Double Auction-Based Two-Level Resource Allocation

Research ArticleDouble Auction-Based Two-Level Resource AllocationMechanism for Computation Offloading in MobileBlockchain Application

Li Li Yue Li and Ruotong Li

State Key Laboratory of Networking and Switching Technology Beijing Laboratory of Advanced Information NetworksBeijing University of Posts and Telecommunications Beijing 100876 China

Correspondence should be addressed to Li Li lili66bupteducn

Received 10 August 2020 Revised 10 December 2020 Accepted 3 January 2021 Published 19 January 2021

Academic Editor Alessandro Bazzi

Copyright copy 2021 Li Li et al is is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

It is increasingly popular that platforms integrate various services into mobile applications due to the high usage and convenienceof mobile devices many of which demand high computational capacities and energy such as cryptocurrency services based onblockchain However it is hard for mobile devices to run these services due to the limited storage and computational capacity Inthis paper the problem of computation offloading that requires sufficient computing resources with high utilization in large-scaleusers and multiprovider MEC system was investigated A mechanism based on the combinatorial double auction G-TRAP isproposed in this paper to solve the above problem In the mechanism resources are provided both in the cloud and at the edge ofthe network Mobile users compete for these resources to offload computing tasks by the rule that the edge-level resources will beallocated at first while cloud-level resources could be the supplement for the edge level Given that the proof-of-work (PoW) thecore issue of blockchain application is resource-expensive to implement in mobile devices we provide resource allocation serviceto users of blockchain application as experimental subjects Simulation results show that the proposed mechanism for servinglarge-scale users in a short execution time outperforms two existing algorithms in terms of social utility and resource utilizationConsequently our proposed system can effectively solve the intensive computation offloading problem of mobileblockchain applications

1 Introduction

With the thriving of mobile communication technology andthe popularity of mobile devices the platform services havebeen expanded on mobile terminals However many ser-vices are restricted on mobile devices owing to complexcomputing or too high latency requirements eg autono-mous driving services and mobile blockchain services [1]Recently blockchain has been continuously combined withmany applications in various fields [2] such as e-commercethe Internet of things [3] and supply chain ence variousresearch institutions attach great importance to this tech-nology and publish academic achievements related toblockchain

Technically the essence of blockchain is a distributedledger based on asymmetric encryption algorithms and it

consists of a combination of blocks linked by hash functionsTo confirm and secure the consistency and validity oftransactions in the blockchain network the participantsneed to complete a computation-intensive task [4] ie theproof-of-work (PoW) puzzle [5] which is characterized bythe need of consuming significant central processing unit(CPU) resources According to [6] the core of the PoWprocess is that the consensus node computes the PoW so-lution to the cryptographic puzzle which is formed based onthe root hash value of the Markle tree calculated by a newlygenerated transactioneMarkle tree will be deeper and thecalculation will becomemore complicated when the numberof transactions generated by blockchain increases which setsan extremely high demand for computing capability of themobile devices Although the CPU of mobile devices hasdeveloped powerfully it still can hardly meet the demand of

HindawiMobile Information SystemsVolume 2021 Article ID 8821583 15 pageshttpsdoiorg10115520218821583

many computing tasks of applications in a short time usblockchain applications cannot be widely used in mobiledevices which limits mobile blockchain applicationsrsquodevelopment

Mobile edge computing (MEC) [7] provides an exem-plary method for solving such problems To support theoffloading of computation-intensive tasks mobile edgecomputing can provide mobile users with computing andstorage resources to solve limitations related to the hardware[8 9] In particular it overcomes the drawbacks of mobilecloud computing which could cause long latency andbackhaul bandwidth congestion [10ndash12] Because thecomputing capacity and appropriate incentive policies are ofgreat importance to users of mobile blockchain applicationsit is vital to decide how to offload the computing tasks of thePoW puzzle to the mobile edge computing in the mobileblockchain system

Given that the resource allocation mechanism involvesan incentive policy to allow participants to maintain long-term resource transactions independently the auctionmechanism can be applied in resource allocation as amarket-incentive mechanism [13] Furthermore consider-ing the characteristics of the PoW consensus mechanism [5]ie low latency and rewarding users for broadcasting a newblock successfully users need computing resources to ac-complish more computing tasks in a short time to have morechances for obtaining rewards Furthermore the edgecomputing service providers hope to get revenues by sellingresources Consequently the auction model can provide afair competition market for resource trading mentionedabove

ere have been several works that focus on usingauctions or other economic methods to solve the compu-tation offloading problem of the mobile blockchain systemJiao et al first investigated resourcemanagement and pricingin the mobile blockchain with an auctionmodel [14] In [14]the resource allocation problem is modeled to maximize thesocial welfare of edge computing service providers (ESPs)considering the competition between miners and the utilityof blockchain network In [15] Xiong et al adopted the two-stage Stackelberg game to maximize both the profits of theESP and the individual utilities of miners Li et al designed along-term auction-based incentive mechanism POEM+ in[16] where the edge servers were encouraged to share theirresources to expedite the PoW process execution of mobiledevices with an approximation ratio However the defi-ciency of the aforementioned works is that no algorithm orsimulation addressed the scenario of large-scale user groupsfor the mobile blockchain system

e lack of edge-level resources has also posed asignificant obstacle in computation offloading In re-sponse Bahreini et al [17] studied resource allocationand pricing in the two-level edge computing system eyproposed a mechanism combining features from bothpositions and combinatorial auctions to meet the com-petition and heterogeneous demand of virtual machine(VM) instances for mobile users e proposed allocationmechanism in [17] provides heterogeneous types of re-sources for multilocation resource selection based on

location information which contributes to solving in-tensive computation offloading problems Unfortunatelythis work only considered resource transactions betweena single provider and mobile application users withoutconsidering that there will be multiple service providersat the same time in the market

With the above observations the promotion of mobileblockchain applications is proposed as a research object inthis paper Correspondingly a two-level combinatorialdouble auction mechanism that includes two levels of re-sources is proposed to solve the computation-intensiveoffloading problem of mobile blockchain applicationsmentioned above In the mechanism the providers who canprovide cloud-edge two-level service are called cloud-edgecomputing service providers (C-ESPs) e C-ESP canschedule cloud-level resources to supplement the edge-levelresources through the cloud computing center Moreoverthis mechanism considered that mobile users usually preferedge-level computing close to applications e main con-tributions of this paper are summarized as follows

(i) An allocation mechanism based on the combina-torial double auction is proposed for cloud-edgecomputing resource allocation In the mechanismthe computing tasks in generating a new block andbroadcasting throughout the whole mobile block-chain network to make consensus can be offloadedto C-ESPs

(ii) Resource allocation and pricing algorithms areproposed to determine winners and final priceswhich satisfy the economic attributes of auctiontruthfulness individual rationality budget balanceand computation efficiency

