maximized cellular trafﬁc ofﬂoading via device-to...

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Maximized Cellular Traffic Offloading viaDevice-to-Device Content Sharing

Jingjie Jiang, Shengkai Zhang, Bo Li, Fellow, IEEE, Baochun Li, Fellow, IEEE

Abstract—In next-generation LTE-advanced cellular networks,Device-to-Device (D2D) communication has emerged as an ef-fective way to offload cellular traffic and improve system per-formance. Conventionally, a device exclusively relies on cellularcommunication to retrieve the content it desires. With D2Dcommunication, however, if the same piece of content is availablein the vicinity of the device, the content can be directly retrievedfrom one of its neighbouring devices. Naturally, the key problembecomes how to maximize content sharing via D2D communi-cation. Existing works on content sharing are mainly concernedwith a multi-hop communication setting, while works on D2Dcommunication have primarily focused on the communicationaspects, including interference avoidance and energy efficiency.In this paper, we study the problem of maximizing cellulartraffic offloading with D2D communication, by selectively cachingpopular content locally, and by exploring maximal matching forsender-receiver pairs. Specifically, we consider an interference-aware communication model and formulate selective cachingas a Knapsack problem, and sender-receiver matching as amaximum weighted matching problem in a bipartite graph. Wepropose decentralized algorithms to solve both problems, and oursimulation results demonstrate that our algorithms are effectivein maximizing cellular traffic offloading.

Index Terms—Device-to-Device Communication, ContentSharing, Collaborative Caching

I. INTRODUCTION

The demand for bandwidth in cellular networks is ex-pected to surge exponentially over the next several years [1].However, traditional ways of improving throughput withinthe context of cellular networks have suffered from twomajor challenges. First, increasing the physical-layer capac-ity of wireless links becomes difficult, since the physical-layer technologies used in 4G/LTE (Long Term Evolution)networks, including MIMO-OFDM ((Multiple Input Multi-ple Output-Orthogonal Frequency Division Multiplexing) withcapacity-achieving codes and interference coordination, haveapproached their theoretical limits. Second, decreasing thecell size by using femto-cell networks is a viable, yet costly,approach for improving throughput, as the cost of providingbackhaul connectivity of these small base stations needs to betaken into account.

Manuscript received May 21, 2013; revised November 15, 2013.This research is supported in part by a grant from Hong Kong Research

Grant Council under the contract 615613 and by a grant from ChinaCacheInt. Corp. under the contract CCNT12EG01.

Jingjie Jiang, Shengkai Zhang and Bo Li are with the Department ofComputer Science and Engineering, Hong Kong University of Science andTechnology. Their email addresses are {jjiangaf, bli}@cse.ust.hk.Shengkai’s email address is [email protected]. Baochun Li iswith the Department of Electrical and Computer Engineering, University ofToronto. His email address is [email protected].

Device-to-Device (D2D) communication has recently at-tracted a substantial amount of attention from both indus-try and academia, mainly due to its unique advantages tooffload cellular traffic, better system throughput, higher en-ergy efficiency and robustness to infrastructure failures. Inthe industry, with its recent announcement of a new open-source cross-platform development platform called AllJoyn,Qualcomm has targeted to address many challenges thatexist in enabling device-to-device communication. With thenew Message Queue Telemetry Transport (MQTT) protocoldesigned specifically for D2D communication, the industry iswell positioned to its real-world deployment.

Even with the recent focus on D2D communication in theindustry, the existing academic literature on D2D commu-nication (e.g., [2], [3], [4], [5]) has still largely focused onhow D2D communication can run efficiently as an underlayto cellular networks. In this paper, we wish to study howD2D communication can be used effectively to offload cellulartraffic from the Internet, as devices request different piecesof content, referred henceforth as messages, over cellularnetworks. Being requested from the Internet, both the sizeand the popularity of these messages, ranging from breakingnews to stock quotes, can vary widely. With the assistance ofD2D communication, if a neighbouring device happens to havethe same message cached locally, it can be retrieved withoutincurring the cost of using cellular bandwidth. As an example,if a piece of breaking news has been requested by one device,it is likely that a nearby device may be interested in the samepiece of news in the near-term future.

With a limited amount of storage on each device, the mainchallenge is how cellular traffic can be maximally offloadedby using D2D communication to satisfy requests for content,and to share messages between neighbouring devices. Thereare two aspects to this challenge. First, since the amount oflocal storage is limited, it is not feasible to cache all messagesthat a device has requested. The decision on whether or not amessage should be cached needs to be made in a decentralizedfashion, such that cached messages are most likely to berequested by neighbouring devices in the future. Second, foreach message being requested, there may be multiple devicesthat are able to send this message; for each device receivingrequests, there may be multiple messages it is able to send. Inorder to maximally offload cellular traffic, one would need todesign a matching algorithm that optimally matches sendersto receivers of messages in a decentralized fashion.

In this paper, we propose to address both of these chal-lenges with decentralized algorithms in an interference-awareD2D communication environment. With respect to caching,

This is the author's version of an article that has been published in this journal. Changes were made to this version by the publisher prior to publication.The final version of record is available at http://dx.doi.org/10.1109/JSAC.2015.2452493

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by exchanging the interest for messages among neighbouringdevices periodically, the popularity of messages are estimatedlocally, based on which caching decisions are made in adecentralized manner. With respect to matching senders toreceivers, we formulate it as a maximum weighted matchingproblem, with D2D link rates as the weights assigned to eachsender-receiver pair. Though the Hungarian algorithm [6] canbe used to solve the matching problem, it is centralized innature and requires global information. Rather, we propose touse an asynchronous and distributed algorithm [7] to solvethis problem, which is at least 0.5 of the optimal matching.As compared to most related work on collaborative caching inmulti-hop wireless networks, the upshot of our work is in itsbest-effort nature with decentralized algorithms. In our work,devices will not proactively cache any content to improvethe cache hit ratio, and message exchanges are completelylocal, with no messages relayed over multiple hops. We believethat such best-effort decentralized algorithms are simpler andmuch easier to be implemented, and are therefore feasible inpractical real-world D2D communications.

