Auction-Based Resource Allocation for Sharing Cloudlets in Mobile Cloud Computing

Transcription

1 1 Auction-Baed Reource Allocation for Sharing Cloudlet in Mobile Cloud Computing A-Long Jin, Wei Song, Senior Member, IEEE, and Weihua Zhuang, Fellow, IEEE Abtract Driven by pervaive mobile device and ubiquitou wirele communication network, mobile cloud computing e- merge a an appealing paradigm to accommodate demand for running power-hungry or computation-intenive application over reource-contrained mobile device. Cloudlet that move available reource cloer to the network edge offer a promiing architecture to upport real-time application, uch a online gaming and peech recognition. To timulate ervice proviioning by cloudlet, it i eential to deign an incentive mechanim that charge mobile device and reward cloudlet. Although auction ha been conidered a a promiing form for incentive, it i challenging to deign an auction mechanim that hold certain deirable propertie for the cloudlet cenario. In thi paper, we propoe an incentive-compatible auction mechanim (ICAM) for the reource trading between mobile device a ervice uer (buyer) and cloudlet a ervice provider (eller). ICAM can effectively allocate cloudlet to atify the ervice demand of mobile device and determine the pricing. Both theoretical analyi and numerical reult how that ICAM guarantee deired propertie with repect to individual rationality, budget balance, truthfulne (incentive compatibility) for both buyer and eller, and computational efficiency. Index Term Mobile cloud computing, cloudlet, truthful double auction, incentive deign. I. INTRODUCTION The pat decade ha witneed an exploive growth of wirele communication network, where a variety of mart mobile device offer a plethora of application. Nonethele, the energy and reource contraint of mobile device till limit the upport of power-hungry or computation-intenive application, even with the rapid progre of hardware technologie. In the mean time, cloud computing i achieving great ucce in empowering end uer with rich experience by leveraging reource virtualization and haring. Extending the ucce of cloud computing to the mobile domain, mobile cloud computing (MCC) create a new appealing paradigm [1,2]. There have been many popular cloud-baed mobile application, e.g., deployed in Apple icloud [3] and Amazon Silk [4]. By offloading power-hungry or computation-intenive tak to cloud, MCC i expected to relax the local contraint of mobile device in torage, energy, and networking [5]. Three typical MCC architecture are reviewed in [6], including the traditional centralized cloud [7], the recently emerged cloudlet [8], and the peer-baed ad hoc mobile cloud [9]. Thi reearch wa upported in part by Natural Science and Engineering Reearch Council (NSERC) of Canada. A-Long Jin and Wei Song are with the Faculty of Computer Science, Univerity of New Brunwick, Fredericton, NB, Canada ( {along.jin, wong}@unb.ca). Weihua Zhuang i with the Department of Electrical and Computer Engineering, Univerity of Waterloo, Waterloo, ON, Canada ( [email protected]). BS AP Centralized cloud ISP backbone Cloudlet Mobile device Fig. 1. Typical MCC architecture: Centralized cloud and cloudlet. The ad hoc mobile cloud i a uer-centric model which pool together a crowd of neighboring mobile device for reource haring. The other two larger-cale cloud architecture are illutrated in Fig.1. The centralized cloud hot hared reource in remote data center and act a an agent between the original content provider and mobile device. To acce reource at the data center, mobile device often need to go through the backbone network. The long latency incurred to acce the centralized cloud can be intolerable for interactive application uch a online gaming and peech recognition. Even with the acceleration of network peed, the network reource will remain inufficient in a fairly long period to accommodate the oaring traffic demand. On the other hand, a cloudlet [8] i a truted, reource-rich, Internet-connected computer or a cluter of computer, which can be utilized by mobile device via a high-peed wirele local area network (WLAN). With uch geographically ditributed cloudlet, the cloe phyical proximity can enable moother interaction with the low one-hop communication latency. Thu, cloudlet offer an economical olution which can take advantage of content ditribution cloe to the network edge. We are particularly intereted in the cloudlet architecture, which can complement the centralized cloud and accommodate communication-intenive or delay-enitive application. If the ervice demand of mobile device can be atified by high-profile cloudlet in their vicinity, the mobile device do not need to requet reource from the centralized cloud, thereby balancing the workload and reducing the acce latency. To achieve the potential benefit of cloudlet, many

2 2 practical iue need to be addreed, uch a the deployment of cloudlet, reliability, buine model, pricing and incentive deign. For geographically ditributed cloudlet, due to their patial location and ditinct capabilitie or hoted reource, mobile device have different preference over the cloudlet. For example, a mobile device may favor a cloudlet that provide a high level of quality of ervice (QoS), and aociate a high valuation with the cloudlet. On the other hand, the cloudlet need to be motivated to hare their reource, e.g., through gaining monetary value paid by the mobile device for uing the ervice. A een, there exit a trade between the mobile device requeting the ervice and the cloudlet providing uch ervice. Auction i a popular trading form that can efficiently ditribute reource of eller to buyer in a market at competitive price. Auction theory [1] i a well-reearched field in economic and ha been applied to other domain, e.g., radio reource management in wirele communication ytem [11]. An auction mechanim i expected to hold certain deirable propertie, uch a individual rationality, budget balance, and ytem efficiency [1]. Beide, incentive compatibility or truthfulne i another important apect of auction deign. Truthfulne i eential to reit market manipulation and enure auction fairne. An auction mechanim i incentivecompatible or truthful if revealing the private valuation truthfully i alway the dominant trategy for each participant to receive an optimal utility, no matter what trategie other participant are taking. In thi work, it i critical to enure truthfulne in the auction mechanim o that the allocation of cloudlet reource i not interfered by untruthful behaviour that aim to boot a participant own benefit. A uch, the cloudlet reource can be allocated to the mobile device in need and atify their ervice demand to the utmot extent. There are many exiting auction mechanim that atify ome of the above propertie but are not directly applicable to the cloudlet cenario. For example, the multi-round auction tudied in [12] [14] are not uitable due to the high communication and computation overhead. We are particularly intereted in double auction, in which buyer and eller ubmit their bid and ak, repectively, to