(iii) e proposed mechanism is simulated in varioussituations e simulation results show that theproposed mechanism is effective with large-scaleuser group participation and outperforms in termsof resource utilization

2 Related Work

To overcome the resource constraints of mobile devices theexisting works have widely studied resource allocationproblem of computation offloading in MEC systems [18]from different fields In [18] the authors analyzed that thecomputation offloading is a critical use case regarding theMEC as it can save energy andor speed up the process ofcomputation from the user perspective In [19] the authorsproposed an adaptive wireless resource allocation strategy ofcomputation offloading service under a three-layered ve-hicular edge cloud computing framework which can ensureendurance mileage of electric vehicles when a large numberof computation-intensive applications bring colossal energyconsumption to the vehicle To support resource-intensiveapplications running on the industrial Internet of things(IIOT) devices the authors in [20] presented a distributedgame-theoretic approach to achieving multihop cooperativecomputing offloading of the IIOT in the edge computingsystem

2 Mobile Information Systems

Second many researchers focused on the resource al-location of multiple service providers and multiple userscenarios by applying the double auction model Moreoverthe double auction model is an economic model widely usedin resource allocation that encourages buyers and sellers tobid simultaneously to reach a deal by the incentive mech-anism And during the auction buyers can bid on combinedgoods and buyers and sellers choose each other based onbidsrsquo details In [21] Singhal et al proposed a combinatorialdouble auction model for resource allocation Buyers bid fora package of resources and pay for it one time which canimprove resource utilization and resource efficiency allo-cation In the [22] the authors proposed a breakeven-baseddouble auction (BDA) and a dynamic pricing-based doubleauction (DPDA) to determine the matched pairs betweenIIOTmobile devices (MDs) and edge servers as well as thepricing mechanisms restricted by the actual situation forhigher system efficiency ese two algorithms mainlymodeled the two-side interaction between MEC servers andIIOT MDs ey described a double auction framework toaddress interaction and maximized the system efficiencywhere IIOP MDs request computing services with claimedbids and servers sell service with a reported price In [23] theauthors further adopted the auction model and proposed aresource allocation mechanism based on combined doubleauction to allocate VM instances of ESPs to miners byconsidering group buying Although this article considersmultiservice provider and multiuser scenarios it lacks theexpansion of future intensive task offloading

Furthermore a few recent computing offloading studieshave brought edge and cloud computing together to supportcomputation-intensive and latency-critical applications earchitecture of MEC can be further extended to serve usersin different scenarios e authors in [24] modeled the data-intensive service as a W-DAG (weight directed acyclicgraph) to investigate the task placement problem for sup-porting data-intensive services with guaranteed QoS ieshorter service delay in a cloud-edge system according to thebusiness logic analysis In [25] the authors derived a closed-form optimal task splitting strategy as a function of thenormalized backhaul communication capacity and thenormalized cloud computation capacity under the collab-oration between cloud computing and edge computing Fuet al proposed an economical and flexible framework forIIOT by integrating the function of data preprocessingstorage and retrieval based on both fog computing andcloud computing [26] In [27] Chen et al proposed amultiuser multitask computation offloading framework for agreen mobile edge cloud computing system where the dy-namics of energy arrivals at the mobile edge cloud and taskarrivals at different mobile devices are jointly considered

With the investigation of these research studies onmultiposition resource allocation and the computationoffloading in mobile blockchain a cloud-edge two-leveldouble auction mechanism is proposed for intensive com-putation offloading scenarios in mobile blockchain appli-cations e rest of the paper is organized as follows esystem model and problem formulation are described inSection 3emechanism is presented in Section 4 Section 5

introduces the simulation setup as well as discusses thesimulation results Finally the conclusion is given in Section6

3 System Model and Problem Formulation

e considered system provides K types of VM instancesfrom cloud-edge two levels In the system users and C-ESPssubmit bids to a central auctioneer separately to buy or sellVM instances When the edge-level computing servercannot satisfy large-scale offloading requests from mobileusers resources are scheduled and supplied for edge com-puting nodes from cloud-level servers to form a cloud-edgetwo-level auction market Moreover a total revenue opti-mization problem of the system is formulated by jointlyconsidering the profit of users and C-ESPs Compared tosingle-level edge computation offloading this model meetsmore needs of multiple users and improves resourceutilization

31 System Model is auction system consists of mobileblockchain networks computing service providers and theauctioneer In our mobile blockchain network the mobiledevices continuously run the consensus protocol to confirmand secure distributed data or information transmission inthe background erefore mobile devices need to solve thePoW problem that involves calculating a nonce output valuethat satisfies a given condition However it is hard for amobile user to continuously run such challenging programsthat require a large volume of CPU computing resources Itis considered that mobile users could offload the task ofsolving the PoW problem to nearby cloud-edge computingservers deployed by C-ESPs to get over the computinglimitation problem of mobile devices In particular C-ESPsannounce to the auctioneer services for the supply of VMinstances and bid information e mobile users submittheir resource demands and bid information to the auc-tioneer After receiving the demands and bids the auc-tioneer selects winners including users and C-ESPsaccording to the allocation algorithm and matching mobileusers and C-ESPs as the allocation matrix X xij1113966 1113967 thedetail of which will be presented in Section 32

As shown in Figure 1 the cloud-edge two-level auctionsystem includes C-ESPs mobile blockchain applicationusers and auctioneers C-ESPs sell VM instances to usersand users purchase the VM instance for completing themathematical puzzles of PoW in blockchain applicationsAssume that VM instances can be differentiated by diversecomputing resources such as memory CPU capacity andstorage It is considered that each C-ESP provides multipleVM instances at two levels edge (l 1) and cloud (l 2)where l denotes the location of VM instances Each userdemands a bundle of diverse sorts of instances to completecomputing tasks

311 Defining Bid Information of Users C-ESPs and userssubmit bid information to the auctioneer and the bid of useri is determined by a 2-tuple (di

vuseri ) In the tuple di

is the

Mobile Information Systems 3

demand vector which is defined as di

(d1

i d2i dk

i ) dki

denotes the demand of user i for the instance k and vuseri

signifies the reward valuation obtained by users after solvingthe PoW problem and broadcasting the result in the wholeblockchain network

312 Calculating Reward Valuation as the Bid of UsersIn the mobile blockchain network users compete to be thefirst to solve PoW problem with correct nonce value toreceive rewards that are considered the value vuseri offeredby users in this auction system thence calculating valuationfor rewards of all users at first Assume that the computingpower of each VM instance is 1 and each user can suc-cessfully purchase required resources With the allocationxij and demand dk

i the proportion of the computing ca-pacity of the user i in the whole blockchain network can berepresented as follows

ci xij 1113936

Ni1 d

ki

1113936Ni1 1113936

Mj1 xij 1113936

Kk1 d

ki1113872 1113873

ci gt 0 and 1113944N

i1ci 1 (1)