The remainder of the paper is organized as follows: InSec. II, we present our system model and a high-level de-scription of our problem. In Sec. III and IV, we present ourdecentralized solutions to the caching and matching prob-lems, respectively. We demonstrate the effectiveness of ouralgorithms through simulations in Sec. V. The extensionsand implementation details of our algorithms are discussed inSec. VI. We discuss our contributions in the context of relatedwork in Sec. VII before the conclusion in Sec. VIII.

II. SYSTEM MODEL AND PROBLEM OVERVIEW

In this section, we present our system model and give ahigh-level overview of the problem that we wish to solvein this paper. In general, we wish to offload cellular trafficby allowing devices to retrieve a piece of content, called amessage in this paper, from a nearby device rather than fromthe Internet. In order to assist nearby devices, a device willneed to cache selected messages locally, taking advantage ofits limited storage capacity. Our objective is to maximize suchcellular traffic offloading using fully decentralized algorithms.

A. System Model

For the sake of simplicity, we only consider the scenario ofa single cell in a cellular network, and ignore the influencefrom devices in adjacent cells. A central base station (BS) isreachable from any device within the cell, and is responsibleto relay requests from each device to the Internet, in order toretrieve messages of interest to the device. Each device makesindependent decisions when it requests for messages.

We assume that there are n devices independently anduniformly distributed within the cell. Let D = {D1, ...Dn}denote the set of devices and M = {M1, ...,Mm} the setof messages potentially desired by devices. Any two deviceswith a distance at most R apart can communicate with eachother. For a device Di, we denote the set of its neighbouringdevices as Ni in Eq. 1, where R is the communication range.The signaling mechanism proposed by Choi et al. in [8] can

be employed to discover the neighbouring devices of anygiven device and acquire its neighbour set. Each device cancommunicate with its neighbouring devices directly, i.e.,

Ni = {Dj ∈ D : ||Di −Dj || < R}. (1)

Effective mechanisms exist to allocate radio resources forboth cellular and D2D communication links [5]. We can thussuppose that no interference exists between cellular and D2Dcommunication. In addition, the Orthogonal Frequency Divi-sion Multiple Access (OFDMA) technique proposed by the802.16 Task Group e (TGe) and other chunk-based approaches[9] [10] can be utilized to schedule D2D links and avoidmutual-interference. Nevertheless, it is still possible that twoconcurrent links at a single device will conflict with each other.Fortunately, Choi et al. in [11] designed a reliable transceiverto enable full-duplex communication. Based on this work, wecan suppose that each device can transmit and receive datasimultaneously, but at most one outgoing link from the deviceand one incoming link to the device can exist. It follows thata device can act as a sender and receiver at the same timewith the limitation that the sending and receiving procedureare both dedicated to another end host respectively.

Furthermore, we stipulate that a device does not behaveproactively, in that it will not prefetch any of the messagesthat have been requested by its neighbours but is not desiredby itself. A device only assists its neighbours in a way that themessages retrieved by itself earlier can be reactively cachedand later shared to others. In other words, the cached messagesare actually a subset of its requested messages. In addition,we impose the restriction that each message is cached andtransmitted in its entirety, and may not be split.

B. Problem DescriptionWith D2D content sharing, each device can act both as a

message sender and receiver. For a receiver, it first inquires itsneighbours whether they have the desired message. If someidle neighbours have the message, the receiver can select oneof them as its sender. Otherwise, the request is resent to theBS After the new message is completely received, the receiverneeds to decide whether to cache this message or not. Asa sender, the device may receive multiple requests from itsneighbouring devices at the same time. But each time it canonly send data to one receiver. Therefore, it has to select oneof the potential receivers to send data to.

It is clear that for each device, there are two types ofdecisions to be made: (1) Which message needs to be cached;and (2) which device it should communicate with. Our prob-lem is to find the effective criteria for making the decisionsin order to meet our objective of maximizing cellular trafficoffloading. With respect to which message should be cached,we should estimate the potential value of each message tothe neighbouring devices, and predict the amount of benefitthe local neighbourhood can obtain if a message is cached.With such a prediction, each device may then cache the mostvaluable messages within its limited storage. With respectto selecting neighbouring partners to communicate with, wefurther illustrate this problem with an example of five devicesin a D2D communication network, as shown in Fig. 1.



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D1

D2D4D3

D5

(a) A D2D Network

D1

D2D4D3

D5

(b) Communication Graph

Fig. 1. (a) An example of D2D communication networks; (b) The commu-nication graph in the D2D network.

In Fig. 1(a), two devices are connected by an edge if they areneighbours. A directed edge from Di pointing to its neighbourDj exists in the communication graph if Dj holds the messagerequested by Di. In Fig. 1(b), D1 holds a message desired byD5. D2 holds the messages requested by D1 and D3. D4

can also satisfy the same demand from D3. We next showthat finding the optimal matching for sender-receiver pairs tomaximize the concurrent communication links is non-trivial,even in such a simple scenario. For now, we assume all thepotential links in the graph are of the same quality and thusD2 arbitrarily chooses D1 or D3 as its receiver. If D2 selectsD1, D3 can turn to D4 for help and the request from D5

can be satisfied by D1. As a result, there are three concurrentD2D links, which is optimal in this graph. However, if D2

happens to select D3, the demand of D1 cannot be fulfilledby any other device and thus only two links are set up in thecommunication graph.

III. INTERFERENCE-AWARE COLLABORATIVE CACHING

In the caching mechanism, each device reactively cachesmessages. Therefore, the cached messages have all been readby the device at an earlier time. To contribute the most tothe neighbourhood, the device would have to cache all themessages it has retrieved. However, the storage capacity ofa device is limited. A device needs to select a subset of itsretrieved messages to be cached in its local storage.