an auctioneer a an intermediate agent who hot and direct the auction proce, e.g., deciding the auction commodity allocation and the clearing price and payment. Well-known example of double auction include McAfee double auction [15] and Vickrey-baed auction [16]. Conidering only homogeneou commoditie, McAfee double auction can achieve three deired propertie, i.e., individual rationality, budget balance, and truthfulne. The Vickreybaed auction propoed in [16] can be budget-balanced and efficient but not truthful imultaneouly, according to [17]. A truthful double auction mechanim (TASC) i propoed in [18] for cooperative communication with heterogeneou trading commoditie, i.e., ervice of relay node. Although TASC addree a cenario imilar to MCC with cloudlet, TASC cannot olve the reource haring problem for cloudlet without loing ome deired propertie. Due to unique feature of cloudlet, TASC cannot guarantee truthfulne for buyer even though it i till individual rational, budget-balanced, and truthful for eller. In thi paper, we focu on deigning an incentive-compatible auction mechanim (ICAM) to timulate cloudlet to erve nearby mobile device, o that the abundant reource of cloudlet are efficiently utilized to reduce the acce latency of mobile device for improved interactivity and balance the workload from the centralized cloud. ICAM enure truthfulne for both buyer and eller. In addition, ICAM i individually rational, budget-balanced, and computationally efficient. The computational efficiency require that the auction outcome (allocation of commoditie, and clearing price and payment) be computed in polynomial time. We provide rigorou analyi proving that the above deirable propertie hold with ICAM. Numerical reult verify that thee propertie are achieved with a reaonable ytem efficiency, which i another crucial property of auction. Here, a higher ytem efficiency implie more mobile device are uccefully aigned to atifactory cloudlet intead of reorting to the centralized cloud. In the remainder of thi paper, we firt review related work in Section II. Section III provide the ytem model, problem formulation, and an example demontrating the deign challenge. Then, we introduce ICAM in Section IV and analyze it propertie in Section V. Numerical reult are preented in Section VI, followed by concluion in Section VII. II. RELATED WORKS In thi ection, we give a brief review on related work in two group, i.e., the incentive mechanim pecifically for mobile cloud computing in the networking literature, and more general auction mechanim in the economic literature. A a promiing paradigm, mobile cloud computing ha attracted coniderable reearch attention and effort. There have been a number of tudie addreing variou apect of MCC, uch a virtual machine migration [19], ervice enhancement with MCC [5], and emerging application with MCC [2,21]. However, the reearch on incentive deign for MCC i limited. In [22], cloud reource are categorized into everal group (e.g., proceing, torage, and communication). Then, the reource allocation problem i formulated a a combinatorial auction with ubtitutable and complementary commoditie. Thi combinatorial auction mechanim i not applicable for the cloudlet architecture ince it key problem i the allocation of M reource of G group in one MCC ervice provider to N uer. In contrat, our ytem model with cloudlet focue on ditinct valuation of cloudlet to mobile uer. Different from [22], we alo conider computational efficiency and budget balance, which are critical to an auction mechanim. Although auction theory ha been widely tudied in the economic literature, the exiting auction mechanim cannot be directly applied to the cloudlet cenario, ince they fail to fully atify the required propertie tated in Section I. One of the mot well-known auction mechanim i the truthful Vickrey- Clarke-Grove (VCG) auction [23] [25]. In [16], Parke et al. propoe a Vickrey-baed double auction, which achieve individual rationality and budget balance. The aignment between buyer and eller i determined to maximize ocial welfare (ytem efficiency), while the player utility equal the incremental contribution to the overall ytem, i.e., the

3 3 difference between the ocial welfare with and without a player participation. However, the well-known reult in [17] reveal that it i impoible to deign a truthful, efficient, and budget-balanced double auction, even putting individual rationality aide. Therefore, the Vickrey-baed double auction in [16] i only fairly efficient and fairly truthful. In [15], McAfee double auction aim at a cenario with homogeneou commoditie, where buyer have no preference over auction item. Each buyer (b i ) ubmit only one bid (D i ) and each eller ( j ) ubmit one ak (A j ). The auctioneer ort the bid in a non-increaing order and the ak in a non-decreaing order to have D il D il+1 and A jl A jl+1, repectively. Let D in+1 denote the mallet poible bid, and A jm+1 the larget poible ak. Then, the auctioneer determine the winning buyer {b i1,...,b ik } and the winning eller { i1,..., ik }, where k i the larget number uch that D ik A jk and D ik+1 < A jk+1. The auctioneer charge each winning buyer a clearing price P b and reward each winning eller a clearing payment P. Here, P b = P = P o and P o = 1 2 (D i k+1 + A jk+1 ), if A jk P o D ik ; otherwie, P b = D ik and P = A jk. Although McAfee double auction can achieve three deirable economic propertie, including individual rationality, budget balance, and truthfulne, the homogeneity of commoditie in McAfee double auction limit it application to the cloudlet cenario of MCC, where the mobile device a ervice buyer have preference over the cloudlet a reource eller. In [18], Yang et al. propoe a truthful double auction mechanim (TASC) for cooperative communication with heterogeneou trading commoditie, i.e., ervice of relay node. In TASC double auction, there are two tage, namely, Aignment and Winner-Determination & Pricing. In the aignment tage, the auctioneer applie an aignment algorithm to determine the winning buyer candidate (ource node), the winning eller candidate (relay node), and the mapping between thee buyer and eller. Depending on the deign objective, the auctioneer can chooe a different aignment algorithm. For example, the optimal relay aignment algorithm [26] can maximize the minimum QoS among all buyer; the maximum weighted matching algorithm [27] can maximize the overall QoS; and the maximum matching algorithm can maximize the number of ucceful trade (final matching). In the winnerdetermination & pricing tage, TASC double auction tightly integrate the winner determination and the pricing operation. Baed on the return of the aignment tage, the auctioneer applie McAfee double auction [15] to determine the winning buyer, the winning eller, and the correponding clearing price and payment. When TASC double auction i ued in the cloudlet cenario, it can atify individual rationality, budget balance, and truthfulne for the eller. However, we illutrate uing an example in Section III-D that a buyer can bid untruthfully to improve it