According to the reference in [14] the generation of newblocks follows a Poisson distribution process with a constantrate 1λ throughout the whole blockchain network Beforethe tournament users collect unconfirmed transactions intotheir blocks e first mobile user to successfully make theblock achieve consensus can get the reward consisted of afixed reward R and a flexible fee r e flexible reward isproportionate to the number of transactions s included inthe block and the proportionality coefficient is denoted as rus the potential rewards of user i can be expressed asfollows

vuseri (R + r middot s)P ci s( 1113857 (2)

where P(ci s) represents the probability where the user i

is the first to work out the computing task and generate anew block However the user will not be rewarded if thenew block cannot reach consensus on the entire network

in time and such blocks are called orphaned blocks [14]e broadcasting time τ is proportional to the transactionvolume contained in a new block and the proportionalitycoefficient can be denoted as ξ then τ ξ middot s Moreoverblocks with large transaction volumes require morepropagation time which may lead to high latency and failto reach consensus so blocks with a larger transactionsize are more likely to become orphaned blocks e timeof generating a new block obeys Poisson distribution sothe orphaning probability can be approximated asfollows

Porphan(τ) 1 minus eminus (1λ)ξmiddots

(3)

e probability that a user creates a new block andrewarded can be described as follows

P ci s( 1113857 ci 1 minus Porphan(τ)1113872 1113873 (4)

e potential reward can be rewritten as follows

vuseri (R + r middot s) middot ci middot e

minus (1λ)ξmiddots (5)

313 Defining Bid Information of C-ESPs e bid ofC-ESPj is specified as a 3-tuple (qlj

pj

πj) where

qj

(q1lj q2lj qk

lj) and pj

(p1

j p2j pk

j) Moreoverqk

lj indicates the number of instances provided by C-ESPj

from the lth level pkj denotes the ideal price of instance k

determined by C-ESP j and πj is the basic energy con-sumption unit for using VM instances provided by C-ESP jBesides K sorts of VM instances are distinguished bycomputing resource configuration in this model and theweight of each kind of VM instance is defined as ωk eenergy consumption function of VM instances is defined ascos t(ωk) ωk middot πj based on ωk which means that the cost ofusing computation resource will be higher with the higherresource configuration of the VM instance

Edge computing

unit

Cloud server

Edgecomputing

unitCloud-edge computing service provider

Sell bidsBuy bids

Auctioneer

Generate allocationand compute prices

Mobile device(bidder)




Mobile blockchain

Allocation algorithmPricing algorithm

Figure 1 Cloud-edge two-level auction system for mobile blockchain


314 Calculating Bids of C-ESPs with CommunicationConsumption e distribution of C-ESPs and users isshown in Figure 2 where the communication transmissionbetween C-ESPs and users comprises the path loss which isassumed to include in the bid of C-ESPs Specifically hprime isdefined as the threshold of the distance between users andC-ESPs When the distance between C-ESPs and users ex-ceeds hprime the bid will increase in proportion based upon theexcess For C-ESP j the price of instance k charged for user i

can be expressed by

pkij

pkj hij le hprime

pkj

hij

hprime hij gt hprime

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(6)

where hij denotes the distance between user i and C-ESP jand we calculate the average prices of all userserefore thebid of instance k determined by C-ESP j is formulated as

pkj

1113936ni1 p

kij

n (7)

32 Problem Formulation e previous section has de-scribed information of C-ESPs and users as the input tothe system is section mainly defines the output of thesystem ie the results of resource allocation and pricingand optimizes this allocation problem as much aspossible

e mechanism proposed (detailed in Section 4) in thiswork is a combinatorial double auction mechanism withresource location information e rules are as follows (i)each user can purchase a bundle of VM instances from nomore than one C-ESP (ii) selling VM instances of cloud levelwill cost more than the edge level due to the consumptioncaused by the resource scheduling (iii) moreover the bids ofusers and C-ESPs should be processed by the auctioneerseparately Assume that there are M C-ESPs and N usersand their matched results can be denoted as a M times N matrixX whose elements can be denoted as xije value of xij canbe indicated as follows

xij 1 if seller j serves buyer i

0 otherwise1113896 (8)

According to auction rule (i) the first restriction can beformulated as follows

1113944

M

j1xij lt 1 forall1le ileN (9)

In addition the supply of each C-ESP is limited Whenallocating VM instances to users the auctioneer will makesure that the remaining resources of the current C-ESP meetthe requirements of the current user Namely the totaldemands of matched users cannot exceed the capacity ofC-ESP e capacity constraint of C-ESPs can be formulatedas follows

1113944N

i1xijd

ki le 1113944

2

l1q

klj 1le jleM 1le kleK (10)

We define the winner set W containing the user who cansuccessfully match C-ESP based on above two constraints

Along with the allocation the auctioneer also calculatesthe payment of users and C-ESPse final charge of user i isdenoted as pi that user i actually pays to the provider pj isemployed to denote the payment of C-ESP j as the revenueobtained from matched users for serving Uj and Ui rep-resent the utility of C-ESPs and users respectively and theutility of the user i is defined as follows

Ui 1113944M

j1xij v

useri minus pi( 1113857 (11)

and the utility of the C-ESP j is defined as follows

Uj pj minus vCminus ESPj minus cj1113872 1113873 (12)

For C-ESP j vCminus ESPj is the total offer of instances supplied

for matched users cj denotes the cost incurred on theprocess that C-ESP j provides service to users As an edgecomputing service provider the costs generated by the edge-level are within its bid considerations while the excessconsumption from the cloud level will affect the C-ESPrevenue erefore we assume that the additional resourceexpenses will only be brought by operating cloud-level VMinstances yk

i represents the number of the instance k

purchased by user i from cloud level of C-ESP j e utilityof C-ESP can be rewritten as follows

Uj pj minus 1113944

N

i1xij 1113944

K

k1d

ki middot p

kj minus 1113944

K

k1p

kj middot cos t ωk( 1113857 middot y

ki

⎛⎝ ⎞⎠

(13)

In this paper we attach importance to economic effi-ciency and aim to maximize the total utility of users andC-ESPs erefore the allocation of VM instances problemin the proposed mechanism can be formulated as follows

User 2

User 1

User i

C-ESPs

hij

bull bull bull

Figure 2 C-ESP distribution structure with users


max 1113944

N

i1Ui + 1113944

M

j1Uj

⎛⎝ ⎞⎠

st 1113944M

j1xij le 1 forall1le ileN

st 1113944i1

i1xijd

ki le 1113944

2

l1q

klj 1le jleM 1le kleK

(14)

where two constraints mean that the user can match with nomore than one C-ESP and the capacity of C-ESPs is limitedis resource allocation problem can be proved as the NP-hard problem which cannot reach the optimal in a limitedtime According to [13] it can be simplified to the winnerdetermination problem Table 1 shows the notation used inthis paper