A. Problem Formulation

We formulate the problem to select messages as a 0-1Knapsack problem. Given a set of items, each with a weightand a value, the Knapsack problem tries to determine whetherto include each item into a collection, so that the total weightis no more than the capacity of the knapsack and the totalvalue of the selected items is as large as possible. In thecontext of our caching problem, the value of each messageis the expected traffic that can be offloaded if the messageis transmitted locally using D2D communication links. Theweight of a message is its size and the cache capacity of eachdevice is the weight limit. Since devices only have limitedstorage capacities, it is impossible to cache all the messagesit has received. The devices have to make local decisions toselect some messages to cache. In this case, each device willchoose the more valuable messages and drop other messages.

For a more formal treatment of the caching problem, wedefine a set of 0-1 variables Xik, where Xik equals to onewhen the message Mk is cached by the device Di. The valueof Pik indicates the probability that one of Di’s neighbours

requests for Mk. The value of message Mk is thus Pik|Mk|,where |Mk| is the size of Mk. Denote the cache capacity of Di

as ci. The optimization problem to maximize the aggregatedcaching value in device Di can be defined as:

max∑

Mk∈MXikPik|Mk|

subject to∑

Mk∈MXik|Mk| ≤ ci, ∀1 ≤ i ≤ n

Xik ∈ {0, 1}

(2)

The problem above is NP-hard, even if the value of eachmessage is priori knowledge. In practice, however, the valueof a message cannot be known beforehand due to the lim-ited scope of information and the time-dependent nature ofmessage values. It follows that the optimal solution to thecurrent system is unnecessarily the best to serve the upcomingrequests. To tackle this problem, we need to estimate the valueof each message. It is equivalent to predicting the probabilitythat a message will be requested in the future. As we considerthe behaviours of mobile devices only in a short time period,historically statistical data can provide a good reference on thetrend of the future requests.

To better estimate the probability a message is desired in thelocal neighbourhood, each device Di records the local requestinformation with respect to each message. Denote the numberof times a message Mk is requested by some device in Ni astik. Since every request generated by a neighbouring devicewill reach Di, Di can keep track of all the requests in itsneighbourhood. Based on such statistical information, we candefine the local popularity Pik of a message in Eq. 3, which isthe most important indicator of the local trend. M(Ni) is theset of messages that have been requested in the neighbourhood.

Pik =tik∑k tik

, ∀Mk ∈M(Ni) (3)

Although the trend of local requests is usually consistent,the local interest may change abruptly. For instance, a pieceof breaking news might become remarkably popular and incura burst of local requests. To better respond to such cases, weallow devices to collect the global popularity information ofa message when the message is transmitted from the basestation. For a globally popular message, most of the devicesin the local area might not have cached it. Nevertheless, oncea local device retrieves the message from the base station,the global popularity will be attached to it and this pieceof information can spread very rapidly in the neighbourhoodthrough frequent information exchanges. As a result, mostlocal devices will consider the message to be valuable andwill cache it with high probability. Later requests to the samemessage are likely to be satisfied locally.

To summarize, the estimation of the local popularity of eachmessage works as follows. If message Mk is requested by oneof the neighbours, the device Di increases tik by 1. WhenDi receives a new message from the neighbour Dj , the localrequest count tjk of Mk in Dj’s neighbourhood is attached tothe message. Then Di updates its local request count tik as

tik = αtik + (1− α)tjk, α ∈ [0, 1] (4)



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Records

Records

Cache

Records

D2

D1

D3

M1M2

M1

M1 M2

M2

(a) Interference-unaware

Records

Records

Cache

Records

D2

D1

D3

M1M2

M1

M1

M2

(b) Interference-aware

Fig. 2. The motivation for interference-aware caching: an example.

When Di receives a new message from the base station, theglobal popularity Pk of the new incoming message is attachedand Di updates its local request count tik as:

tik = αtik + (1− α)Pk|Ni| (5)

where |Ni| is the number of Di’s neighbours. After recordingthe number of local request for each message, Di can calculatethe local popularity Pik for each message Mk.

B. Interference-Aware Estimation of Popularity

With wireless communication, each device cannot receivemultiple messages simultaneously. In other words, if a deviceis currently a receiver, it cannot generate any more requestsunless the current receiving process finishes. This is of greatimportance for a device to make caching decisions. In Fig. 2,D1 can only cache one of the messages M1 and M2. Throughhistorical requests, D1 finds out that D2 has retrieved M1

and D3 has retrieved M2. The local popularities of the twomessages are thus both 0.5. In an interference-unaware cachingmechanism, D1 believes that caching either message makes nodifference, and it will therefore randomly choose M1 or M2

when making its caching decision.Nevertheless, a neglected fact is that D2 is already a receiver

and cannot generate any request for a rather long period. Itfollows that only the potential request for M1 is valid andcaching M2 would be much less valuable. In our mechanism,whenever a device makes a cache decision, it will inquire thecurrent states of its neighbors. The device then realizes that nomore requests can be sent from D2 and the potential requestfrom D3 is more valuable. As a result, D1 will cache M1 inthe interference-aware mechanism.

The key to enable the interference-aware estimation is topredict the desired messages of the receiving devices. Suchmessages are defined to be weakly desired in our framework.In contrast, messages that are not desired by receiving devicesare defined to be strongly desired. As the neighboring devicesshare common interest, the popular yet unread messages arelikely to attract a device. Based on this observation, we affirmthat a message is weakly desired if it has not been requestedby a receiving device. To avoid caching a weakly desiredmessage instead of a strongly desired message, a weaklydesired message is marked and will be replaced first if itspopularity is similar to a strongly desired candidate. In thisway, the weakly desired messages become less competitivewhen they contend for caching positions.

Popularity

Popularity Popularity

D3 D2

D1

M1 0.6M2 0.4

M1 0.6M2 0.4

M1 0.6M2 0.4

(a) Independent caching

Popularity

Popularity Popularity

D3 D2

D1

M1 0.6M2 0.4

M1 -0.4M2 0.4

M1 0.1M2 0.1

(b) Collaborative caching

Fig. 3. The motivation for collaborative caching: an example.

