βi will be close to 0.Alternatively, these parameters can be set by the service soas to normalize the virtual currency benefit with the benefitsof the served data. The linear form of Hi(zi, z

outi ) implies

that users are risk neutral [19]. After introducing the virtualcurrency system, the payoff of each user becomes the sum ofJi(·) and Hi(·).

B. Bargaining Problem

The users are self-interested, and only participate in thecrowdsourced connectivity service if this ensures higher pay-offs for them. In this work, we propose a resource sharingscheme based on the Nash bargaining solution (NBS), whichhas the following desirable properties [19], [41]:

Strong Efficiency: The solution is Pareto optimal. Hence,there is no other feasible solution which yields a better payoffthan the NBS for one user, and no worse payoff for all theother users.



Individual Rationality: The solution offers to each user apayoff that is no worse than the payoff she has when she doesnot participate in the bargaining game (disagreement point).This property is especially important for our problem, as afairness rule based on direct resource allocation only (e.g.,an equal energy or bandwidth sharing scheme) may fail toincentivize all users to join the service.

Scale Covariance: If we apply an affine transformation tothe players’ utility functions, then the initial solution can yieldthe corresponding bargaining solution for the new problemunder the same affine transformation. This property ensuresthat the resource allocation is fair and optimal, independentlyof the way that we measure the players’ utilities.

Symmetry and Independence of Irrelevant Alternatives:These two properties ensure that outcomes which would nothave been selected (i.e., they are not favorable to users), donot affect the bargaining solution. Moreover, the payoff thateach user receives does not depend on her identity/label.

We define an |I|-person bargaining game [18], whereusers can exchange services and pay each other with virtualcurrency. Hence, the produced welfare (service capacity andcurrency) can be divided in an arbitrary fashion among theusers. In line with similar commercial services, e.g., [13], weassume that when a user joins the UPN she may cooperatewith any of the other nearby users, i.e., there is no optionfor selecting with whom to cooperate. Hence, this is a purebargaining problem.

However, the formulation and distributed algorithm designfor solving this NBS problem are highly non-trivial and departsignificantly from previous related approaches, e.g., [41].Namely, the coupling of the decisions of different users intheir payoff functions (i.e., they need to agree on channelsand allocated rates per commodity) and in the constraints set(e.g., when computing the link capacities), as well as theexistence of the virtual currency payments call for a newapproach.

Let us first give the formal NBS definition. Consider thegame G = 〈I,A, {wi}〉, where I � {1, 2, ..., I} is the playerset, and A � A1 ×A2 × ... ×AI is the strategy space whereAi is the set of strategies (actions) available to player i. Thepayoff of each player i, wi(·), depends on the strategy profileof all players, a = (a1, a2, ..., aI), with ai ∈ Ai. The NBSfor this game is [19]:

Definition 1 (Nash Bargaining Solution–NBS): Thestrategy profile a∗ = (a∗1, a∗2, . . . , a∗I) is an NBS, if it solvesthe following problem:

maxa∈A

Πi∈I(

wi(a) − wdi

)

s.t. wi(a) ≥ wdi , ∀ i ∈ I (19)

where wdi is the disagreement point of player i, i.e., her payoff

when an agreement is not reached.Next we consider an equivalent formulation, where the

product of terms in (19) is substituted by the sum of the cor-responding logarithms [41]. Hence, we define the BargainingOptimization Problem (BOP):

maxx,y,z

∑

i∈Ilog

(

Ji(xi,xini ,yi) +Hi(zi, z

outi ) − Js

i − βiDi

)

s.t. (9), (10), (11), (12), (13)

∑

n∈I

(∑

j∈In(i)

zji(n) −∑

j∈Out(i)

zij(n))

≤ Di + γ, i ∈ I

(20)

Ji(xi,xini ,yi) +Hi(zi, z

outi ) ≥ Js

i + βiDi, i ∈ I (21)

0 ≤ xfij(n) ≤ Cf

ij , i, j, n ∈ I, f ∈ F , (22)

0 ≤ yci (n) ≤ Cc

i , i ∈ I, n ∈ I, (23)

0 ≤ yfi (n) ≤ Cf

i , i, n ∈ I, f ∈ F , (24)

0 ≤ zij(n) ≤∑

i∈I(Di + γ), i, j, n ∈ I, (25)

where the disagreement point for each user is the sum ofthe standalone performance Js

i she can achieve, and thenormalized virtual currency βiDi she has at the beginningof the period. Eq. (20) states that users cannot have a virtualcurrency deficit. Eq. (21) is the individual-rationality constraintindicating that each user will agree to cooperate only if thisdoes not make her payoff worse. Eq. (22)-(24) ensure thatall flows will satisfy the capacity constraints of the respectivelinks. Finally, notice that in (25), each payment decision zij(n)is bounded by the total virtual currency at the system. Thisrestrains users from asking or promising payments that exceedthe volume of this virtual economy (hence being infeasible)and as we will explain in the sequel, it will also facilitate theconvergence of the distributed algorithm.