4 The Resource Auction Mechanism GreedyTwo-Level Resource Allocation andPricing (G-TRAP)

In this section a corresponding auctionmechanism is proposedto solve the VM instance allocation and pricing problem eproposed mechanism G-TRAP can be divided into two partsas follows In the first part a greedy mechanism is designed tocomplete VM instances allocation since it is unlikely to find apolynomial-time optimal solution of the allocation problemmentioned in Section 3 Moreover this allocation mechanismtrades resource in the two-level resource system under theconsideration of combining location information and weightsof VM instances which can improve resource utilization esecond part is pricing in which an improved VickreyndashClarkendashGroves (VCG) mechanism [28] is applied to calculatethe payments of participants to ensure the truthfulness of theauction

41 Allocation Algorithm e first algorithm contained inG-TRAP is the allocation algorithm Given bids of C-ESPsand users our objective is to maximize the total utility ofparticipants during allocation e resource allocation is anNP-hard problem so the greedy algorithm is customized tosolve the problem in this work

411 Calculating Bid Density and Ranking In the first stagethe bids of C-ESPs and users are sorted based on biddensities Considering that users and C-ESPs prefer to tradein edge-level resources rather than cloud-level resources wedefine the size of resources owed by C-ESP j sj related tothe type and the location of VM instancese bid density ofthe C-ESP can be calculated as follows

bdj vjsj

1113968

sj 11139442

l11113944

K

k1αl middot ωk middot q

klj

(15)

Similarly the userrsquos bid density can be expressed asfollows

bdi visi

radic

si 1113944K

k1ωk middot d

ki

(16)

where αl is defined as the preference factor for level l and setto distinguish the weight of resources between cloud leveland edge level and vivj is the valuation of bidders enC-ESPs are sorted in ascending order and users are sorted indescending order based on the bid density

412 Allocating in Order In the second stage users areassigned to the C-ESPs in sorted order When a user matchesa C-ESP the C-ESP will firstly check whether there areenough resources at the edge level or not If (1) the biddensity of user i is not less than C-ESP jprimes and (2) thenumber of K sorts of instances required by user i does notexceed the remaining resource at the edge level of C-ESP jC-ESP j and user i will match each other Suppose onlycondition (1) is satisfied and the remaining of edge levelcannot meet the demands of user i In this case C-ESP j willassign cloud-level instances as complements to user i

according to the constraints en C-ESP j updates thecapacity if sufficient resources are available to the currentuser Besides we denote yk

i as the number of kth VM in-stances purchased by user i from the cloud level

It is explained here that each user can only purchase allneeded VM instances from one C-ESP e user i willcontinue to match with the next C-ESP ranked behindC-ESP j if the two fail to match e element xij of matrix X

is marked after matching successfully and user i is added tothe winner set W e specific details of the allocation areshown in Algorithm 1

Table 1 Notation

Notation DescriptionN Number of C-ESPsM Number of C-ESPsvi Valuation of user i

K Types of VM instancesdki Demand of user i for the instance k

qklj Quantity of the kth instance C-ESP j providespkj Price of instance k determined by C-ESP j

πj Basic cost for C-ESP j

ωk Weight of instance k

xij Relationship matrix of users and C-ESPsyki Number of kth instances from cloud levelUi Utility of user i

Uj Utility of C-ESP j

cj e extra cost of C-ESP j

vCminus ESPj Offering by C-ESP j for allocated instancespi Payment of user i

pj Payment of C-ESP j

αl Weight of VM instance for level l


42 Pricing Schema and Calculating Total Utility Aftermatching C-ESPs and users through the allocation algo-rithm the payment of users and the revenue of C-ESPs willbe calculated separately We employ the improved VCGprice mechanism to pricing VCG auction always charges thewinner the highest bid of losers [28] In this paper we definethe VCG price vcg p of a user as the product of the size ofresources obtained by user i and the biggest bid densityamong losers

vcgpi si

radicmiddot bdmax loser (17)

To make sure individual personality and maximize theeffectiveness of C-ESP the final charge price of user i is themaximum value of VCG price the offer of matched C-ESPand the compromise price e compromise price is definedas the average value of the next lower bid density of C-ESPand VCG price e final payment of users can be expressedas follows

pi max bdmax loser bdjbdj+1 + vcgpi

21113896 1113897 middot

si

radic (18)

After calculating the charge of users the payment ofC-ESPs can be figured out as follows

pj xij 1113944

N

i1pi minus cj

⎛⎝ ⎞⎠ (19)

e total utility includes the utility of users and C-ESPse details of pricing are shown in Algorithm 2

43 Properties of G-TRAP In the following it is shown thatG-TRAP is actually an incentive mechanism to solve thedistribution problem defined above and it satisfies theeconomic properties include truthfulness individual ratio-nality budget balance and computing efficiency [29]

Definition 1 (truthfulness) An auction is truthful if anyparticipantrsquos utility is maximized for the actual valuation ofbidders Four properties including monotonicity critical-ness exactness and participation form the sufficiency for amechanism with truthfulness

Theorem 1 Algorithm G-TRAP is truthful

Proof 1 From the allocation algorithm it can be seen thatusers are first sorted in descending order according to biddensity and join in allocation erefore users can improvetheir ranking by raising the bids or reducing the config-uration of purchased resources to make allocation morelikely Accordingly the winner decision algorithm of ourmechanism is monotonous Secondly the VCG price iscalculated by multiplying the size of resources and themaximum bid density among losers who would win if thewinner does not participate in the auction Obviously ourmechanism is of exactness and participation ereforeour mechanism is truthful

Definition 2 (individual rationality) Individual rationalitymeans that each participantrsquos utility is non-negative ieUi gt 0 Uj gt 0 forforalli j isinW

Theorem 2 Algorithm G-TRAP is individually rational

Proof 2 Charges of users are determined by the largestamong VCG price the offer of matched C-ESP and theaverage value of the next lower bid density of C-ESP andVCG price VCG price is the product of

si

radic andvmax loser

smax loser

radic which is the highest bid density oflosers us VCG price is generally lower than the userrsquosvaluation As shown in the 6th to the 12th line of pricingalgorithm the value of pi is certainly less than userrsquos val-uation which means that user utility must be non-negativeAccording to the 5th line of allocation algorithm and the 5thand 8th lines of pricing algorithm it can be concluded thatthe return of C-ESP must be greater than its valuation andindividual rationality of C-ESP is also proved

Definition 3 (budget balance) Budget balance means thatthe final payment of users is not less than the sum of C-ESPrsquosconsumption