utility. Hence, TASC double auction cannot be applied to the MCC cenario of thi tudy. III. SYSTEM MODEL AND PROBLEM FORMULATION A. Reource Allocation for Cloudlet A depicted in Fig. 1, the cloudlet offer reource pool cloer to the network edge. The cloe proximity of cloudlet can be exploited to reduce the acce overhead of mobile device in energy conumption and communication latency. The cloudlet may value differently to mobile uer depending on variou factor [28], uch a computation capability, communication cot, and wirele link performance (e.g., throughput, latency, and link variation). Such valuation of a mobile uer toward a cloudlet varie with the channel condition and i alo aociated with the ervice requirement. For intance, when a mobile uer offload a computation-intenive tak, it value high a cloudlet with rich computing reource of memory and CPU capacity. In contrat, a mobile uer with a real-time tak prefer a cloudlet with a low communication latency, which require large network bandwidth, high power level, and hort phyical ditance. On the other hand, the cloudlet can be paid for haring reource a compenation for it computation and communication cot. Clearly, the trading between the cloudlet and the mobile device hould meet certain requirement to benefit both partie. The cloudlet need to be incentivized to provide the reource, and the demand of the mobile uer hould be atified. In particular, a cloudlet cannot be paid le than it cot, while the allocated reource of the cloudlet mut fulfill a mobile uer ervice requet. The more mobile uer erved by the cloudlet, the higher the reource utilization for cloudlet. To maximize the reource utilization, the incentive mechanim hould properly aign the matching between the cloudlet reource and the mobile uer demand. B. Auction Model Focuing on the MCC cenario with cloudlet in Fig. 1, we conider a dicrete-time ytem o that in each time period mobile uer ubmit their bid to a central controller, depending on the traffic arrival and ervice demand. The ak of the cloudlet offering ervice in the vicinity are alo collected. Then, we can deign an incentive-compatible mechanim to allocate the reource of m cloudlet among n mobile device. Similar to the ingle-round multi-item double auction model in [18], the mobile device are buyer in thi auction, while cloudlet are eller. A control center cloet to the participant can erve a the auctioneer to reduce the communication cot and delay. Conidering the potential gain of erving mobile uer by nearby cloudlet, the communication overhead in the auction procedure i affordable and worthwhile. Conidering a ealed-bid auction, each buyer (rep. eller) can ubmit it bid (rep. ak) privately to the auctioneer o that everyone ha no information of other bid or ak. For each buyer b i B, B = {b 1,b 2,...,b n }, it bid vector i denoted by D i = (Di 1,D2 i,...,dm i ), where D j i i the bid for eller j S, S = { 1, 2,..., m }. The bid matrix coniting of the bid vector of all buyer i defined a D = (D 1 ;D 2 ;...;D n ). For all eller in S, the ak vector i denoted by A = (A 1,A 2,...,A m ), where A j i the ak of eller j S. A een, the ak of eller do not differentiate among buyer ince the eller only aim at collecting payment for uing their reource. In contrat, the bid of buyer differ with repect to eller, a mobile device have preference over

4 4 cloudlet that vary in available reource and acce overhead in energy conumption or communication latency. Given B,S,D and A, the auctioneer decide the winning buyer et B w B, the winning eller et S w S, the mapping between B w and S w, i.e., σ : {j : j S w } {i : b i B w }, the price Pi b that the winning buyer b i B w i charged, and the payment Pj that the winning eller j S w i rewarded 1. To highlight the utilitie for the particular matching between b i and j, we alo ue Pij b and P ij in certain cae to denote the price and payment, repectively. In addition to the price and payment, the utilitie of the buyer and eller further depend on the valuation of the buyer toward the acquired ervice and the cot for providing uch ervice by the eller. Let V j i be the valuation to buyer b i for having the ervice from eller j, and C j be the cot to eller j for providing the ervice. The valuation vector of buyer b i i denoted by V i = (Vi 1,V i 2,...,V i m ). Given a buyer-eller mapping, i = σ(j), the utility of buyer b i and that of eller j are repectively defined a follow: { Ui b V j = i Pi b, if b i B w, otherwie { P Uj = j C j, if j S w, otherwie. Here, utility Ui b > mean that mobile uer b i a a buyer i aigned to a cloudlet with a valuation greater than the charged price. Thu, Ui b indicate the atifaction level of the mobile uer on the allocated cloudlet. On the other hand, utility Uj of cloudlet j a a eller repreent the urplu of the received payment over it cot. In other word, Uj characterize the profit of a cloudlet for haring it reource. We alo ue Uij b anduij when neceary to emphaize that the utilitie are with repect to the matching between buyer b i and eller j. Some important notation are ummarized in Table I. C. Deirable Propertie and Deign Objective The auction model in Section III-B i repreented by Ψ = (B, S, D, A). Accordingly, the auctioneer hould follow an auction mechanim to determine the et of winning buyer B w, the et of winning eller S w, the mapping σ between B w and S w, the et of clearing price Pw b charged to the winning buyer, and the et of clearing payment Pw rewarded to the winning eller. An effective auction mechanim hould atify four deirable propertie in the following. Individual Rationality: No winning buyer i charged more than it bid and no winning eller i rewarded le than it ak. With repect to the auction model Ψ, thi mean that for every winning matching between b i B w and j S w, we have Pi b D j i and P j A j. Budget Balance: The total price that the auctioneer charge all winning buyer i not le than the total payment that the auctioneer reward all winning eller, 1 To ditinguih the price charged to buyer and the payment rewarded to eller, we ue b and in the normal form a the upercript, repectively. The ame naming routine i alo applied to the utilitie of buyer and eller. Symbol b i b ij j n m B B S B S TABLE I IMPORTANT NOTATIONS. Buyer (mobile device) Definition Buyer b i with poitive valuation toward eller j Seller (cloudlet) Total number of buyer Total number of eller Set of buyer (mobile device) Extended et of buyer with poitive valuation Set of eller (cloudlet) Sorted buyer lit of B in a decending order of poitive valuation Sorted eller lit of S in an acending order of ak B c Set of winning buyer candidate (B c B) S c Set of winning eller candidate (S c S) B a Set of winning buyer before elimination (B a B c) S a Set of winning eller before elimination (S a = S c) B w Set of winning buyer (B w = B a) S w Set of winning eller (S w S a) ˆσ( ) σ( ) D j i D i D A j A A j V j i V i C j P b i P j P b ij P ij U b i U j U b ij U ij Mapping function from the indice of S a to B a Mapping function from the indice of S w to B w Bid of buyer b i on eller j Bid vector of buyer b i Bid matrix of all buyer Ak of eller j Ak vector of all eller Ak vector of all eller except j Valuation of buyer b i on ervice from eller j Valuation vector of buyer b i Cot of eller j for providing ervice Price charged to buyer b i Payment rewarded to eller j Price charged to buyer b i for ervice of eller j Payment rewarded to eller j with aigned buyer b i Utility of buyer b i Utility of eller j Utility of buyer b i with aigned eller j Utility of eller j with aigned buyer b i o that there i no deficit for the auctioneer. That i, b i B w P b i j S w P j. Truthfulne or Incentive Compatibility: We need to firt give the definition of a weakly dominant trategy in the following. Baed on thi definition, we can further expre the property of truthfulne or incentive compatibility. Definition 1. For player i, trategy a i weakly dominate trategya i if the utilitie atify u i(a i,a i ) u i (a i,a i) for all partial action profile a i of the other player except i. For player i, trategy a i i weakly dominant if