C. Enabling Collaborative Caching

Information exchange can help devices to identify popu-lar messages timely and facilitate the devices to cache themost popular messages that are likely to be requested byneighbouring devices. Nevertheless, since the devices in aneighbourhood share similar popularity information, they tendto cache the same set of popular messages. The followingexample exposes the defect of an independent caching policy.

Consider Fig. 3, where three devices with unit cache ca-pacity reside in the local network and the popularities ofthe messages M1 and M2 with unit size are 0.6 and 0.4,respectively. Initially, the caches of the three devices are allempty. In Fig. 3(a), the devices make their own cachingdecisions independently and all cache M1. As a result, thelocal message availability is low: if a device desires M2, noneof the local devices can satisfy this request. The reason forthis phenomenon is the imbalance between the demand fora message and the proportion of storage used to cache thismessage. Two out of three devices caching M1 is sufficientto satisfy future requests, which implies that the third replicaof M1 is of little value. In contrast, the probability to ask forM2 is as high as 40%, whereas the storage used to cache M2

is zero. The gap between demand and supply decreases localmessage availability and caching value.

To tackle this problem, collaborative caching is integratedinto our mechanism. Instead of caching the most popularmessages, we enable devices to collect the information ofits neighbours’ caches and choose the messages with thebiggest gap between its popularity and caching proportion.In Fig. 3(b), when device D1 starts to collect information, thecaches of the other two devices are still empty. It finds out thecache proportions of the two messages are both zero, whichmeans that the difference between the popularity and the cacheproportion is 0.6 for M1 and is 0.4 for M2. D1 chooses tocache M1. At the time D2 collects information, D1 has cachedM1 and the cache of D3 is empty. Then the cache proportionof M1 becomes 1. Suppose that within a short time period,the popularities of the messages remain unchanged. The gapsof M1 and M2 become -0.4 and 0.4. D2 decides to cache M2

accordingly. Later when D3 tries to cache a message, it willdiscover that the cache proportions of the two messages areboth 0.5 and it will cache M1. After this caching cycle, theoverall cache proportions of M1 and M2 are 0.67 and 0.33,which matches the distribution of local popularity much better.



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Each time a device Di makes a caching decision, it willgenerate a broadcast message to all of its neighbours, queryingabout the messages currently cached in their storage. Once thecaching information is collected, the device is able to calculatethe proportion of storage used to cache each message Mk,denoted as CPik. The gap between the local popularity andthe caching proportion, denoted as Gik, can be calculated asPik−CPik. We revise the value of Mk as Gik|Mk|, indicatingthe benefit Di will get if it caches Mk locally.

D. Distributed Caching AlgorithmA device makes separate caching decisions under two

circumstances: 1) When the cache is not full, always cache thereceived message; 2) when the cache is already full, apply thecache replacement algorithm to select a subset of the messagesto cache. For the latter cases, the devices should run the cachereplacement algorithm to remove less valuable messages andto make room for more beneficial messages. Suppose there arec messages currently cached in the device Di. After retrievinga message (denoted as message Mc+1) from the base station orsome neighbouring device, Di updates the caching informationand communication states of all its neighbouring devices. Aftercollecting all the necessary information, the new popularitiesof all the (c + 1) messages can be computed. Di can thendetermine the caching gaps of all the candidates and run thereplacement algorithm to determine the messages to be cached.

Here, we apply the classical greedy algorithm for the Knap-sack problem and sort the messages in decreasing order of theirunit values. Equivalently, the messages are sorted accordingto the local caching gaps. The complexity of this algorithm isdominated by its sorting process, which is O(c log c).

Algorithm 1 Greedy Replacement1: Hk ← Gik . Monitor the cache gaps (value) of messages2: Sorting messages in decreasing order of Hk

3: Wi ← ci, wk = |Mk|, Ci ← Φ4: for k = 1 to c+ 1 do5: if wk < Wi then6: Wi = Wi − wk7: Ci = Ci ∪Mk

With our collaborative and interference-aware cachingmechanism, the devices always cache the messages that willpotentially contribute most to the system.

IV. MATCHING SENDERS TO RECEIVERS

Based on the messages provided in D2D network, a devicecan find its desired message in its neighbouring devices andsatisfy the request locally. However, as we have previouslymentioned, if multiple neighbours can send this message, thedevice has to select one of them as its sender. Similarly, oncea device starts sending data, it cannot set up another outgoingcommunication link. It is thus necessary for the device toscrutinize the incoming requests and to select one of them toconstruct a communication link. This observation inspires usto formulate the problem of selecting communication partnersas a maximum weighted matching problem, with link rates asthe weights assigned to each sender-receiver pair.

D1 D5

D3

D2

D4

(a) Communication graph

D3D1 D2

D2 D1 D4D3

D4

D5

D5

Sender

Receiver

(b) Bipartite system view

Fig. 4. Conversion from Communication Graph to Bipartite Graph

A. Matching for Communication Pairs

Each sender-receiver pair corresponds to a directed edge inthe communication graph. In the context of content sharing,senders and receivers are both local devices. Therefore, thecommunication graph G = (V,E) is non-bipartite. But wecan reconstruct an undirected bipartite graph G′ = (V ′, E′) todepict the same system, where V ′ consists of two disjoint Svand Rv . Sv contains the nodes representing all the senders, andRv represents all the receivers. As each device can be a senderor a receiver at any time, |Sv| = |Rv| = n. Furthermore, theundirected edges in G′ are constructed as follows:

e = [Di, Dj ] ∈ E′, iff (Di, Dj) ∈ E, ∀Di ∈ Rv, Dj ∈ Sv (6)