Theorem 3 Algorithm G-TRAP is budget balanced

Proof 3 e payments of users are paid to C-ESP and all ofthe actual income of C-ESP comes from users ereforethere is no auctioneer charged which means the algorithm isbudget balanced

Definition 4 (computing efficiency) If an algorithm canterminate in polynomial time it can be considered ascomputing efficient

Theorem 4 Algorithm G-TRAP is computing efficient

Proof 4 For G-TRAP sorting takes O(N logN) time andallocation takes O(NMK) time If the number of users farexceeds the number of C-ESPs the maximum time com-plexity of allocation algorithm is O(NK) and O(MK)otherwise In the algorithm of pricing and calculating totalutility pricing takes O(N) time and calculating total utilitytakes O(NM) time As a result the time complexity ofG-TRAP is O(NMK + N logN)

5 Simulation and Performance Analysis

51 Numerical Simulation Setup In previous researchstudies on mobile blockchain application computationoffloading [14ndash16 21 23] the number of users tested in thesimulations did not exceed 900 ere were no tests for alarge-scale user group To build an intensive computationoffloading scenario we expend the number of users grad-ually increases from 1 to 5000 during the simulation processwhile keeping the number of C-ESP as 200 and the numberof K types of VM instances unchanged Moreover the effectof the cloud-edge capacity ratio of the algorithm is alsotested based on 5000 users Note that the simulation results


obtained in this section are based on an average overmultiple iterations

Two comparing algorithms proposed in existing work[23] are added to evaluate the performance difference be-tween G-TRAP and edge-only computing systems

STGA this scheme is a combinatorial double auction[23] called step greedy algorithm Computing tasks willmatch edge computing providers (only supply edgecomputing resources) according to the bid size Aftermatching the utility in this scheme calculated followsthe VCG mechanismSMGA compared with the STGA the only difference isthat the smooth greedy algorithm [23] depends on acurve discount function to solve the allocation problembetween a group of users and edge computing pro-viders (only supply edge computing resources) e

evaluation results show that it performs better thanSTGA

In order to test the three algorithms legally we use thesame input file All data in the figures are obtained bysimulation on MATLAB R2019b

511 Calculating Rewards of Users in Mobile BlockchainNetwork Firstly we calculate the rewards of the PoWconsensus algorithm which depends on whether the mobileuser broadcasts a block successfully in the mobile blockchainas the bid of each user According to Section 312 the rewardof successfully adding to the chain is divided into two partsincluding fixed bonus R and variable r middot s In the simulationwe set R 20 and r 004 and assume that the size of block s

follows the uniform distribution U(0 1000) Hence each

(i) Input bid information of C-ESPs M and users N(ii) Calculate bid density of user i⟶ mb[i] and calculate bid density of C minus ESP j⟶ eb[j]

(iii) Sort users in nonincreasing order of their mb[i] and sort C-ESPs in nondecreasing order of their eb[i]

(iv) X⟵ 0 i⟵ W⟵ 0 l⟵ 0 y⟵0(v) for i 1 n do(vi) l⟵1 j⟵ 0(vii) while (jlem) and (f[i] 0) do(viii) if eb[j]le mb[i] then(ix) access⟵ true(x) for k 1 K do(xi) if (q[[l minus 1] jk] + q[ljk]) lt d[ik] then(xii) access⟵ false(xiii) break(xiv) if access then(xv) for k 1 K do(xvi) if l 2 then(xvii) if d[ik]ge q[1jk] then(xviii) d[ik]⟵ d[ik] minus q[1jk]

(xix) q[1jk]⟵0(xx) q[2jk]⟵q[2jk] minus d[ik]

(xi) y[ik]⟵y[ik] + d[ik]

(xii) else(xiii) q[1jk]⟵q[1jk] minus d[ik]

(xiv) else(xv) q[ljk]⟵ q[ljk] minus d[ik]

(xvi) x[ij]⟵1(xvii) W[i]⟵user[i]

(xviii) f[i]⟵ 1(xix) else(xx) if l 1 then(xxi) l⟵l + 1(xxii) else(xxiii) j⟵ j + 1(xxiv) continue(xxv) end if(xxvi) end if(xxvii) end if(xxviii) end while(xxxi) end for(xxx) Output set of winners W relation matrix X

ALGORITHM 1 G-TRAP resource allocation algorithm


user who successfully adds a new block in the public chainwill gain 20 + 004 middot s

512 Calculating the Bids of C-ESPs Based on the Distri-bution of the Network e network model is assumed to bea topological graph where the locations of C-ESPs and usersare generated randomly According to the nodesrsquo distribu-tion we assume that the distance between the user i andC-ESP j hij is randomly generated in the range of [40 60]and the threshold hprime is fixed to 50 e bid of C-ESPs thatincludes communication consumption is averagely esti-mated based on the ratio of hij and hprime

513 Setting Related Parameters of Auction Assume thatthere are four types of VM instances demanded by users andthe amount of VM instances required is set to obey theuniform distribution of U(1 5) Based on Amazonrsquos ElasticCompute Cloud (EC2) M3 series instances we consider thatthese four types of VM instances provided by C-ESPs aredefined as medium large xlarge and 2xlarge each equippedwith a combination of three types of resources includingvCPU memory and storagee resources are sold by cloudlevel and edge level of C-ESP en we assume that thenumber of VM instances for each C-ESP is subject to auniformly distributed dataset of U(30 35)

e unit price of C-ESP is randomly generated duringthe range of [ 01 middot Wk minus 005 01 middot Wk + 005 ] in which Wk

is the weight corresponding to each VM instance of C-ESPand 01 middot Wk denotes the basic unit price of k

th instance Weassign the weight αl to differentiate instance in edge-level(α2) and cloud-level (α1) and set four combinations of αl

which are (α1 02 α2 08) (α1 04 α2 06)(α1 07 α2 03) and (α1 09 α2 01) to constructsets of VM instances e basic energy consumption unit πj

is set with three different value ranges

([ 0 05 ] [05 1] [1 15 ]) and C-ESPs will pay differentresource costs for diverse types of VM instances e dis-tribution of parameters of VM instances generated insimulations is shown in Table 2

514 Setting Cloud-Edge Ratio We define a parametercalled cloud-edge capacity ratio Cr which is the ratio of thecapacity for each VM instance at the cloud and the capacityat the edge level e values of Cr are expressed asCr 1 (64) (73) (82) (91)

52 Analysis of Results

521 Impact of Reward Parameters for Successful Broad-casting of Users Firstly we consider the impact of fixedbonus R and the transaction fee r for broadcasting a block onthe mechanism It is observed from Figure 3 that if theblockchain network raises R and r the total utility and thepercentage of winners will be increased nearly in proportione reason is that users can obtain more rewards bycompleting computing tasks as expected and the bids in-crease correspondingly