5 5 TABLE II AN ILLUSTRATIVE EXAMPLE. (a) Bid matrix of 5 buyer b b b b b (b) Ak vector of 7 eller. Seller Ak b 1 b 4 b 5 b 2 b Fig. 2. Aignment reult with truthful bidding and aking: A bipartite graph of winning buyer candidate and winning eller candidate and their mapping. 9+δ b 3 b 4 b 5 b 2 b 1 it weakly dominate all other trategie of player i. Then, an auction mechanim i truthful or incentivecompatible if playing (bidding or aking) truthfully i a weakly dominant trategy for each player (buyer or eller). In other word, no buyer can improve it utility by ubmitting a bid different from it true valuation, and no eller can improve it utility by ubmitting an ak different from it true cot. Specifically, it implie the following for our auction model: b i B, U b i i maximized when the bidding D i = V i ; and j S, U j i maximized when the aking A j = C j. Computational Efficiency: The auction outcome, which include the winning et of buyer and eller, their mapping, and the clearing price and payment, i tractable with a polynomial time complexity. D. Technical Challenge A dicued in Section II, the exiting auction mechanim cannot atify the preceding deirable propertie when directly applied to the MCC cenario with heterogeneou cloudlet a auction commoditie. The pioneer work in [18] provide a promiing olution. Unfortunately, the following example how that TASC double auction (i.e., the enhanced verion in [18]) cannot guarantee truthfulne of buyer, although there i no problem with individual rationality, budget balance, and truthfulne of eller. To illutrate that buyer can gain higher utilitie by bidding untruthfully, we conider a bid matrix of 5 buyer with true valuation in Table II(a), and the ak vector of 7 eller with true cot in Table II(b). Suppoe that the auctioneer ue the maximum weighted matching algorithm in the aignment tage to maximize the overall QoS. According to the aignment algorithm, the winning buyer candidate, the winning eller candidate and the mapping between them are hown in Fig. 2. Then, following the TASC trategy for winnerdetermination & pricing, we have the et of wining buyer B w = {b 1,b 4 }, the et of winning eller S w = { 6, 2 }, the clearing pricep b w = {8}, and the clearing paymentp w = {6}. The utility of b 3 i ince it i not within the winner et B w. If buyer b 3 bid untruthfully by increaing it bid D 6 3 from it true valuation 9 to 9+δ (δ > 1), the new aignment reult Fig. 3. Different aignment reult with untruthful bidding of buyer b 3, which increae it bid D3 6 from it true valuation 9 to 9+δ (δ > 1). i hown in Fig. 3. The et of winning buyer become B w = {b 3,b 4 }, while the et of winning eller i till S w = { 6, 2 }. The clearing price and payment remain unchanged according to TASC, i.e., Pw b = {8} and P w = {6}. The new utility of b 3 become 9 8 = 1. A een, b 3 can improve it utility from to 1 by bidding untruthfully. Hence, we cannot apply TASC double auction to the cloudlet cenario. In Section IV, we propoe a new double auction mechanim, ICAM, which can guarantee truthfulne of both eller and buyer, while holding the other deirable propertie. IV. PROPOSED AUCTION MECHANISM FOR CLOUDLETS A dicued in Section II, the well-known Vickrey-baed double auction [16] cannot imultaneouly achieve truthfulne in addition to individual rationality and budget balance, while McAfee double auction [15] cannot be directly applied to the cenario with heterogeneou commoditie. TASC double auction overcome the limitation of McAfee double auction and accommodate heterogeneity. When TASC i applied to reource haring with cloudlet, we have een from the example in Section III-D that TASC i ubject to the manipulation of untruthful buyer in the aignment tage. In thi ection, we propoe ICAM to reolve thi problem. Firt of all, we change the equence of the aignment tage and the winner-determination & pricing tage. In ICAM, the auctioneer firt identifie the winning candidate. Then, each winning eller candidate i aigned to one winning buyer candidate. Alo, the clearing price charged to each buyer candidate and the clearing payment rewarded to the eller candidate are determined accordingly. More importantly, ICAM can keep potentially multiple eller for a ingle buyer until a new lat tage. In the end, the new tage of winner elimination can guarantee that a winning buyer i aigned to only one winning eller. Next, we give the detailed algorithm of ICAM, followed by a walk-through example. The propertie of ICAM are analyzed

6 6 Algorithm 1 ICAM(B, S, D, A). Input: B, S, D, A Output: B w,s w,σ,pw,p b w 1: (B c,s c,d qϕ p ϕ,a jφ ) ICAM-WCD(B,S,D,A); 2: (B a,s a,ˆσ,p a,p b a) ICAM-A&P(B c,s c,d qϕ p ϕ,a jφ,d); 3: (B w,s w,σ,pw,p b w) ICAM-WE(B a,s a,ˆσ,p a,p b a,d); 4: return (B w,s w,σ,pw,p b w); Algorithm 2 ICAM-WCD(B, S, D, A). Input: B, S, D, A Output: B c,s c,d qϕ p ϕ,a jφ 1: B c, S c ; 2: Contruct a et B = {b pq : Dp q >,b p B} according to D; 3: Sort all buyer in B to obtain an ordered lit B = b p1 q 1,b p2 q 2,...,b pxqx uch that D q 1 p 1 D q 2 p 2 Dp qx x ; 4: Sort all eller in S to obtain an ordered lit S = j1, j2,..., jm uch that A j1 A j2 A jm ; 5: Find the median ak A jφ of S, where φ = m+1 ; 2 6: Find the mallet ϕ, uch that D q ϕ+1 p ϕ+1 < A jφ ; 7: B c B ϕ, where B ϕ i the ublit with firt ϕ buyer in B; 8: for b pq B c do 9: if A q A jφ then 1: B c B c \{b pq}; 11: ele 12: if q / S c then 13: S c S c { q}; 14: end if 15: end if 16: end for 17: return (B c,s c,d qϕ p ϕ,a jφ ); in Section V. A. Detail of ICAM Following the preceding deign rationale, we propoe ICAM in Alg. 1, which include three tage, namely, winning candidate determination, aignment & pricing, and winner elimination. In the tage of winning candidate determination, Alg. 2 i ued by the auctioneer to hortlit the buyer and eller candidate. Alg. 2 firt contruct a new buyer et B from the original buyer et B. Specifically, buyer b i B become b ij in B if D j i >. That i, a buyer can appear for a number of time with repect to the eller for which the buyer ha poitive valuation. Then, B i ranked to B in an acending