Fig. 4 illustrates the transition from a communication graph,as shown in Fig. 1(b) previously, to a bipartite graph of aD2D network. Let’s revisit the demand and supply of messagesin the communication graph: D1 holds a message desired byD5. D2 holds the messages requested by D1 and D3. D4

can also satisfy the same demand from D3. In this case, D1,D2 and D4 act as the message senders, whereas D1, D3 andD5 are message receivers. The sender set actually consists ofthree devices, whose incoming degrees in the communicationgraph are nonzero and the other two devices can be viewed asisolated nodes in the bipartite graph. The same rule applies forthe receiver set. To meet the interference restrictions, at mostone of the edges incident to a node in the bipartite graph canbe selected. We observe that the selection procedure yieldsa maximum matching problem. Apart from maximizing thenumber of requests satisfied locally, user experience is anotherimportant factor to select the communication links. Amongall the senders a receiver can retrieve its desired message,the receiver would like to select the sender with the highesttransmission rate on the link between them. In accordance withthis requirement, each edge in the bipartite graph is furtherassociated with a weight, which is the transmission rate ofthe corresponding link. We can then formulate the problem ofselecting communication partners as:

max

n∑i=1

n∑j=1

Lij · rij

subject to∑n

j=1Lij ≤ 1, ∀1 ≤ i ≤ n∑n

i=1Lij ≤ 1, ∀1 ≤ j ≤ n

Lij ∈ {0, 1}, rij ≥ 0

(7)

Here, Lij indicates whether a communication pair (Di, Dj) isactually selected and rij represents the available rate of the



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link between Di and Dj . Note that if a device is receiving amessage, its downlink rate is zero. Similarly, the uplink of asending device is also zero. The optimization problem above isto find the maximum weighted matching in a bipartite graph.We can add dummy edges e = [Di, Dj ] with zero weight ifthere is no edge between Di and Dj in G′. In this way, we canconvert the bipartite graph with n vertices in each partition intoa complete bipartite graph. Correspondingly, the optimizationproblem is to find the optimal matching in this graph.

B. Matching as an Auction

Denote the maximum matching problem as the primal, thenits dual problem defines a non-negative variable ui for eachdevice. We consider the procedure of mutual selections amongsenders and receivers as a multiple-goods auction, where thegoods are D2D links. Each potential buyer Dj has its ownvaluation vij for the potential link sold by Di. Essentially, thevaluation for a link from Di to Dj is the rate of this link,denoted as rij . The payoff of Di is the price it successfullysells its link, namely ui. If the receiver Dj wins the linksold by Di, which means this link is selected in the optimalmatching, its payoff uj is defined as vij − ui. It is clear tosee that the maximization of overall payoffs is the same as themaximization of the weighted matching, as shown in Eq. 8.

n∑i=1

ui +

n∑i=1

n∑j=1

Lij(vij − ui) =

n∑i=1

n∑j=1

Lijvij (8)

Both the sender and receiver intend to maximize their payoffs.Initially, all the prices are set to be zero. Each receiver selectsthe senders that can maximize its payoff as the preferredsenders. The edges between a receiver and its potential sendersare built in the Preferred Graph, denoted as Gp. According tothe Weak Duality Theorem, if a perfect matching can be foundin Gp, then the matching is optimal. Otherwise, a ConstrictedSet of receivers exists in the current Gp. The senders that areneighbours of some receiver in the constricted set would raisetheir prices. The next round of auction then begins with newprices. The iterative procedure above is proved to terminate inpolynomial time [6]. We can then obtain an optimal solutionto the original maximum weighted matching problem.

However, the global information of a bipartite graph isneeded in the Hungarian algorithm, which means that theoptimal solution can only be found in a centralized fashion. Itfollows that the optimal construction of communication linkscan only be manipulated by the base station. Not only thecomputation of maximum matching in the global bipartitegraph will consume a considerable amount of computationresources at the base station, but also the control and as-signment procedures will generate extra traffic between thedevices and the base station, adding additional burden to thecellular network. To make things worse, control packets beingexchanged between the local devices and the base station maybe lost or delayed when the congestion of cellular networks issevere. For these reasons, a distributed algorithm is desirable tosolve the problem locally, without involving the base station.

C. Distributed Matching Algorithm

Matching is a classical problem in graph theory and hasbeen widely studied [6]. We leverage the asynchronous anddistributed algorithm in [7] to find the maximum weightedmatching between senders and receivers. Through informationexchange among neighbouring devices, the algorithm triesto reach a consensus between senders and receivers. Thenegotiation procedure goes as follows in our system.

Each device maintains two lists Lc and Lw. For a sender,devices in Lc are its neighbours in G′ with unsatisfied requests.Similarly, for a receiver, devices in Lc are its neighbours inG′ without involving in any sending procedure. Di selects itscandidate partner as Eq. 9 illustrates, sends a communicationrequest to it, and then waits for its response. Devices in Lw arethe neighbours who have selected Di as the candidate partner,and are waiting for Di to respond.

candidate(Di) = Dj , iff vij ≥ vik, ∀Dk ∈ Lc (9)

If the candidate device also selected Di, namely, the twodevices are the most valuable partner to each other, the nego-tiation succeeds and a link can be constructed. Both devicesthen send connection failure messages to all the other devicesthat are still waiting for their responses. If the candidate deviceprefer some other device, Di will receive a failure message andexclude this device from its list of available neighbours. Di

then has to select the next valuable device as its new candidate,and repeat the procedure above.

Algorithm 2 Distributed Matching Algorithm for Di

1: Lc ← N′

i , Lw ← Φ2: Send 〈Req〉 to c3: while Lc 6= Φ & ∃Dj ∈ Lc, s.t rij > 0 do4: c← candidate(Di)5: Receive 〈Msg〉 from Dj

6: if 〈Msg〉 = 〈Req〉 then7: Lw ← Lw ∪Dj

8: if 〈Msg〉 = 〈Fail〉 then9: Lc ← Lc \Dj

10: if c ∈ Lw then11: for Dk ∈ Lw \ c do12: send 〈Fail〉 to Dk

13: Lc = Φ

N′

i is the neighbor set of Di in G′. Recall that the availableuplink rate of a sending device is zero. Therefore, the sendingdevices will not be further considered as possible senders. Asthere is always a sender-receiver pair with the highest link rate,the two devices will first reach a consensus and establish acommunication link successfully. Then the devices connectedby the second fastest link will go through the same procedure.It is now clear to see that this algorithm actually imitatesthe global greedy algorithm precisely and thus can achievean approximation ratio of 0.5. A proof of this conclusion canbe found in [7]. After the lists of available neighbours of allthe devices become empty, the algorithm terminates and wewill have a solution to the weighted matching problem as theguidance for matching senders to receivers.