522 Impact of the Number of Mobile Users N We nextinvestigate the effects of user amount on the performance ofG-TRAP with different sets of VM instances of C-ESPs Forthis purpose we keep the number of resources provided tousers unchanged and increase the number of users con-tinually And we also compare the performance of G-TRAPagainst that of STGA and SMGA in [23]

e total utility of G-TRAP is shown in Figure 4(a)which shows that as the number of users increases the totalutility also increases Moreover Figure 4(a) shows that thegreater relative weight of VM instances of edge level bringsmore total utility It is due to the fact that users and C-ESP

(i) for i 1 n do(ii) vcg plarr findmax mb[i]nsubW

(iii) for i 1 n do(iv) if user[i] in W then(v) if vcgp le mb[i] then(vi) pilarrmax vcg p eb[j] (eb[j + 1] + vcg p)21113864 1113865lowastradic(s[i])

(vii) else(viii) if ((eb[j + 1] + vcgpi)2)le mb[i] then(ix) pilarrmax eb[j] (eb[j + 1] + vcg pi)21113864 1113865lowastradic(s[i])

(x) else(xi) pilarreb[j] lowastradic(s[i])

(xii) end if(xiii) end if(xiv) end if(xv) u[i]larrvindashpi(xvi) u[j]larr u[j] + pindash(v[j] ndash cos t[j])

(xviii) end for(xix) Calculate sum of u[i] and sum of u[j]

(xx) Output payment of users total utility

ALGORITHM 2 G-TRAP pricing and total utility algorithm


prefer to trade VM instances of the edge level As shown inFigure 5(a) the total utility of STGA and STMA is far lessthan that of G-TRAP since they only provide edge-levelresources and offer group buying discounts without ap-plying cloud-level resources

Figure 4(b) shows the percentage of winners with dif-ferent sets of instances When the number of users does notexceed 4300 the percentage of winners exceeds 70 up to90 and not less than 55 at worst It can be consideredthat G-TLRA performs well in intensive scenarios ofcomputation offloading Again the winning ratio is highestwith the setting of α1 09 and α2 01 As shown inFigure 5(b) the winning ratio of G-TRAP is much higherthan that of STGA and STMA In the STGA and STMA eachuser can purchase VM instances from one C-ESP and theresources of edge level are insufficient which reduces theprobability of users successfully obtaining a bundle of VMinstances However C-ESPs in G-TRAP can serve moreusers by providing more VM instances from cloud level

It can be seen from Figure 4(c) that when the number ofusers increases the resource utilization of G-TRAP firstreaches 1 with the setting of α1 09 and α2 01 usG-TRAP performs better with the rise in the weight of edge-level resources However STGA and STMA cannot achievethe full utilization of resources as shown in Figure 5(c) InSTGA and STMA the provider sells VM instances of theedge level where remaining resources cannot satisfy the

demands of resources requested from the user behind Insummary G-TRAP is more suitable for various scenarios ofintensive computation offloading than STGA and STMA

523 Impact of Communication Distance of Users In Fig-ure 6 we vary the distance range between users and C-ESPsas [40 70] [40 80] and [40 90] and then compare withprevious results As expected the larger communicationdistance range will lower the percentage of winners andlower the resource usage ratiois is because that the longeruploading distances of tasks cause more communicationloss and the bids of C-ESPs will increase which lowers theranking of several C-ESP and reduces the matching betweenC-ESPs and users in turn

524 Impact of Cloud-Edge Capacity Ratio Further weexamine the impact of cloud-edge ratio Cr on the perfor-mance of G-TRAP e total number of VM instances ofC-ESPs is set to follow the uniform distribution ofU(0 2000) and the number of users is set to 5000 then wechange the value of Cr in G-TRAP

Figure 7(a) shows the effects of Cr on the execution timeof G-TRAP with different sets of VM instances It can beseen that the execution time of G-TRAP is insensitive tovariations in Cr and is less than 0018 seconds which can

Table 2 Types of VM instance used in the simulations

Type Weight Price rangeMediumLargeXlarge2Xlarge

1357

[01 W1minus 005 01 W1][01 W2minus 005 01 W2][01 W3minus 005 01 W3][01 W4minus 005 01 W4]

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

0

2

4

6

8

10

12

14

Tota

l util

ity

times104

R = 20 r = 004R = 20 r = 003

R = 5 r = 004R = 5 r = 003

(a)

03504

04505

05506

06507

07508

08509

095

Tota

l util

ity500 1000 1500 2000 2500 3000 3500 4000 4500 5000

User amount

R = 20 r = 004R = 20 r = 003

R = 5 r = 004R = 5 r = 003

(b)

Figure 3 e effect of R and r for PoW consensus mechanism on total utility and winning ratio (a) Total utility (b) User winning ratio


times104

2

4

6

8

10

12

14

Tota

l util

ity

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(a)

055

06

065

07

075

08

085

09

Use

r win

ning

ratio

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(b)

0

01

02

03

04

05

06

07

08

09

1

VM

usa

ge ra

tio

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(c)

Figure 4e effect of the total number of users on total utility winning ratio of users and VMusage ratio (a) Total utility (b) User winningratio (c) VM usage ratio

2

4

6

8

10

12

14times104

Tota

l util

ity

00

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

G-TRAPSTGASMGA

(a)

03504

04505

05506

06507

07508

08509

Use

r win

ning

ratio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

G-TRAPSTGASMGA

(b)

Figure 5 Continued


verify that the computing efficiency of G-TRAP is well whenserving a large-scale user group

Figure 7(b) shows the impacts of Cr on the number ofserved users When Cr is 1 the value of α1 and α2 has littleeffect on the number of usersmatched with C-ESP successfullywhile the higher Cr is the larger the difference of served useramount with different sets of α1 and α2 is Moreover the largerdifference between α1 and α2 brings a greater change in thenumber of served users With the increasing of Cr the serveduser amount of the last two sets increases well thatis(α1 07 α2 03) and (α1 09 α2 01) while de-creasing in the first two setsis is because that the total bids of

C-ESPs remains unchanged when Cr increases and the totalamount of resources raises because of the increase in ratiobetween α1 and α2 As a result the bid density of C-ESPdecreases so that it matches more users In a word increasingthe difference between α1 and α2 and the value of Cr canencourage more users to participate in the auction

Figure 7(c) shows the effects of the total utility of G-TRAPwith varying settings of instances Similarly the total utilitydoes not change much with different sets of α1 and α2 whenCr is 1 As Cr increases and α1 is less than 05 the bid densityof C-ESP increases which can lead to a reduction in thenumber of served users and reduce the total utility

00

01

02

03

04

05

06

07

08

09

1

VM

usa

ge ra

tio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

G-TRAPSTGASMGA

(c)

Figure 5e comparison of total utility winning ratio of users and VM usage ratio of G-TRAP with STGA and STMA (a) Comparison oftotal utility (b) Comparison of user winning ratio (c) Comparison of VM usage ratio