The BOP problem always has a non-empty feasible region.Therefore, due to (21) there is no user of whom the pay-off will decrease by participating in the service. Hence,all users are incentivized to join the service in each timeperiod. Technically, this is ensured due to the virtual cur-rency system and specifically the rewarding parameter γ.We should emphasize, however, that it is not necessary thatall participating users will serve other users at the NBS.The optimal solution depends on the properties of the UPNgraph G and the users’ needs and resources. The solu-tion of BOP is unique. In particular, the following lemmaholds:

Lemma 1: The BOP problem has a unique optimal solution.Proof: The objective function is strictly concave, since it

is a composition of (strictly) concave functions. Additionally,the constraint set is compact, convex and non-empty. Noticethat constraint (21) can always be satisfied by some solutionpoint. For example, each user i can choose not to route anytraffic, i.e., xf

ij(n) = xfji(n) = 0, ∀ i, j, n ∈ I, f ∈ F ,

and only download data for herself. This way, she achievesher standalone performance, but still improves her payoffdue to the participation reward γ. This also ensures that thelogarithmic arguments are non-zero. Therefore, the problemhas always a unique solution (x∗,y∗, z∗) [24].

We can derive the solution of the BOP problem by solvingthe KKT conditions [24]. This will yield the efficient and fairInternet access and routing decisions as well as the preferablechannel for each communication link. Additionally, it willdetermine the currency transfers among the users. Based on thesystem parameters, i.e., connection capacities, battery energy,and data plans, the service can offload data to Wi-Fi networksor onload data to cellular networks.



However, in all cases, the critical question is whetherwe can find this solution in a distributed fashion, so asto enable the distributed execution of the resource shar-ing mechanism. This is an important feature for suchcrowdsourced mobile Internet access services without centralcontrollers.

V. DISTRIBUTED ALGORITHM DESIGN FOR BOP

The difficulties to solve the BOP problem in a distributedfashion are twofold. First, the decision variables of differentusers are coupled in the constraints. That is, the routingdecisions of each user should take into account the capac-ity constraints of her neighboring nodes. Second, there iscoupling in the objective functions. Namely, the logarithmiccomponent of the BOP objective that corresponds to each useri is dependent on the decision variables of her neighbors.We address these issues by introducing new auxiliary localvariables for each user and consistency constraints for eachpair of neighboring users (for the coupled objectives) [23]. Thetransformed problem then has coupling only in the constraints,and can be solved using a primal-dual Lagrange iterativedecomposition method [23].

Let us focus on user i ∈ I. Her payoff depends on herown decisions (xi,yi, zi) and the decisions xin

i , and zouti

of her one-hop neighbors. Clearly, node i can route datato her upstream neighbors In(i) only if they agree on theservicing rate and the respective payments. To deal with thesedecision couplings, we introduce the auxiliary variables andcomponent-wise equality constraints as follows:

ξfji(n) = xf

ji(n), ∀ i ∈ I, j ∈ In(i), n ∈ I, f ∈ F , (26)

σij(n) = zij(n), ∀ i ∈ I, j ∈ Out(i), n ∈ I. (27)

We also define the matrices ξi = (ξfji(n) ≥ 0 : j ∈ In(i), n ∈

I, f ∈ F) and σi = (σij(n) : j ∈ Out(i), n ∈ I) that aremaintained locally by every node i ∈ I. Technically, theselocal variables substitute the decisions xin

i , and zouti of i’s

neighbors, and hence enable her to optimize independentlyher payoff function. This way, each user can independentlydetermine her downloading, routing, and payment variables,subject to coordination with her one-hop neighbors that isachieved when (26) and (27) are satisfied.

Accordingly, we relax constraints (9), (10), (13), (20), (26),and (27), and introduce the respective Lagrange multipliers:

λ = (λi(n) : i ∈ I, n ∈ I, n �= i), μ = (μi ≥ 0, i ∈ I)ψ =

(

ψfij ≥ 0, ∀ (i, j) ∈ E , f ∈ F

)

, ρ = (ρi ≥ 0 : i ∈ I)

τ =(

τfji(n) : i, n ∈ I, j ∈ In(i), f ∈ F

)

,

π =(

πij(n) : i, n ∈ I, j ∈ Out(i))

.

Then, we define the (partial) Lagrangian shown in eq. (34),as shown at the bottom of this page, which is separable in user-specific components Li(·), i ∈ I. In each iteration q of theprimal-dual update, the user maximizes the Lagrange functionin terms of the primal variables and uses the obtained valuesto update the dual variables. More specifically, each user i ∈ Isolves the following problem in every iteration:

maxxi,yi,zi,ξi,σi

Li

(

xi, ξi,yi, zi,σi

)

(29)

Jci (xi, ξi,yi) +Hi(zi,σi) − Js

i − βiDi > 0 (30)∑

n∈Iyc

i (n) ≤ Cci ,

∑

f∈F

∑

n∈I yfi (n)

Cfi

≤ 1, (31)

∑

f∈F

∑

n∈N xfij(n)

Cfij

≤ 1, ∀j ∈ Out(i), (32)