7

0 20 40 60 80 100Time slot

30

60

100

Performan

ce gain(%) Cache hit ratio

Offloading ratio

Fig. 5. System performance with an average message size of 10, a standarddeviation of 1, and a storage capacity of 100.

V. SIMULATION RESULTS

In this section, we evaluate the performance of our systembased on the implementation in a time-slotted simulator usingC++. We assume that no mobility of users occurs duringthe simulation period. 1000 devices are uniformly randomlydistributed in one cell. For simplicity, we assume deviceshave equal storage capacities and the rates of D2D linksare identical. Each non-receiving device independently sendsa message request with a probability of 50% in each timeslot. The popularity of messages in the repository followsa Zipf-like distribution as previous studies (e.g. [12], [13])have demonstrated. We do not restrict our system to anyspecific fading model for D2D communication. Instead, weexamine our system under both the UDG (Unit Disk Graph)radio model [14] and the Quasi-UDG radio model [15] todepict the irregular communication area caused by multipathinduced fading and shadow fading. Furthermore, the size of themessages follows a normal distribution. We examine the cachehit ratio and the offloading ratio of our system. The cache hitratio indicates the percentage of requests that result in cachehits in neighbouring devices, and the offloading ratio is theratio between D2D traffic and overall traffic for transmittingall the messages requested within the simulation period.

A. Overall Performance

Fig. 5 gives a first glance of the system performance over100 time slots. Initially, the caches of all devices are emptyand all requests are responded to by the base station. After 10time slots, the caches of most devices are saturated and thecache replacement algorithm comes into effect. It can be seenthat our system can offload cellular traffic significantly: 60%network traffic is transmitted through D2D communication.This figure also reveals that the convergence of the systemperformance is fast. After 20 time slots, the cache hit ratio andthe offloading ratio stabilizes around 60%. Such a high D2Dresponse rate demonstrates that our system can effectivelyshare the burden of the base station through D2D commu-nication. In what follows, the cache capacities of devices arefixed to be 100 if no explicit specification is made.

In Fig. 6(a), we focus on the transient response of thecontent sharing system to a message that has recently becomepopular. The top curve illustrates the varying percentage ofrequests generated for the message, and the bottom curvepresents the changing proportion of devices that has thismessage cached. The result demonstrates that our design is

0 20 40 60 80 100Time slot

1

2

Performan

ce gain(%) Popularity

Cache proportion

(a)

0 50 100 150 200Message Index

1.5

3.0

Performance gain(%)

Cache proportionPopularity

(b)

Fig. 6. (a) The popularity and cache proportion of a popular message. (b)Comparison of the popularity and cache distribution of 200 messages.

very agile to a surge in popularity, and can satisfy mostof the requests for a popular message locally. We furthermake a comparison between the popularity distribution of themessages and their caching proportions in all devices. Wesample 200 messages and collect their caching and requestinformation after the system stabilizes. From Fig. 6(b), wecan see that although some gaps exist between the two distri-butions, their tendencies match very well, which is consistentwith our design objective to mitigate the gap between contentdemand and local supply and thus efficiently use the cachecapabilities of devices to serve local requests.

B. Influence of the Request CommonalityThe commonality of local content requests depends both on

the popularity distribution of messages and the communicationrange of devices. We first evaluate the system performancesunder different popularity distributions in Fig. 7(a). Zipf -likedistributions have relative probability of a hit for the ith

most popular message proportional to i−α. It is clear to seethat cache hit ratios and offloading ratios highly depend onthe popularity distribution. The two metrics vary from from30% to 60% with different values of α. Trace-based analysishas found that α typically ranges from 0.9 to 0.97 [16] incommon university and enterprise networks. In the contextof D2D networks, we believe that α could be larger withthe prevalence of location-based information services. Evenif the commonality in a neighbourhood is limited and theredundancy of network traffic is small, the content sharingsystem can still offload the redundant traffic effectively.

We explore the system performance under different com-munication ranges in Fig. 7(b). Obviously, with a larger com-munication range, a device has more neighbouring devices. Asa result, it is more likely to find the desired messages in theneighbourhood. When the average number of a device is 5.5,there are 15 isolated devices in the network. Such isolateddevices will always send requests to the base station. Thecache hit ratio and offloading ratio are only about 40%. Whenthe average number of neighbors reaches 8.3, we encounter thethreshold of keeping the network connected. In this situation,the offloading ratio reaches 50.9%. When the network becomesdenser, the cache hit ratio and the offloading ratio keep increas-ing significantly. However, the larger communication rangeimplies a higher possibility to introduce mutual-interference.The largest possible communication range depends on the

underlay scheduling scheme and devices’ battery life.



8

(a) (b)

Fig. 7. (a) System performance with different popularity distributions. (b)System performance under various communication ranges, with an averagemessage size of 10, a standard deviation of 1.

(a) (b)

Fig. 8. (a) System performance with varying mean values. The standarddeviation is fixed as 1. (b) System performance with varying standarddeviations. Average message size is fixed as 10.

C. The Size Distribution of Messages

We conduct several groups of experiments under differentstandard deviations and mean values of the size distributionin Fig. 9(a). As the storage capacity is fixed, the mean size ofmessages actually represents the relative storage capacity ofeach device. For a larger mean value, the cache hit ratio andoffloading ratio are lower due to the relatively small storagecapacity of devices. In contrast, the smaller mean value impliesa relatively stronger storage capacity to cache more valuablemessages in the system. Consequently, the cellular offloadingratio is much higher. When the average size is 20, namely,each device caches 5 messages on average, the cache hit ratiois still 49% and the offloading ratio is 24%.