035

04

045

05

055

06

065

07

075

08

085

09

Use

r win

ning

ratio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

hijisin[40 60]hijisin[40 70]


(a)

00

01

02

03

04

05

06

07

08

09

1

VM

usa

ge ra

tio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount



(b)

Figure 6 e effect of communication distance on user winning ratio and VM usage ratio (a) User winning ratio (b) VM usage ratio


6 Conclusions

In this paper an efficient resource allocation with a pricingmechanism G-TRAP is proposed to support the offloadingof compute-intensive tasks generated by mobile blockchainfrom mobile devices to the cloud-edge computing systemIn this mechanism the two-level resource allocation systemprovides users more bidding options which increases thematching probability between users and C-ESPs And theimproved VCG pricing mechanism guarantees the indi-vidual rationality of participants and maximizes the ben-efits of C-ESPs as much as possible Moreover theproposed mechanism is proved to satisfy the economicproperties of the auction model by theoretical analysis esimulated results prove that this mechanism can run withshort execution time and the near optimality of resource

utilization which make it a suitable candidate for de-ployment in current and future mobile blockchain systemsand other service applications involving massive com-puting tasks

Data Availability

e simulation data of our algorithm implementationwhich is used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

1 64 73 82 91Cloud-edge capacity ratio

0

0002

0004

0006

0008

001

0012

0014

0016

0018

Exec

utio

n tim

e (s)

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(a)

0

50

100

150

200

250

300

350

400

Serv

ed u

sers

1 64 73 82 91

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

Cloud-edge capacity ratio

(b)

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

Tota

l util

ity


a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(c)

Figure 7 e effect of cloud-edge capacity ratio Cr on the execution time served user amount and total utility (a) Execution time (b)Served users (c) Total utility


Acknowledgments

is research was supported by the project of NationalScience and Technology Major Project of the Ministry ofScience and Technology of China (no 2018ZX03001014-003)

References

[1] K Suankaewmanee D T Hoang D Niyato S SawadsitangP Wang and Z Han ldquoPerformance analysis and applicationof mobile blockchainrdquo in Proceedings of the 2018 InternationalConference on Computing Networking and Communications(ICNC) pp 642ndash646 Maui HI USA March 2018

[2] Y Zou T Meng P Zhang W Zhang and H Li ldquoFocus onblockchain a comprehensive survey on academic and ap-plicationrdquo IEEE Access vol 8 pp 187182ndash187201 2020

[3] K Christidis and M Devetsikiotis ldquoBlockchains and smartcontracts for the internet of thingsrdquo IEEE Access vol 4pp 2292ndash2303 2016

[4] M Liu F R Yu Y Teng V C M Leung and M SongldquoComputation offloading and content caching in wirelessblockchain networks with mobile edge computingrdquo IEEETransactions on Vehicular Technology vol 67 no 11pp 11008ndash11021 2018

[5] S Nakamoto Bitcoin A Peer-To-Peer Electronic Cash System2008 httpsbitcoinorgbitcoinpdf

[6] J Garay A Kiayias and N Leonardos ldquoe bitcoin backboneprotocol analysis and applicationsrdquo in Advances in Cryp-tology - EUROCRYPT 2015 34th Annual InternationalConference on the Deory and Applications of CryptographicTechniques Part II pp 281ndash310 Springer Berlin Germany2015

[7] W Shi J Cao Q Zhang Y Li and L Xu ldquoEdge computingvision and challengesrdquo IEEE Internet of Dings Journal vol 3no 5 pp 637ndash646 2016

[8] J Ren G Yu Y Cai and Y He ldquoLatency optimization forresource allocation in mobile-edge computation offloadingrdquoIEEE Transactions onWireless Communications vol 17 no 8pp 5506ndash5519 2018

[9] S Yu R Langar X Fu L Wang and Z Han ldquoComputationoffloading with data caching enhancement for mobile edgecomputingrdquo IEEE Transactions on Vehicular Technologyvol 67 no 11 pp 11098ndash11112 2018

[10] F Bonomi R Milito J Zhu and S Addepalli ldquoFog com-puting and its rolein the internet of thingsrdquo in Proceedings ofthe MCC Workshop on Mobile Cloud Computing HelsinkiFinland August 2012

[11] Y C Hu M Patel D Sabella N Sprecher and V YoungMobile Edge Computing Introductory Technical White PaperETSI Sophia Antipolis France 2014

[12] Y Hu M Patel D Sabella N Sprecher and V YoungldquoMobile edge computing a key technology towards 5Grdquo ETSIWhite Paper vol 11 no 11 pp 1ndash16 2015

[13] V KrishnaAuctionDeory Academic Press Cambridge MAUSA 2009

[14] Y Jiao P Wang D Niyato and Z Xiong ldquoSocial welfaremaximization auction in edge computing resource allocationfor mobile blockchainrdquo in Proceedings of the 2018 IEEE In-ternational Conference on Communications (ICC) pp 1ndash6Kansas City MO USA May 2018

[15] Z Xiong S Feng D Niyato P Wang and Z Han ldquoOptimalpricing-based edge computing resource management inmobile blockchainrdquo in Proceedings of the 2018 IEEE

International Conference on Communications (ICC) pp 1ndash6Kansas City MO USA May 2018

[16] Y Li J Wu and L Chen ldquoPOEM+ pricing longer for mobileblockchain computation offloading with edge computingrdquo inProceedings of the 2019 IEEE 21st International Conference onHigh Performance Computing and Communications IEEE17th International Conference on Smart City IEEE 5th In-ternational Conference on Data Science and Systems (HPCCSmartCityDSS) pp 162ndash167 Zhangjiajie China August2019

[17] T Bahreini H Badri and D Grosu ldquoAn envy-free auctionmechanism for resource allocation in edge computing sys-temsrdquo in Proceedings of the 2018 IEEEACM Symposium onEdge Computing (SEC) pp 313ndash322 Seattle WA USAOctober 2018

[18] P Mach and Z Becvar ldquoMobile edge computing a survey onarchitecture and computation offloadingrdquo IEEE Communi-cations Surveys amp Tutorials vol 19 no 3 pp 1628ndash1656 2017

[19] X Li Y Dang M Aazam X Peng T Chen and C ChenldquoEnergy-efficient computation offloading in vehicular edgecloud computingrdquo IEEE Access vol 8 pp 37632ndash37644 2020

[20] Z Hong W Chen H Huang S Guo and Z Zheng ldquoMulti-hop cooperative computation offloading for industrial IoT-edge-cloud computing environmentsrdquo IEEE Transactions onParallel and Distributed Systems vol 30 no 12 pp 2759ndash2774 2019