0 ≤ xfij(n) ≤ Cf

ij , n ∈ I, f ∈ F , j ∈ Out(i), (33)

0 ≤ ξfji(n) ≤ Cf

ji, n ∈ I, f ∈ F , j ∈ Out(i), (34)

0 ≤ yfi (n) ≤ Cf

i , n ∈ I, f ∈ F , (35)

0 ≤ yci (n) ≤ Cc

i , n ∈ I, (36)

0 ≤ zji(n) ≤ K, n ∈ I, j ∈ In(i), (37)

where the objective Li(·) is:

Li = log(

Ji(xi, ξi,yi) +Hi(zi,σi) − Jsi − βiDi

)

+∑

n∈I

[

λi(n)(yci (n) +

∑

f∈Fyf

i (n))

−∑

j∈Out(i)

∑

f∈Fxf

ij(n)(λi(n) − λj(n))]

−ρi

∑

n∈I

∑

j∈In(i)

zji(n)

L =∑

i∈I

[

log(

Jci (xi, ξi,yi) +Hi(zi,σi) − Js

i − βiDi

)

+∑

n∈Iλi(n)

(∑

j∈In(i)

∑

f∈Fxf

ji(n) + yci (n) +

∑

f∈Fyf

i (n)

−∑

j∈Out(i)

∑

f∈Fxf

ij(n))

+∑

n∈I

∑

j∈In(i)

∑

f∈Fτfji(n)(ξf

ji(n) − xfji(n)) +

∑

n∈I

∑

j∈Out(i)

πij(n)(σij(n) − zij(n)) − ρi

(∑

n∈I

∑

j∈In(i)

zji(n) −Di − γ

−∑

n∈I

∑

j∈Out(i)

zij(n))

− μi

(∑

k∈In(i)

∑

f∈F

∑

n∈I xfki(n)

Cfki

+∑

j∈Out(i)

∑

f∈F

∑

n∈I xfij(n)

Cfij

+∑

f∈F

∑

n∈I yfi (n)

Cfi

− ki

)

−

∑

j∈Out(i)

∑

f∈Fψf

ij

(∑

(k,m)∈I(i,j)

∑

n xfkm(n)

Cfkm

+

∑

n xfij(n)

Cfij

+∑

k∈N e(i)∪N e(j)

∑

n yfk (n)

Cfk

− 1)]

. (28)



+∑

j∈In(i)

(

ρj

∑

n∈Izji(n) +

∑

n∈I

∑

f∈Fτfji(n)ξf

ji(n))

−∑

n∈I

[∑

j∈Out(i)

(∑

f∈Fxf

ij(n)τfij(n) − πij(n)σij(n)

)

+∑

j∈In(i)

πji(n)zji(n)]

−∑

j∈Out(i)

μj

∑

f∈F

∑

n∈I xfij(n)

Cfij

−μi

[∑

j∈Out(i)

∑

f∈F

∑

n∈I xfij(n)

Cfij

+∑

f∈F

∑

n∈I yfi (n)

Cfi

]

−∑

j∈Out(i)

∑

f∈Fψf

ij

[

∑

n∈I xfij(n)

Cfij

+∑

n yfi (n)

Cfi

]

−∑

k∈N e(i)

∑

f∈Fψf

ki

[

∑

n yfi (n)

Cfi

+∑

m∈Out(i)

∑

n∈I xfim(n)

Cfim

]

.

The solution yields the optimal (in the current iteration q)values x(q)

i ,y(q)i , z

(q)i , ξ

(q)i ,σ

(q)i .

User i then uses the above values of the primal variables tocalculate the gradients and update the dual variables [24]:

λ(q+1)i (n) = λ

(q)i (n) + s(q)

[∑

j∈In(i)

∑

f∈Fx

f (q)ji (n) + y

c (q)i (n)

+∑

f∈Fy

f (q)i (n) −

∑

j∈Out(i)

∑

f∈Fx

f (q)ij (n)

]

(38)

τf (q+1)ji (n) = τ

f (q)ji (n) + s(q) ·

(

ξf (q)ji (n) − x

f (q)ji (n)

)

(39)

π(q+1)ij (n) = π

(q)ij (n) + s(q) ·

(

σ(q)ij (n) − z

(q)ij (n)

)

(40)

ρ(q+1)i =

[

ρ(q)i + s(q)

(∑

n∈I(

∑

j∈In(i)

z(q)ji (n)

−∑

j∈Out(i)

z(q)ij (n)) − γ −Di

)]+(41)

where [·]+ denotes the projection onto the non-negative orthantand s(q) ≥ 0 is a properly selected step during iteration q [24].A similar formula is also applied for updating μi ≥ 0 andψf

ij ≥ 0, based on the set of equations (9) and (10), respec-tively. Finally, each user passes the updated dual variables toher one-hop neighbors, who will use them to optimize theprimal variables in the next iteration.