order of all poitive bid (valuation), denoted by D = Dp q1 1,...,Dp qx x, where x = B. Seller et S i orted to S in a decending order of A, where the ordered lit of A i denoted by A = A j1,...,a jm. The ak of the median eller in S, denoted by A jφ, where φ = m+1 2, i ued to find the mallet ϕ uch that Dp qϕ+1 ϕ+1 < A jφ. The two elected threhold, Dp qϕ ϕ and A jφ, are ued to elect winning candidate. Buyer b pq i a winning buyer candidate in B c if Dp q Dp qϕ ϕ and A q < A jφ. Seller q i a winning eller candidate in S c if A q < A jφ and at leat one winning buyer candidate bid for q with a poitive bid. It i worth mentioning that φ i not limited to the median. A dicued later in Section VI-A, ytem efficiency varie with φ though other propertie of ICAM tay the ame with different φ. The reaon for etting φ to the median in Alg. 2 i to balance the ize of S c or B c, o a to achieve a reaonable ytem efficiency. Algorithm 3 ICAM-A&P(B c,s c,d qϕ p ϕ,a jφ,d). Input: B c,s c,d qϕ p ϕ,a jφ,d Output: B a,s a,ˆσ,p a,p b a 1: B a, S a S c, Pa b, Pa ; 2: for j S a do 3: Pj = A jφ,pa Pa {Pj}; 4: B j = {b ij : b ij B c}; 5: if B j = 1 then 6: B a B a {b ij},ˆσ(j) = i; 7: Pij b = D qϕ p ϕ,pa b Pa b {Pij}; b 8: ele 9: Sort B j to an ordered lit B j uch that D j i (1) D j i (2) D qϕ p ϕ ; 1: if the firt t (t 2) bid of B j are the ame then 11: Randomly elect a b ij from the firt t buyer of B j ; 12: ele 13: Select the firt buyer b ij of B j with the highet bid; 14: end if 15: B a B a {b ij},ˆσ(j) = i; 16: Pij b = D j i (2),Pa b Pa b {Pij}; b 17: end if 18: end for 19: return (B a,s a,ˆσ,p a,p b a); Algorithm 4 ICAM-WE(B a,s a,ˆσ,p b a,p a,d). Input: B a,s a,ˆσ,p b a,p a,d Output: B w,s w,σ,p b w,p w 1: B w B a, S w S a, σ ˆσ, P b w P b a, P w P a; 2: for any two buyer b σ(α)α,b σ(β)β B w,α β do 3: if σ(α) = σ(β) then 4: U b σ(j)j = D j σ(j) Pb σ(j)j,j = {α,β}; 5: if U b σ(α)α = U b σ(β)β then 6: j randomly elected from {α,β}; 7: ele 8: j argmin j {α,β} {U b σ(j)j }; 9: end if 1: B w B w \{b σ(j )j },Sw Sw \{ j }; 11: P b w P b w \{P b σ(j )j },P w P w \{P j }, σ(j ) = ; 12: end if 13: end for 14: return (B w,s w,σ,p b w,p w); In the aignment & pricing tage, we tightly couple winner determination and pricing to prevent poible untruthful manipulation. A given in Alg. 3, the auctioneer firt determine the winning buyer for each winning eller candidate j. If only one buyer candidate b ij bid for j, then b ij i added into the winning buyer et B a and charged a clearing price Dp qϕ ϕ. If more than one buyer candidate bid for j, the buyer candidate with the highet bid i added into the winning buyer et and charged a price of the econd highet bid. Seller j i paid the median ak, A jφ. When there i a tie among the highet bid of buyer candidate, the auctioneer randomly elect a winning buyer from the candidate. For example, uppoing Dp qϕ ϕ = 3 and Dα j = D j β = 1, the winning buyer for j can be either b αj or b βj, each with a 5% chance. If the next lower bid for j by b γj i Dγ j = 5, the winning buyer i charged 1 intead of 5, becaue the firt two highet bid in the orted lit are both 1, i.e., D j i (1) = D j i (2) = 1. Thi i eential to avoid untruthful action of buyer. In the lat tage, if a buyer in the original buyer et B win two or more eller in S a, the auctioneer, depending on ytem

7 b 16 b 42 b 36 b 54 b 27 b 47 b 53 b 11 b 33 b 15 b 21 b 24 b Fig. 4. Initial bipartite graph howing the ordered lit of the new buyer et and the eller et. requirement, can chooe only one eller for uch a buyer uing Alg. 4. For example, if both b iα and b iβ belong to B a, it mean that b i in the original buyer et B win two eller, α and β. The auctioneer can elect only one eller o that the correponding buyer achieve the highet utility. Likewie, when there i a tie in term of the achievable utilitie, one eller i randomly elected. At the end of the winner elimination tage, every buyer b σ(j)j B w ha a one-to-one mapping with only one winning eller j S w. For the auction model in [18], each eller can be aigned to at mot one buyer, while one buyer need at mot one eller. It i worth noting that our propoed auction mechanim can be eaily modified to retain multiple winning eller for one buyer by kipping the above elimination tage. Then, one buyer (a mobile device) i allowed to acquire reource from multiple eller (cloudlet), e.g., for different reource of proceing, torage, or networking. B. A Walk-Through Example Conidering the bid matrix in Table II(a) and the ak vector in Table II(b), the following how how ICAM work for the auctioneer to derive the auction outcome. Winning candidate determination according to Alg. 2: Contruct the new buyer et from original et B: B = {b 11,b 15,b 16,b 21,b 24,b 27,b 33,b 36,b 42,b 47,b 52,b 53,b 54 }; Sort buyer in B in a decending order to obtain: B = {b 16,b 42,b 36,b 54,b 27,b 47,b 53,b 11,b 33,b 15,b 21,b 24,b 52 }; Sort eller in S in an acending order to obtain: S = { 6, 2, 1, 5, 3, 4, 7 }; Baed on B and S, contruct an initial bipartite graph between B and S a hown in Fig. 4; Decide two threhold: A jφ = A 5 = 4, Dp qϕ ϕ = D2 1 = 4; Determine the et of winning buyer candidate: B c = {b 16,b 42,b 36,b 11,b 21 }; Determine the et of winning eller candidate: S c = { 6, 2, 1 }. According to the output of Alg. 2, a bipartite graph between B c and S c i contructed a hown in Fig. 5. Then, Alg. 3 i run to identify the winning buyer and eller. Aignment & pricing according to Alg. 3: The et of winning buyer: B a = {b 16,b 42,b 11 }; The et of winning eller: S a = { 6, 2, 1 }; b 16 b 42 b 36 b 11 b Fig. 5. Bipartite graph between winning candidate B c and S c. The aignment (mapping) between winning buyer and eller (B a and S a ): ˆσ( ) = {ˆσ(6) = 1,ˆσ(2) = 4,ˆσ(1) = 1}; The clearing price charged to winning buyer: Pa b = {P16 b = D6 3 = 9,Pb 42 = Dqϕ p ϕ = 4,P11 b = D1 2 = 4}; The clearing payment rewarded to winning eller: Pa = {P6 = P2 = P1 = A jφ = 4}. Alg. 3 return the mapping between B a and S a, ˆσ( ) = {ˆσ(6) = ˆσ(1) = 1,ˆσ(2) = 4}, which mean that b 1 B win two eller ( 6 and 1 ). If the auctioneer require to keep only one winning eller for buyer b 1, Alg. 4 i run to remove redundant eller. Winner elimination according to Alg. 4: Compute the utilitie of buyer b 1 with repect to eller 6 and 1, repectively: U16 b = D6 1 Pb 16 = 1 9 = 1, U11 b = D1 1 Pb 11 = 6 4 = 2; Since U16 b < Ub 11, eller 6 i eliminated o that a higher utility i provided to buyer b 1 by eller 1. Then, the et of winning buyer i obtained a: B w = {b 16,b 42,b 11 }\ {b 16 } = {b 42,b 11 } = {b 4,b 1 }; Update the et of winning eller: S w = { 6, 2, 1 } \ { 6 } = { 2, 1 }; Update the clearing price charged to winning buyer: Pw b = {Pb 16,Pb 42,Pb 11 }\{Pb 16 } = {Pb 16 = 9,Pb 42 = 4} = {P1 b = 9,P4 b = 4}; Update the clearing payment rewarded to winning eller: Pw = {P 6,P 2,P 1 }\{P 6 } = {P 2 = 4,P 1 = 4}; Update the final one-to-one mapping between winning buyer and eller (B w and S w ): σ( ) = {σ(2) = 4,σ(1) = 1}. Recall that one motivation for the propoed ICAM i to olve the problem illutrated by the example in Section III-D.