Fig. 9(b) shows the system performance under differentstandard deviations of message sizes. Interestingly, the largerthe standard deviation, the greater the gap between the cachehit ratio and the offloading ratio. As the content availability isrestricted by the storage capacity of devices, it is easier to fitthe small messages into the cache, whereas the larger messagesare more frequently dropped since they are at a higher riskof overflowing the storage. With a large standard deviation,the average size of messages cached in the devices is smallerthan the average size of all the requested messages. Therefore,although the cache hit ratio remains high, the offloading ratiodecreases with larger standard deviations since most of thelocally unsatisfiable messages are usually large and incursubstantial amount of cellular traffic.

D. Comparison of Different Algorithms

We conduct a series of experiments to compare the per-formance gains under different caching algorithms. The first

All CollaborateGreedy RandomScheme

25

50

75

Performan

ce gain (%

) Cache hit ratioSatisfaction rateOffloading ratio

(a)

0.1 0.3 0.5 UDGNeighbour model

25

50

75

Performan

ce gain (%

) Cache hit ratioOffloading ratio

(b)

Fig. 9. (a) System performance with varying mean values. The standarddeviation is fixed as 1. (b) System performance with varying standarddeviations. Average message size is fixed as 10.

group of data in Fig. 9(b) is collected using our interference-aware collaborative caching strategy. The second group onlyuses collaborative caching strategy without considering in-terference. The third group applies naive popularity-basedapproach, which greedily caches the locally popular messages.Devices in the last group randomly kick out a message. FromFig. 9(b) we can see that our caching approach improvesthe system performance significantly. The cache hit ratio andoffloading ratio increase by 19.3% and 17.1% respectivelycompared to the baseline method, and increase by 7.3% and5.7% in comparison with the popularity-based method. Takingpossible interference into consideration, however, do not haveobvious influence on the system. We can eliminate this partfrom the caching algorithm to save computation overhead.

To examine the approximation ratio of the matching al-gorithm, we further define satisfaction rate to indicate thepercentage of requests that are satisfied through D2D com-munication. It is obvious that the cardinality of the optimalmatching is less than or equal to the number of cache hits. Itfollows that the cache hit ratio acts as an upper bound of thesatisfaction rate essentially. From Fig. 9(b) we can see that thesatisfaction rates are all greater than 90% of the correspondingcache hit ratios in all the four groups of data. We can concludethat the approximation ratio of the matching algorithm is muchlarger than the theoretical bound (i.e. 0.5).

E. Impact of Radio Models

To highlight the robustness of our method, we evaluate thesystem with a more realistic radio model, Quasi-UDG, whichhas a tunable parameter 0 < α < 1 to control the level ofirregularity of the radio range. In the Quasi-UDG model, alink between Di and Dj exists with probability Prij as

Prij =

1, |Di, Dj | ≤ (1− α)Rη, (1− α)R < |Di, Dj | ≤ (1 + α)R0, |Di, Dj | > (1 + α)R

(10)

where 0 < η < 1 and |Di, Dj | denotes the Euclidean distancebetween Di and Dj . The larger the α, the more uncertainthat a link between two nearby nodes is likely to exist, whichmimics the irregular radio patterns found in reality.

We can see that our system is insensitive to the changeof the radio models and can achieve satisfying performanceunder different circumstances, which makes our system strongenough to be extended to real-world applications.



9

VI. DISCUSSIONS

Although our solution is discussed under the single-cellassumption, it can be extended to a multi-cell environmentwithout major modifications. We only need to focus on thedevices that reside near the boundary of a cell. When suchdevices try to discover their neighbours, it is possible thatsome of the neighbors currently subscribe to a different basestation in an adjacent cell. As the D2D communication utilizesseparate radio resources from the cellular communication, aD2D link between two devices subscribed to different basestations will not influence the cellular communication. TheD2D link between them, however, should be allocated to oneof the cells so that the corresponding wireless scheduler in theassigned cell will treat this link as the other links in the cellequally. Obviously, this situation will not influence our cachingmechanism and matching algorithm, and thus no change isneeded for the multi-cell extension.

To implement the D2D content sharing system, devices needto implement the caching and the matching algorithm locally.The caching mechanism can collect and record popularity andcaching proportion information of messages in the neighbour-hood, and help devices to make cache decisions accordingly.The matching algorithm guides devices to find their partnersand set up D2D links. Devices without the caching andmatching mechanism cannot utilize D2D communication, andonly communicate with the base station directly.

VII. RELATED WORK

Caching is a traditional approach to improve content acces-sibility in wireless networks. Yin and Cao in [17] designeda scheme to enable distributed caching. Based on the sizeof the passing-by message, an intermediate node caches thesmall passing-by messages and caches the path to the nearestnode that stores the large messages. As their concern is howto route the request to the nearest node, their perspective iscompletely different from ours, in that we focus on whichsubset of messages should be cached in each device, ratherthan where to find these messages. Tang et al. in [18] presentedan approximation algorithm to solve the cache placementproblem and maximize the reduction of message access costs.However, they assumed implicitly that the access frequencyof each node to a message is priori knowledge, but did notprovide any mechanism to estimate such access frequency.In contrast, we effectively estimate the access frequencythrough exchanging the local interest for messages, and usethe estimated probabilities to guide caching decisions.

Golrezaei et al. in [19] proposed an architecture for cachingpopular video content without any deployment of additionalinfrastructure. By identifying the conflict between collabo-ration distance and interference, they derived a scaling lawanalysis of the optimal distance, and gave a closed-formexpression as a function of the modelling parameters. Thiswork is largely theoretical without providing any mechanismto enable content sharing. Golrezaei et al. in [20] proposeda centralized caching mechanism in cellular networks. Byintroducing helpers with low-rate backhaul and high storagecapacity, requests from devices can be satisfied by the nearby

helpers. Due to the need for extra auxiliary facilities, thissolution may be very costly. Through message sharing amongneighbouring devices, we utilize the limited storage capacityof each device, and maximize D2D traffic without additionalinfrastructure. Besides, the centralized caching mechanism in[20] suffers from the performance bottleneck of a centralcontroller and is thus not scalable, whereas our cachingmechanism is completely distributed.