The Algorithm is executed in a synchronous fashion, whichrequires a common clock of all users and a small delay formessage passing (circulation of the dual and primal variables).This is a reasonable assumption for small-scale crowdsourcedconnectivity networks in a small neighborhood. The completealgorithm is summarized in Algorithm 1 and is provablyconverging to the optimal solution.

Lemma 2: Algorithm 1 globally converges to the optimalsolution (x∗,y∗, z∗) of the BOP problem, under properlychosen step sizes s(q) for each iteration q.

Proof: BOP has a strictly concave objective and a closed,non-empty and convex constraint set. Thus, Algorithm 1converges to optimal solution [24] if (i) the step sequence s(q),q = 1, 2, . . . , is properly selected, and (ii) the gradients usedin (38)-(41), are bounded. Consider user i, and we see that thevariables xf

ij(n), yfi (n), yc

i (n), ξfji(n) are upper bounded by

constraints (33) - (36) and the energy cost function (since it

Algorithm 1 Distributed Solution of BOPoutput: x∗, y∗, z∗

1 q ← 0;2 Set x(0), y(0), z(0), ξ(0), σ(0), λ(0), τ (0), π(0), ρ(0), μ(0),ψ(0), ε;

3 conv_flag ← 0; # initialize the convergence flag4 while conv_flag = 0 do5 q ← q + 1;6 for i = 1 : I do7 Solve (29- 37) for primal vars x(q)

i ,y(q)i , z

(q)i , ξ

(q)i ,σ

(q)i

8 Send xf (q)ij (n),∀n ∈ I \ {i}, f ∈ F , to j ∈ Out(i);

9 Send z(q)ji (n),∀n ∈ I \ {i}, to j ∈ In(i);

10 for j = 1 : I , n = 1 : I do11 Calculate dual vars

λ(q+1)i (n), τ

f (q+1)ji (n), π

(q+1)ij (n),

ρ(q+1)i , ψ

f (q+1)ij , μ

(q+1)i using (38-41);

end12 Send λ(q+1)

i (n), τf (q+1)ji (n), μ

(q+1)i ∀n ∈ I \ {i},

f ∈ F , to j ∈ In(i);13 Send ρ(q+1)

i , π(q+1)ij (n), ψ

f (q+1)ij ∀n ∈ I \ {i}, f ∈ F ,

to j ∈ Out(i);end

14 if |[λ(q+1)i (n)− λ(q)

i (n)]/λ(q)i (n)| < ε and

|[ρ(q+1)i − ρ(q)

i ]/ρ(q)i | < ε and

|[π(q+1)ij (n)− π(q)

ij (n)]/π(q)ij (n)| < ε and

|[τ f (q+1)ji (n)− τ f (q)

ji (n)]/τf (q)ji (n)| < ε and

|[ψf (q+1)ij − ψf (q)

ij ]/ψf (q)ij | < ε |[μ(q+1)

i − μ(q)i ]/μ

(q)i | < ε

∀i, n ∈ I, f ∈ F , j ∈ Out(i) thenconv_flag← 1;

endend

is strictly convex), and zji(n), n ∈ I, j ∈ Out(i) are positiveand upper bounded by K . Hence, if we employ a diminishingstep size, e.g. s(q) = (1 +m)/(t+m) with m ≥ 0, then theconvergence is guaranteed [23], [24].

Notice that each user passes messages for each commodityn ∈ I, only to her one-hop neighbors. Hence, the messagepassing overhead of the algorithm is O(d|I||F|), where d isthe average degree of the graph G. However, we expect thatthe number of users in the group will be small (due to the needto be in proximity), hence even a complexity of O(|F||I|2)(assuming a fully connected graph) is affordable. Finally, notethat this required exchange of messages will induce energycost to the devices, additional to the energy expenditure due tothe data downloading and relaying. The actual energy impactof this coordination depends on the technology used (e.g., howoften the UPN is reconfigured, as we experimentally showedin [28]) and it’s study is beyond the scope of this work.

VI. PERFORMANCE EVALUATION

In this section we employ a representative system setup,and demonstrate how the collaborative connectivity serviceperforms in a variety of different scenarios. The systemparameters follow experimental studies [35], [36], [42], [43].

Simulation Setup: We consider a set of |I| = 6 users ran-domly placed in a geographic area, and study their interactionsfor a time period of T = 100 seconds. The Internet access



capacity of each user depends on whether she uses a cellularLTE-A, 3G, or a Wi-Fi connection. Field experiments havemeasured the actual average speed to be 12.74 Mbps forLTE-A, 4.12 Mbps for Wi-Fi, and 1 Mbps for 3G networks[36], [42]. Moreover, we assume that there are 3 orthogonalchannels for Wi-Fi which, in general, may have differentcapacities due to the surrounding (background) interferencebeyond the UPN transmissions.