8 8 9+δ b 36 b 16 b 42 b 11 b Fig. 6. Bipartite graph between winning candidate B c and S c, when b 3 deviate it bid D3 6 from it true valuation 9 to 9+δ (δ > 1). Next, we briefly how how ICAM prevent uch an untruthful buyer bidding, and leave the formal proof of truthfulne and other propertie in Section V. Suppoe imilarly that buyer b 3 increae it bid D 6 3 from it truthful valuation 9 to 9 + δ, where δ > 1. The winning candidate obtained from Alg. 2 will change to the bipartite graph in Fig. 6. A a reult, b 3 need to pay a price 1 to win eller 6, and it utility i 9 1 = 1 <. Therefore, biding truthfully hould be the dominant trategy of b 3. V. ANALYSIS OF DESIRABLE PROPERTIES In thi ection, we analyze the propoed auction mechanim ICAM with repect to the four deirable propertie dicued in Section III-C. The following theorem prove that all four propertie hold with ICAM. We leave the proof for truthfulne in the end, which require complex and rigorou reaoning. Theorem 1. ICAM i computationally efficient. Proof. In the winning candidate determination tage, Alg. 2 involve at mot nm buyer in the new buyer et B. Sorting the buyer in B take O(nmlog(nm)) time, while orting the eller in S take O(mlogm) time. In Line 7, there are at mot n m+1 2 buyer in the winning candidate et B c. Hence, the for-loop (Line 8 Line 16) ha a time complexity O(n m+1 2 m+1 2 ) = O(nm2 ). Note that the for-loop can alo be improved to have a time complexity of O(nm) with a pace complexity of O(m). Since we focu on the wort-cae time complexity, Alg. 2 take O(nm (m+logn)) time. In the aignment & pricing tage, Alg. 3 procee at mot n m+1 2 buyer in B c and m+1 2 eller in S c. Line 4 determine ubet B j B c for the buyer with poitive valuation toward eller j S a, which take O(n m+1 2 ) = O(nm) time. Taking advantage of the ordered lit B, we can ort B j without cot to obtain B j. Since there are at mot n buyer in B j, it take O(n) time to determine the winning buyer for j. Hence, the for-loop (Line 2 Line 18) cot O(nm m+1 2 ) = O(nm2 ). Thu, Alg. 3 take O(nm 2 ) time. In the winner elimination tage, we know that et B a before elimination ha a ize B a = S a m+1 2. Thu, the forloop (Line 2 Line 13) take O( Ba ( Ba 1) 2 ) = O(m 2 ) time. Thu, Alg. 4 take O(m 2 ) time. Therefore, the overall time complexity of ICAM in Alg. 1 i O(nm (m+logn)). In other word, ICAM converge to the final aignment and pricing reult in a polynomial time with repect to n and m. Theorem 2. ICAM i individually rational. Proof. For each winning eller j S w S c, the payment rewarded to eller j i P j = A j φ > A j according to ICAM. Thu, the winning eller atify individual rationality. Next, conider the winning buyer etb a produced by Alg. 3. For each winning buyer b ij B a B c, there are two cae. In the firt cae, buyer b ij win j without competition, which mean that b ij i the only buyer in B c that bid for j. In thi ituation, we know that Pij b = Dqϕ p ϕ D j i. In the econd cae, buyer b ij win j with competition, which mean that more than one buyer in B c bid for j, and D j i i the highet. In thi ituation, b ij i charged the econd highet bid in B j. Obviouly, Pij b Dj i. Therefore, individual rationality alo hold for the winning buyer et B a determined by Alg. 3. If a winning buyer,b i B, win multiple eller, e.g., b iα B a and b iβ B a, running Alg. 4 can eliminate redundant eller and keep only one bet eller for each winning buyer. Among all the eller that buyer b i win, Alg. 4 imply keep the eller, j (e.g., α or β ), which give b i the highet utility. It i evident that thi procedure doe not change the charging price Pij b to the winning buyer. Thu, the buyer in B w after the winner elimination till atify individual rationality. In ummary, ICAM i individually rational. Theorem 3. ICAM i budget-balanced. Proof. After the winner elimination tage, every winning buyer b i B w ha only one winning eller j S w. Conidering thi one-to-one mapping between B w and S w, we have B w = S w. For each matching σ(j) = i between winning buyer b i and aigned winning eller j, it i true that P b σ(j) Dqϕ p ϕ A jφ = P j. Then, it can be eaily hown that i Pj = ( P b σ(j) P ) j j S w j S w b i B w P b which complete the proof. Before drawing a concluion on truthfulne of ICAM, we firt derive Lemma 1 and Lemma 2 in the following. Lemma 1. ICAM i truthful for eller. Proof. Lemma 1 can be proved by Propoition 1-3, which are preented and proved in Appendix A (in the upplementary file). Let k = φ = m+1 2, S l 1 = S <k \S c and S l2 = S a \S w. Then, according to Propoition 1-3, telling truth (A j = C j ) i a weakly dominant trategy for each eller j S in ICAM, which complete the proof of Lemma 1. Lemma 2. ICAM i truthful for buyer. Proof. Similar to the proof of Lemma 1, we provide Propoition 4-7 in Appendix B (in the upplementary file), which lay the bai for Lemma 2. Following the notation therein and letting D ϕ = A ϕ = A jφ, B l1 = B ϕ \B c and B l2 = B c \B a, we can draw a logical concluion that telling truth i a weakly

9 9 dominant trategy for each buyerb i B in ICAM. Thi prove Lemma 2. Theorem 4. ICAM i truthful (incentive-compatible). Proof. Lemma 1 and Lemma 2 together prove that ICAM i truthful (incentive-compatible). According to Theorem 1-4, we can draw the final concluion in Theorem 5. Theorem 5. ICAM i computationally efficient, individually rational, budget-balanced and truthful (incentive-compatible). A dicued in Section IV, ICAM alo work when the elimination tage i kipped o that a mobile device (buyer) can acquire ervice from more than one cloudlet (eller). The four deired propertie in Theorem 5 till hold. VI. NUMERICAL RESULTS In thi ection, we preent numerical reult to validate the propertie of ICAM analyzed in Section V. In addition, we evaluate the performance of ICAM in term of ytem efficiency. A een in the proof in Section V and the appendice (in the upplementary file), ICAM guarantee individual rationality, budget balance, truthfulne for both buyer and eller, and computational efficiency. The proof doe not et any preumption on the bid of buyer or the ak of eller. Thu, the concluion are valid for any poible data et of the bid and ak. Becaue there are no exiting tatitic on ervice demand of mobile uer or reource cot of real cloudlet [28], for generality, we randomly generate the bid of buyer and the ak of eller according to uniform ditribution