Interference can occur not only between two communi-cation links with different sender-receiver pairs [21] [22][23], but also among concurrent links at each sender orreceiver. Existing work circumvents the difficulty of avoidinginterference among concurrent links by introducing dedicatedcache servers. It is nontrivial, however, to avoid interferencein pure D2D networks. We propose a distributed algorithm tomatch message senders and receivers to tackle this problem.Our strategy to match the senders and receivers is to select theset of links to be constructed and scheduled. In other words, wedeal with the self-interference problem rather than the mutual-interference problem, and as a result our work is orthogonalto existing works on wireless link scheduling.

VIII. CONCLUSION

In this paper, we designed and evaluated a distributedcaching mechanism to effectively enable content sharingamong mobile devices and maximize the offloading traf-fic from the cellular networks. Specifically, we consider aninterference-aware environment and incorporate the collabo-ration among devices into the caching mechanism to improvelocal content availability. Furthermore, the strategy for match-ing senders to receivers subject to self-interference constraintsis formulated as a classical maximum weighted matchingproblem, to which the optimal solution can be derived whennetwork-wide information is known, and also an effectivedistributed algorithm with bounded approximation ratio can beapplied. Our simulation results have shown that the proposedmechanism can offload traffic from the cellular networkssignificantly with quick convergence to a stable state. Inaddition, the system is very agile to a burst of popular content.

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[5] P. Janis, V. Koivunen, C. Ribeiro, J. Korhonen, K. Doppler, andK. Hugl, “Interference-aware resource allocation for device-to-deviceradio underlaying cellular networks,” in Proc. IEEE Vehicular Technol-ogy Conference (VTC), 2009.

[6] H. W. Kuhn, “The Hungarian method for the assignment problem,”Naval Research Logistics Quarterly, vol. 2, no. 1-2, pp. 83–97, 1955.

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[16] A. Anand, C. Muthukrishnan, A. Akella, and R. Ramjee, “Redundancyin network traffic: findings and implications,” in Proc. ACM SIGMET-RICS, 2009.

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Jingjie Jiang received the B.Engr. degree fromthe Department of Automation, Tsinghua University,China, in 2012. Since 2012, she has been with theDepartment of Computer Science and Engineering atthe Hong Kong University of Science and Technol-ogy, where she is currently a PhD candidate. Sheis now visiting the Department of Electrical andComputer Engineering at the University of Toronto.She is a member of IEEE. Her current researchinterests include: Device-to-Device communication,computing offloading, content distribution, datacen-

ter networking and scheduling.

Shengkai Zhang received his B.Engr. degree inCollege of Physical Science and Technology, CentralChina Normal University, 2009. He received theM.S. degree from Huazhong University of Scienceand Technology in 2012, and the MPhil. degreefrom the Department of Computer Science andEngineering at Hong Kong University of Scienceand Technology in 2014. He is currently a re-search assistant in the Department of Electronic andComputer Engineering of Hong Kong Universityof Science and Technology. His research concerns

wireless networking, Wi-Fi localization and multi-sensor fusion for mobilerobot applications.

Bo Li is a professor in the Department of ComputerScience and Engineering, Hong Kong University ofScience and Technology. He is a Fellow of IEEE.He was the Chief Technical Advisor for ChinaCacheCorp.(NASDAQ CCIH), the largest CDN operator inChina. He was a Cheung Kong Visiting Chair Pro-fessor in Shanghai Jiao Tong University (2010-2013)and an adjunct researcher in Microsoft ResearchAsia (1999-2007) and in Microsoft Advance Tech-nology Center (2007-2009). His current researchinterests include: multimedia communications, the

Internet content distribution, datacenter networking, cloud computing, andwireless sensor networks.

He made pioneering contributions in the Internet video broadcast with thesystem, Coolstreaming, which was credited as the world first large-scale Peer-to-Peer live video streaming system. The work appeared in IEEE INFOCOM(2005) received the IEEE INFOCOM 2015 Test-of-Time Award. He has beenan editor or a guest editor for over a dozen of IEEE journals and magazines.He was the Co-TPC Chair for IEEE INFOCOM 2004.

He received five Best Paper Awards from IEEE. He received the YoungInvestigator Award from Natural Science Foundation of China (NFSC) in2005, the State Natural Science Award (2nd Class) from China in 2011.He received his B. Eng. (summa cum laude) in the Computer Science fromTsinghua University, Beijing, and his PhD in the Electrical and ComputerEngineering from University of Massachusetts at Amherst.

Baochun Li received the B.Engr. degree from theDepartment of Computer Science and Technology,Tsinghua University, China, in 1995 and the M.S.and Ph.D. degrees from the Department of Com-puter Science, University of Illinois at Urbana-Champaign, Urbana, in 1997 and 2000.

Since 2000, he has been with the Department ofElectrical and Computer Engineering at the Univer-sity of Toronto, where he is currently a Professor. Heholds the Nortel Networks Junior Chair in NetworkArchitecture and Services from October 2003 to

June 2005, and the Bell Canada Endowed Chair in Computer Engineeringsince August 2005. His research interests include large-scale distributedsystems, cloud computing, peer-to-peer networks, applications of networkcoding, and wireless networks.

Dr. Li has co-authored more than 290 research papers, with a total of over13000 citations, an H-index of 59 and an i10-index of 189, according toGoogle Scholar Citations. He was the recipient of the IEEE CommunicationsSociety Leonard G. Abraham Award in the Field of Communications Systemsin 2000. In 2009, he was a recipient of the Multimedia Communications BestPaper Award from the IEEE Communications Society, and a recipient of theUniversity of Toronto McLean Award. He is a member of ACM and a Fellowof IEEE.



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