The users communicate with each other using Wi-Fi Direct,and each user i has one NIC, i.e., ki = 1. The achievable rateamong two users i and j decreases with their distance dij

(in meters). In order to account for a representative settingwith random channel conditions, we assume that two usersseparated by 1 meter can achieve a maximum communicationspeed of 64Mbps; the speed drops to 0.1 Mbps when thedistance increases to 30 meters. The rate will be smaller ifthere is interference, and zero when the distance is larger than30 meters. Therefore, the average data rate Cf

ij that can betransferred over each link (i, j) ∈ E and channel f satisfies:

Cfij = bfij · 100 log(1 + 0.9/d2

ij). (42)

where bfij ∈ [0.5, 1] is a uniformly random variable modelingthe effect of surrounding interference in channel f ∈ {1, 2, 3}.

The energy consumed by a data transfer is proportional tothe data volume, the transmission power and rate, and thechannel conditions (e.g., due to distance and packet retransmis-sions [43]) [35]. We use here eq. (15), where the parametersare selected according to [36]: the energy consumption for3G links is twice as for LTE links, and 4 times higher thanWi-Fi. Also, uplink transmission consumes 8 times moreenergy in LTE and 3G, and 2 times more in Wi-Fi, thandownlink transmissions. Note that for our comparative studythe above relative values are adequate enough.

Every user i ∈ I has a logarithmic utility function

Ui = αi log(

1 + ri)

, (43)

which satisfies the principle of diminishing marginal returns,and ri is given by eq. (14). Parameter αi ∈ [0, 1] captures thedifferent communication needs of the different users. Also,the virtual currency parameters βi, ∀i ∈ I, are uniformlydistributed in (0, 1]. Finally, regarding the cellular data costs,we employ two approaches to make our study more compre-hensive. First, we assume that the user’s dissatisfaction canbe a simple linear function of consumed data amount, andwe use the representative price reported by ITU (for UK) [5],i.e., 0.002$/Mbit. Second, we also use the psychological pricegiven by eq. (16), where the quotas are selected randomly fromthe interval [0, 5]GBytes, unless otherwise specified. Finally,for both cases, we set pi = 0 for users who have an unlimitedcellular data plan or using Wi-Fi connections.

1) Comparison of Bargained and Independent Solutions:Our first goal is to study the UPN operation from the point-of-view of the user. That is, we wish to demonstrate theimpact of collaboration on the amount of data that eachuser consumes, and on the users’ payoff. We compare the“bargained” payoff JG

i for each user i with the “independent”payoff Js

i . We consider a setting with 6 users, where user 1

Fig. 4. Comparison of independent, and bargained solution. Sys-tem parameters: {Ci}i = {9.7, 0.0, 1.0, 1.0, 4.12, 2.1}Mbps, {pi}i ={0.02, 0.02, 0.008, 0.001, 0.0, 0.0} $/Mbit. User 2 has higher demand thanother users, i.e., αi = 2, i ∈ {1, 3, 4, 5, 6} and α2 = 4. The figure showsthe total amount of downloaded, consumed, and relayed data per second.

Fig. 5. Detailed example of the UPN operation under the Nash bargainingsolution. Users’ parameters are given in caption of Fig. 4. In the graph on theright, blue squares represent amounts of downloaded data by each node, andlight-blue shaded boxes the amounts of consumed data. Dotted lines showconnectivity and red lines represent the amount of relayed data. Actual valuesare shown on the left table.

has an LTE connection, user 2 does not have Internet access,users 3 and 4 have 3G connections, and users 5 and 6 haveWi-Fi connections. The Internet access capacity and pricevalues (linear cost is assumed here) are shown in the captionof Figure 4. Also, user i = 2 has higher utility (α2 = 4)compared to the other users (αi = 2, i �= 2). For simplicity,all other system parameters have been set equal for all users.The results represent the average obtained over 50 experimentsfor different user locations, namely uniformly distributed in the[0, 100m]× [0, 100m] plane.

In Figure 4 we plot the total amount of data each userdownloads, consumes, and relays for both scenarios (partic-ipation in UPN or not). We observe that users download(almost) the same amount of data in both cases, apart fromuser 2 who cannot access the Internet independently. In thebargained scenario, users consume different amounts of datasince some of them relay traffic for others. For example, user 1consumes on average 46% less data in the bargained scenariocompared to her standalone operation (she routes the rest 54%to her neighbors). This cooperation depends heavily on user 1’svaluation for the virtual currency, and thus for receiving UPNservice in the future. It is clear that the extent to which theusers will relay traffic for others depends on the relative valueof the virtual currency to their aggregate opportunity cost (notdownloading for their own needs), Internet usage, and energyconsumption costs. To further help the reader build intuition,



Fig. 6. Impact of user diversity on collaboration benefits. All results areaveraged over 30 runs with uniformly distributed user locations in [0, 100m]×[0, 100m]. Users are identical in all aspects, except the following parameters(a): Diverse Internet access: C01 = C02 = C0H = 12.7 Mbps, C03 =C04 = C05 = C06 = C0L Mbps; (b): Diverse energy consumption perdownloaded byte: ec

1 = ec2 = ec

L, and the remaining four have the samehigher value ec

H ; (c): Diverse data plan parameters: o1 = o2 = oL, and theother four have the same higher value oH .

we present a detailed snapshot of the UPN operation for oneof the 50 experiments in Figure 5.