within (,V max ] and within (,1], repectively. Intuitively, V max will affect the auction outcome, and even the parameter φ that i ued to determine the auction threhold and winning candidate. In the following, we firt illutrate the impact of φ and it variation with V max, o that the numerical reult thereafter will be mainly baed on fixed φ and V max. At the end of thi ection, we alo relax the etting of uniformly ditributed bid and ak to invetigate the enitivity of ytem efficiency on uch tatitic. A. Impact of Parameter φ In the winning candidate determination tage of ICAM, buyer and eller candidate are elected baed on the φ-th ak of the acending ordered lit of all eller ak, A jφ. The candidate et, B c ands c, are determined in Alg. 2. Intuitively, a larger value of φ reult in a maller et for B c. On the other hand, S c can be too mall if φ i too mall. The candidate et directly affect the auction outcome. Fig. 7 how the impact of φ on the performance of ICAM with different value of V max, with 1 buyer and 1 eller. Fig. 7(a) how the number of ucceful trade (N ST ) veruφ. The variation therein i due to the oppoite effect of φ on the ize of B c and S c. When φ i too mall or too large, the ize of S c or B c i too mall, repectively. A a reult, the number of ucceful trade (i.e., matching between winning Number of ucceful trade Total valuation of winning buyer V max = 1.2 V max = 1 V max = φ (a) Number of ucceful trade v. φ. V max = 1.2 V max = 1 V max = φ (b) Total valuation of winning buyer v. φ. Fig. 7. Impact of φ on the performance of ICAM. buyer and eller) i mall. In addition, examining the peak point of the curve with different V max, we find out that the optimal value of φ that attain the highet N ST increae with a larger V max. The highet N ST alo increae accordingly. Thi i becaue a largerφ can be elected whenv max increae o a to enlarge B c and S c. Thu, the highet N ST increae with a larger V max. Fig. 7(b) how the impact of φ on the total valuation of winning buyer, with different V max. It i clear that Fig. 7(b) exhibit a imilar trend a Fig. 7(a). The reaon i that the total valuation i proportional to the number of ucceful trade. Given the obervation in Fig. 7, we can ee that φ hould be adapted to V max for the bet performance. In the following experiment, ince V max i fixed to 1, we et φ = m+1 2 baed on the obervation in Fig. 7. The relative difference between the number of buyer (n) and the number of eller (m) may alo affect the election of φ. In fact, the performance of ICAM can be improved when the optimal φ i elected according to different value of n and m. B. Computational Efficiency To confirm our analyi on time complexity in Theorem 1, we obtain the computation time of ICAM with different etting in Table III. For each etting, we randomly generate 1 intance and average the reult. All the tet run on a

10 1 n = 1 m = 1 TABLE III COMPUTATION TIME. m Time (m) n Time (m) Window PC with 3.16 GHz Intel R Core TM 2 Duo proceor and 4 GB memory. A een, ICAM i ubject to a polynomial computation time with repect to n and m, which are the number of buyer and eller, repectively. C. Individual Rationality To validate Theorem 2 regarding individual rationality of ICAM, we preent the bid and price of winning buyer in Fig. 8(a), and the payment and ak of winning eller in Fig. 8(b). Clearly, each winning buyer i charged a price not higher than it bid, while each winning eller receive a payment not le than it ak from the auctioneer. Therefore, ICAM i individually rational. The reult demontrate that the winning mobile uer and cloudlet that are uccefully matched gain poitive utilitie, i.e., benefit from uing or providing the demanded reource. The winning cloudlet receive ufficient compenation a incentive to hare their reource. On the other hand, the winning mobile uer are allocated the demanded reource and pay no more than their valuation toward thee reource. Thu, the mobile uer are alo timulated to requet reource from the cloudlet intead of the centralized cloud. D. Budget Balance Theorem 3 prove that ICAM i budget-balanced, which mean that the total price charged to the winning buyer i not le than the total payment rewarded to the winning eller. Fig. 9 how the total price and the total payment with different etting. Here, we fix the number of buyer to1, and vary the number of eller from 5 to 15 with an increment of 1. A een, the total price from the winning buyer i alway greater than the total payment to the winning eller. Therefore, the auctioneer conduct the auction without a deficit, and i thu inclined to ait in the reource allocation for cloudlet. E. Truthfulne To verify truthfulne of ICAM, we randomly pick two buyer and two eller to examine how their utilitie change when they bid or ak different value. The reult are depicted in Fig. 1. Fig. 1(a) how a cae that buyer b iα win the eller jα and gain utility Ui b α =.2131 when it bid truthfully with D jα i α = V jα i α = It can be een that buyer b iα cannot improve it utility no matter what other bid it take. Fig. 1(b) how a different cenario that buyerb iβ doe not win the eller jβ when it bid truthfully with D j β i β = V j β i β = Thu, b iβ achieve zero utility (Ui b β = ) without having the ervice. Bid & price Payment & ak Bid Price Winning buyer (a) Bid & price of winning buyer. Payment Ak Winning eller (b) Payment & ak of winning eller. Fig. 8. Individual rationality of ICAM. Fig. 1(b) how the utility cannot be greater than zero even when b iβ bid untruthfully. Fig. 1(c) how an example with winning eller jη that ak truthfully with A jη = C jη =.176 and achieve utility U j η = A een, the utility with a truthful ak i the highet among all poible ak. Fig. 1(d) how that eller jξ loe when aking truthfully with A jξ = C jξ =.8564 and thu obtain zero utility (U j ξ = ). For all other ak, the achievable utility i either zero or negative, but cannot be more than zero. In ummary, ICAM guarantee truthfulne for both buyer and eller ince the utility cannot be improved by bidding or aking untruthfully. Thu, ICAM can be freed from the interference of untruthful participant (cloudlet and mobile uer) that try to trategize over other. F. Sytem Efficiency Both the theoretical proof in Section V and the numerical reult how that ICAM i computationally efficient, individually rational, budget-balanced and truthful. Sytem efficiency i another important metric for an auction mechanim. Unfortunately, it ha been hown in [17] that a double auction i impoible to achieve truthfulne, budget balance, and ytem efficiency imultaneouly. Depending on the ytem requirement, we can evaluate ytem efficiency in term of