2) Impact of Users Diversity on UPN Performance: Nextwe investigate how the performance benefits of the UPNservice depend on the users’ diversity, specifically on thedifferences in their (i) Internet access capacity, (ii) energyconsumption parameters, and (iii) data plan parameters. Start-ing with case (i), we assume that two users have the samehigh Internet access capacity (C0H = 12.7 Mbps) and theother four identical low Internet capacity C0L that graduallyincreases from 1 Mbps to 5 Mbps. All other parameters arefixed and equal for all six users. In Fig. 6(a) we plot theaggregate amount of downloaded data for the bargained andindependent solutions. We observe that as users become lessdiverse (value of C0L increases), the gap of total downloadeddata (per time period) for the bargained solution compared tothe standalone solution decreases from 29.36% to almost 0%.We can observe a similar trend regarding the user diversity interms of energy consumption. Namely, we consider the abovesetup and assume that two users have low energy consumptioncost ec

L = 0.15 J/Mbit and the other four identical high energy

consumption parameter ecH = 1.13 J/Mbit which decreases

gradually to 0.24. In this case, the benefit of the servicedecreases from 15% to almost 0%, as is shown in Fig. 6(b).The intuition is that the more diverse the Internet capacities orthe energy consumption parameters of the users are, the largerthe benefits from their cooperation.

Finally, we study the impact of data plan diversity inFigure 6(c). We assume that the cellular access cost is givenby function Qi(y

ag,ci ) (eq. (16)), and that the only difference

of users is in parameter oi (similar results obtained whenthe diversity is in Ai). That is, two of them have lowervalue (oL) than the other four users (oH ), and this ratioincreases along the x-axis, becoming eventually oL/oH = 1(no diversity case). As it is expected, the cooperation benefitdiminishes as the diversity among the psychological prices ofthe users decreases. Interestingly, however, for very diversescenarios (oL/oH < 0.2), the nodes download more dataunder the independent operation than the bargained operation.In this case, the four users with the expensive data plansfind it much more beneficial to buy data (using the virtualcurrency) from the other two users in the bargained scenario.Correspondingly, the two users with the low-cost data plansassess the trade off between consuming data and downloading(and relaying) for their neighbors, and find the latter to bemore beneficial (due to the virtual currency payments). Such adecision reduces the total data downloaded by these two users,due to the additional energy consumption when relaying datafor others. This simple example reveals that the parameters ofthe users can have complicated impacts on the final networkoperation. Our algorithm ensures that the UPN operationis optimal as it maximizes the users’ payoffs according tothe NBS.

3) Offloading and Onloading Capabilities of UPNs: Finally,we consider the UPN operation from the networks’s point ofview, and explore how the traffic is shifted among differentnetworks due to cooperation. Namely, the cooperating usersmay route data that was intended for a cellular networkto a Wi-Fi network (offloading), or the other way around(onloading). The latter option becomes attractive when Wi-Filinks are congested and the cellular access capacity of someusers is high and of low cost. For this specific experiment,we employ the setup shown in Figure 3 where two users, onewith Wi-Fi Internet access (user 1) and the other with a cellularaccess (user 2), form a UPN.

First we study onloading (Figure 3 right). We assume thatthe cellular capacity (10 Mbps) is 5 times larger than theWi-Fi capacity (2 Mbps). The rest of the parameters areidentical for the two users. The mobile data price is equalto p = 0.002 $/Mbit, and the LTE link energy consumption3-times larger than the Wi-Fi link energy consumption. In thissetting we aim to investigate how the onloading is affectedby the energy consumption that the gateway node incurs.In the upper subfigure of Figure 7 we depict the amount ofonloaded data, i.e., the data that user 2 (gateway) downloadsand delivers for user 1 (client), as a function of the relayingenergy consumption (ef,s

21 ). The latter can vary if, for example,the distance among the two nodes changes. We observe thatfor a certain value range of ef,s

21 the amount of onloaded data is



Fig. 7. Upper subfigure (Onloading): LTE-A capacity (10 Mbps) is 5times larger than the Wi-Fi capacity (2 Mbps), mobile data price is p =0.002 $/Mbit, and the LTE link energy consumption 3-times larger than theWi-Fi link energy consumption. Lower subfigure (Offloading): LTE capacity(4 Mbps) is twice the Wi-Fi capacity, and data usage price increases.

maximum and constant. However, as ef,s21 increases the BOP

solution yields smaller amounts of relayed data. This resultverifies again that the BOP solution takes into account all theusers’ characteristics and balances in a fair fashion the costsand benefits of the UPN nodes.

Next we explore the offloading case (Figure 3 left).We assume the cellular capacity is only twice of the Wi-Fione (4 Mbps versus 2 Mbps). Having all the other parametersfixed (and equal for the two nodes), we investigate how theamount of data that user 1 (gateway) offloads for user 2 (client)varies as the Internet access price increases. As we observe inthe lower subfigure in Figure 7, the amount of offloaded datainitially increases with the price per byte paid by the LTEuser 2. This is expected since, as the mobile Internet becomesmore expensive, user 2 prefers to pay the Wi-Fi user withvirtual currency for the offloading, instead of downloadingthe content from her cellular link. More interestingly, aftera certain point (when cellular pricing reaches 0.44), theoffloaded data decreases (compared to its maximum value)and then remains constant despite the further cellular priceincrease. This interesting result is due to the employed fairnesscriterion which determines the performance that each user willreceive in the UPN in analogy to her standalone performance.Therefore, since here the standalone performance Js

2 of user2 is reduced (i.e., due to the increasing prices user 2 woulddownload less data in standalone operation), the respectiveperformance J2 within the UPN (and hence the amountof offloaded data) first decreases and accordingly remainsconstant.

VII. RELATED WORKS

One of the first UPN examples is the Wi-Fi communitynetworks [11]. The key challenges there include securityissues [44] and user participation incentives [45]. Similarmechanisms have been studied for ad hoc networks [46], andwireless mesh networks [58]. These results are not directlyapplicable to mobile UPNs, since they do not account forusers’ different types of resources nor for their data usagecost. Also, most UPN users can access the Internet without

relying on others’ help, while this is typically not the casefor other autonomous networks. The characterization of suchstandalone operations is critical in determining whether a userwill agree to join the service or not. This is the reason weemploy the Nash bargaining solution [18], [41].

UPN services can be centralized (as in FON), or decentral-ized where users negotiate with each other. For the former, [48]studied a pricing rule for inducing service adoption, and [49]analyzed the price competition among FON-like opera-tors and conventional operators. For decentralized services,[31] and [33] performed game-theoretic analysis to predictthe prices users charge to each other. Our scheme differs inthat each user can have many roles and that multiple userscan concurrently collaborate. Furthermore, these prior studiesdid not account for the limited data quotas and the energylimitations of users. On the contrary, we propose a detailedapproach for studying the impact of quota dynamics [40]on users’ collaboration. We follow the same approach toqualitatively study the effects of energy consumption, sinceit is known that the analytical relation of energy consump-tion and mobile transmissions (especially in the unlicensedband) is essentially intractable, e.g., [37]–[39]. Finally, anotherunique aspect of our model is that the interactions amongusers from heterogeneous networks (cellular and Wi-Fi), apartfrom offloading, enable also the onloading of Wi-Fi traffic tocellular networks [22] as illustrated in Figure 3. Such flexiblecooperation framework differs from previous offloading-onlyarchitectures [21].

In the context of mobile cooperative networks, references[50] and [51] proposed energy-prudent architectures thataggregate the cellular bandwidth of multiple hosts to buildmobile hotspots. Similarly, [52] presented a scheduling schemethat allows hosts to dynamically admit client requests so as tomaximize their revenue. When each user can serve both asa client and host, a decision framework should assign theseroles to users, based on their residual battery energy [53].A similar model was proposed in [54]. Many related worksin this area assume that users have strong social ties [55]or they are interested in the same content [56], hence thereis no need for incentive provision schemes. This assumptionwas relaxed in [57] that proposed a rewarding scheme forone-hop UPNs. Moreover, the above works did not considerheterogeneous Internet access links nor multihop data deliverysolutions, as they mainly studied the collaboration among twousers over single-hop connections. Such architectures are nowimplementable due to software defined networking (SDN) aswe demonstrated recently in [28].

The proposed Internet access and routing decisions canbe supported either by distributed scheduling and routingalgorithms that were proposed for ad hoc and mesh networks[25], [26], if we assume that the devices can operate ina perfectly synchronous fashion (e.g., employing a TDMMAC protocol [32]), or they can be implemented by thetypical CSMA/CA protocol which does not require tightsynchronization. However, there might be a gap between thetheoretical performance studied in this paper and the practicalimplementation of such schemes, which we intent to analyzein our future works.



VIII. CONCLUSIONS AND DISCUSSION

User-provided networks take advantage of the technicalcapabilities of handheld user-owned devices; and connectdifferent and possibly heterogeneous networks in a bottom upfashion. This constitutes a paradigm shift with the potentialto increase the effective capacity of wireless networks byunleashing dormant network resources. One of the main chal-lenges in UPNs is to incentivize the participation of users, onthe basis of a fair resource contribution and capacity allocation.In this work, we proposed an optimization framework whichmaximizes the UPN efficiency, and allocates the producedcapacity in a fair fashion. The mechanism is amenable todistributed implementation, and is lightweight in terms ofcommunication overheads. We verified numerically that thesystem ensures a higher performance than the independentoperation of the nodes, and that the UPN benefits increasewhen users have more diverse needs and/or resources.

Interestingly, the proposed framework constitutes a methodfor unifying energy and monetary costs, based on the users’needs and demands, and enables the monetization of thetechnical capabilities of user devices. Unlike other coopera-tive mechanisms that rely on auctions or centralized pricingschemes, this bargaining-based solution is self-enforcing andcan be implemented in a decentralized fashion. Furthermore,the proposed framework involves interactions only betweenone-hop neighbors. Besides, it was made clear in the analysisthat UPNs extend the offloading architectures by enablingonloading traffic from Wi-Fi to cellular networks, hence pro-vide a flexible solution for addressing the increasing interfer-ence and collision problem in the ISM band.