11 11 Price & payment Price from buyer Payment to eller Number of ucceful trade Optimal trategy ICAM TASC Number of eller Number of eller Fig. 9. Budget balance of ICAM. Fig. 11. Sytem efficiency with uniformly ditributed bid and ak Utility Bid.4 (a) Buyer b iα B w. Utility Bid.1 (b) Buyer b iβ / B w. Normalized ytem efficiency ICAM uniform TASC uniform ICAM exponential TASC exponential Utility Utility Number of eller Ak (c) Seller jη S w Ak (d) Seller jξ / S w. Fig. 1. Truthfulne of buyer and eller with ICAM. the number of ucceful trade or the total valuation of winning buyer. Uually, the total valuation i proportional to the number of ucceful trade, which ha been oberved in Fig. 7. Hence, we focu on the number of ucceful trade (N ST ) in the following to evaluate ytem efficiency. Fig. 11 compare the number of ucceful trade among three different auction mechanim when the bid and ak are uniformly ditributed within (, 1]. In the optimal trategy, the auctioneer maximize N ST with complete information in matching the buyer and eller. A een, N ST increae with the number of eller, which i intuitive ince more eller can better atify the divere demand of buyer. ICAM achieve around 5% of the ytem efficiency of the optimal trategy, where the lo i mainly due to the cot of maintaining truthfulne. Moreover, ICAM outperform TASC in ytem efficiency in addition to completing the truthfulne guarantee of TASC. The higher ytem efficiency of ICAM i attributed to the fact that ICAM involve much more winning buyer candidate in the aignment & pricing tage, and remove very few winning player in the winner elimination tage. Therefore, ICAM can achieve all the deirable propertie while maintaining a reaonable ytem efficiency. To further invetigate the enitivity of the auction mech- Fig. 12. Normalized ytem efficiency with uniformly or exponentially ditributed bid and ak. anim to the random ditribution of bid and ak, Fig. 12 how the ytem efficiency normalized with repect to that of the optimal trategy. Here, we how the normalized ytem efficiency when the bid and ak are uniformly or exponentially ditributed with the ame mean. A een, both ICAM and TASC are inenitive to the tatitic of bid and ak, while ICAM maintain a table improvement over TASC. Alo, it i noticed that the normalized ytem efficiency only fluctuate lightly with the number of eller. Thi i becaue the ytem efficiency of ICAM, TASC, and the optimal trategy all increae with the number of eller. VII. CONCLUSIONS AND FUTURE WORKS In thi paper, we focu on a promiing paradigm of MCC with cloudlet that provide reource to nearby mobile device. Due to patial location of cloudlet and their ditinct capabilitie or hoted reource, the cloudlet offer heterogeneou valuation toward mobile device. The mobile uer can acquire ervice from different cloudlet to maximize their utilitie. To improve reource utilization of cloudlet, we have propoed a double auction mechanim ICAM, which coordinate the reource trading between mobile device a ervice uer (buyer) and cloudlet a ervice provider (eller). ICAM can effectively allocate the cloudlet reource among mobile uer to atify their ervice demand, while maintaining

12 12 the deirable propertie, including computational efficiency, individual rationality, budget balance, and truthfulne for both buyer and eller. We have provided rigorou proof on thee propertie of ICAM and confirmed the analyi with extenive imulation reult. There are till many open iue and thi reearch can be extended in the following apect. A hown in Fig. 12, the ytem efficiency of ICAM and TASC i around5% of that of the optimal trategy. Thu, more effort are needed to further improve the ytem efficiency of the auction mechanim while maintaining other deirable propertie. In addition, more ophiticated feature can be incorporated into the ytem model. For example, we can ditinguih the type of ervice available at each cloudlet. Some cloudlet may only provide torage ervice, while other cloudlet may provide computing and networking ervice. Thu, the mobile uer need to aign it ervice requet to the compatible cloudlet. 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A-Long Jin received hi B.Eng. degree in communication engineering from Nanjing Univerity of Pot and Telecommunication, Nanjing, China, in 212. He received hi M.Sc. degree in computer cience from Univerity of New Brunwick, Fredericton, NB, Canada, in 215. Hi reearch interet include cooperative wirele network, mobile cloud computing, game theory for wirele network, and machine learning. Wei Song (M 9-SM 14) received the Ph.D. degree in electrical and computer engineering from Univerity of Waterloo, Waterloo, ON, Canada, in 27. In 29, he joined the Faculty of Computer Science, Univerity of New Brunwick, Fredericton, NB, Canada, where he i now an Aociate Profeor. Her current reearch interet include mobile cloud computing, cooperative wirele networking, energy-efficient wirele network, and device-todevice communication. She received a UNB Merit Award in 214, a Bet Student Paper Award from IEEE CCNC 213, a Top 1% Award from IEEE MMSP 29, and a Bet Paper Award from IEEE WCNC 27. She i the Communication/Computer Chapter Chair of IEEE New Brunwick Section. She i alo an editor for IEEE Tranaction on Vehicular Technology and Wirele Communication and Mobile Computing (Wiley). Weihua Zhuang (M 93-SM 1-F 8) ha been with the Department of Electrical and Computer Engineering, Univerity of Waterloo, Waterloo, ON, Canada, ince 1993, where he i a Profeor and a Tier I Canada Reearch Chair in Wirele Communication Network. She received the Outtanding Performance Award 4 time ince 25 from the Univerity of Waterloo, and the Premier Reearch Excellence Award in 21 from the Ontario Government. Dr. Zhuang wa the Editor-in-Chief of IEEE Tranaction on Vehicular Technology (27-213), and the Technical Program Sympoia Chair of IEEE GLOBECOM 211. She i alo a Fellow of the Canadian Academy of Engineering (CAE), a Fellow of the Engineering Intitute of Canada (EIC), and an elected member in the Board of Governor of the IEEE Vehicular Technology Society.