Finally, it worths mentioning that our approach is motivatedby the concept of collaborative consumption, which promotesbusiness models and systems for sharing resources. The termwas introduced in 1978 by Felson and Spaeth [59] and hasbeen recently revisited in a comprehensive fashion [60]. Inter-estingly, several innovative startups [12]–[14], have recentlyintroduced respective services for mobile users. Besides, recentmeasurement studies have reveled the potential gains ofmobile user collaboration in cellular networks [17], whichcan nowadays be implemented due to recent technologicaladvancements in wireless networking [6], [27], [28], [47].

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George Iosifidis received the Diploma degreein electronics and telecommunications engineeringfrom Greek Air Force Academy in 2000, and theM.S. and Ph.D. degrees in electrical engineeringfrom the University of Thessaly, Greece, in 2007and 2012, respectively. He was a Post-DoctoralResearcher with CERTH, Greece, and Yale Uni-versity, USA. He is currently an Ussher AssistantProfessor of Future Networks with Trinity College,University of Dublin, Dublin, Ireland, and also aFunded Investigator with the Telecommunications

Research Centre CONNECT, Ireland. His research interests include in thebroad area of wireless network optimization and network economics.

Lin Gao (S’08–M’10–SM’16) received the M.S.and Ph.D. degrees in electronic engineering fromShanghai Jiao Tong University in 2006 and 2010,respectively. He is currently an Associate Professorwith the College of Electronic and Information Engi-neering, Harbin Institute of Technology, Shenzhen,China. He was a Post-Doctoral Research Fellowwith the Network Communications and EconomicsLaboratory, The Chinese University of Hong Kong,from 2010 to 2015. His research interests are inthe interdisciplinary area combining telecommuni-

cations and microeconomics, with a particular focus on the game-theoreticand economic analysis for various communication and network scenarios,including cognitive radio networks, TV white space networks, cooperativecommunications, 5G communications, mobile crowd sensing, and Internet-of-Things. He is a recipient of the IEEE ComSoc Asia-Pacific OutstandingYoung Researcher Award in 2016.

Jianwei Huang (S’01–M’06–SM’11–F’16) receivedthe Ph.D. degree from Northwestern University in2005. He was a Post-Doctoral Research Associatewith Princeton from 2005 to 2007. He is currentlyan Associate Professor and Director of the Net-work Communications and Economics Laboratorywith the Department of Information Engineering,The Chinese University of Hong Kong. He is aco-recipient of the eight international best paperawards, including the IEEE Marconi Prize PaperAward in wireless communications in 2011. He

has coauthored six books, including the first textbook on Wireless Net-work Pricing. He has served as an Associate Editor of the IEEE/ACMTRANSACTIONS ON NETWORKING, the IEEE TRANSACTIONS ON COG-NITIVE COMMUNICATIONS AND NETWORKING, the IEEE TRANSACTIONS

ON WIRELESS COMMUNICATIONS, and the IEEE JOURNAL ON SELECTED

AREAS IN COMMUNICATIONS - Cognitive Radio Series. He has served asthe Chair of the IEEE ComSoc Cognitive Network Technical Committee andthe IEEE ComSoc Multimedia Communications Technical Committee. He iscurrently a Distinguished Lecturer of the IEEE Communications Society andthe Thomson Reuters Highly Cited Researcher of Computer Science.

Leandros Tassiulas (S’89–M’91–SM’06–F’07)received the Ph.D. degree in electrical engineeringfrom the University of Maryland, CollegePark, MD, USA, in 1991. He has held facultypositions with Polytechnic University, NY, USA,the University of Maryland, College Park, and theUniversity of Thessaly, Greece. He is currently theJohn C. Malone Professor of Electrical Engineeringand member of the Institute for Network Science,Yale University, New Haven, CT, USA. Hisresearch interests are in the field of computer and

communication networks with emphasis on fundamental mathematical modelsand algorithms of complex networks, architectures and protocols of wirelesssystems, sensor networks, novel Internet architectures, and experimentalplatforms for network research. His most notable contributions include themax-weight scheduling algorithm and the back-pressure network controlpolicy, opportunistic scheduling in wireless, the maximum lifetime approachfor wireless network energy management, and the consideration of jointaccess control and antenna transmission management in multiple antennawireless systems. His research has been recognized by several awards,including the IEEE Koji Kobayashi Computer And Communications Award(2016), the Inaugural INFOCOM 2007 Achievement Award for fundamentalcontributions to resource allocation in communication networks, theINFOCOM 1994 Best Paper Award, the National Science Foundation (NSF)Research Initiation Award (1992), the NSF CAREER Award (1995),the Office of Naval Research Young Investigator Award (1997), and theBodossaki Foundation Award (1999).

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IEEE/ACM TRANSACTIONS ON NETWORKING 1 Efﬁcient and Fair