[21] R Singhal and A Singhal ldquoA combinatorial economicaldouble auction resource allocation model (CEDARA)rdquo inProceedings of the 2019 International Conference on MachineLearning Big Data Cloud and Parallel Computing (COM-ITCon) pp 497ndash502 Faridabad India February 2019

[22] W Sun J Liu Y Yue and H Zhang ldquoDouble auction-basedresource allocation for mobile edge computing in industrialinternet of thingsrdquo IEEE Transactions on Industrial Infor-matics vol 14 no 10 pp 4692ndash4701 2018

[23] X Liu J Wu L Chen and C Xia ldquoEfficient auctionmechanism for edge computing resource allocation in mobileblockchainrdquo in Proceedings of the 2019 IEEE 21st InternationalConference on High Performance Computing and Commu-nications IEEE 17th International Conference on Smart CityIEEE 5th International Conference on Data Science and Sys-tems (HPCCSmartCityDSS) pp 871ndash876 ZhangjiajieChina August 2019

[24] X Li Z Lian X Qin and J Abawajyz ldquoDelay-aware resourceallocation for data analysis in cloud-edge systemrdquo in Pro-ceedings of the 2018 IEEE International Conference on Parallelamp Distributed Processing with Applications UbiquitousComputing amp Communications Big Data amp Cloud ComputingSocial Computing amp Networking Sustainable Computing ampCommunications (ISPAIUCCBDCloudSocialComSustain-Com) pp 816ndash823 Melbourne Australia December 2018

[25] J Ren G Yu Y He and G Y Li ldquoCollaborative cloud andedge computing for latency minimizationrdquo IEEE Transactionson Vehicular Technology vol 68 no 5 pp 5031ndash5044 2019

[26] J-S Fu Y Liu H-C Chao B K Bhargava and Z-J ZhangldquoSecure data storage and searching for industrial IoT by in-tegrating fog computing and cloud computingrdquo IEEETransactions on Industrial Informatics vol 14 no 10pp 4519ndash4528 2018

[27] W Chen D Wang and K Li ldquoMulti-user multi-task com-putation offloading in green mobile edge cloud computingrdquoIEEE Transactions on Services Computing vol 12 no 5pp 726ndash738 2019


[28] Y Narahari Game Deory and Mechanism design pp 231ndash273 China Remin University Press (CRUP) Beijing China2017

[29] G Gao M Xiao J Wu H Huang S Wang and G ChenldquoAuction-based VM allocation for deadline-sensitive tasks indistributed edge cloudrdquo IEEE Transactions on ServicesComputing 2019 In press


many computing tasks of applications in a short time usblockchain applications cannot be widely used in mobiledevices which limits mobile blockchain applicationsrsquodevelopment

Mobile edge computing (MEC) [7] provides an exem-plary method for solving such problems To support theoffloading of computation-intensive tasks mobile edgecomputing can provide mobile users with computing andstorage resources to solve limitations related to the hardware[8 9] In particular it overcomes the drawbacks of mobilecloud computing which could cause long latency andbackhaul bandwidth congestion [10ndash12] Because thecomputing capacity and appropriate incentive policies are ofgreat importance to users of mobile blockchain applicationsit is vital to decide how to offload the computing tasks of thePoW puzzle to the mobile edge computing in the mobileblockchain system

Given that the resource allocation mechanism involvesan incentive policy to allow participants to maintain long-term resource transactions independently the auctionmechanism can be applied in resource allocation as amarket-incentive mechanism [13] Furthermore consider-ing the characteristics of the PoW consensus mechanism [5]ie low latency and rewarding users for broadcasting a newblock successfully users need computing resources to ac-complish more computing tasks in a short time to have morechances for obtaining rewards Furthermore the edgecomputing service providers hope to get revenues by sellingresources Consequently the auction model can provide afair competition market for resource trading mentionedabove

ere have been several works that focus on usingauctions or other economic methods to solve the compu-tation offloading problem of the mobile blockchain systemJiao et al first investigated resourcemanagement and pricingin the mobile blockchain with an auctionmodel [14] In [14]the resource allocation problem is modeled to maximize thesocial welfare of edge computing service providers (ESPs)considering the competition between miners and the utilityof blockchain network In [15] Xiong et al adopted the two-stage Stackelberg game to maximize both the profits of theESP and the individual utilities of miners Li et al designed along-term auction-based incentive mechanism POEM+ in[16] where the edge servers were encouraged to share theirresources to expedite the PoW process execution of mobiledevices with an approximation ratio However the defi-ciency of the aforementioned works is that no algorithm orsimulation addressed the scenario of large-scale user groupsfor the mobile blockchain system

e lack of edge-level resources has also posed asignificant obstacle in computation offloading In re-sponse Bahreini et al [17] studied resource allocationand pricing in the two-level edge computing system eyproposed a mechanism combining features from bothpositions and combinatorial auctions to meet the com-petition and heterogeneous demand of virtual machine(VM) instances for mobile users e proposed allocationmechanism in [17] provides heterogeneous types of re-sources for multilocation resource selection based on

location information which contributes to solving in-tensive computation offloading problems Unfortunatelythis work only considered resource transactions betweena single provider and mobile application users withoutconsidering that there will be multiple service providersat the same time in the market

With the above observations the promotion of mobileblockchain applications is proposed as a research object inthis paper Correspondingly a two-level combinatorialdouble auction mechanism that includes two levels of re-sources is proposed to solve the computation-intensiveoffloading problem of mobile blockchain applicationsmentioned above In the mechanism the providers who canprovide cloud-edge two-level service are called cloud-edgecomputing service providers (C-ESPs) e C-ESP canschedule cloud-level resources to supplement the edge-levelresources through the cloud computing center Moreoverthis mechanism considered that mobile users usually preferedge-level computing close to applications e main con-tributions of this paper are summarized as follows

(i) An allocation mechanism based on the combina-torial double auction is proposed for cloud-edgecomputing resource allocation In the mechanismthe computing tasks in generating a new block andbroadcasting throughout the whole mobile block-chain network to make consensus can be offloadedto C-ESPs

(ii) Resource allocation and pricing algorithms areproposed to determine winners and final priceswhich satisfy the economic attributes of auctiontruthfulness individual rationality budget balanceand computation efficiency

(iii) e proposed mechanism is simulated in varioussituations e simulation results show that theproposed mechanism is effective with large-scaleuser group participation and outperforms in termsof resource utilization

2 Related Work

To overcome the resource constraints of mobile devices theexisting works have widely studied resource allocationproblem of computation offloading in MEC systems [18]from different fields In [18] the authors analyzed that thecomputation offloading is a critical use case regarding theMEC as it can save energy andor speed up the process ofcomputation from the user perspective In [19] the authorsproposed an adaptive wireless resource allocation strategy ofcomputation offloading service under a three-layered ve-hicular edge cloud computing framework which can ensureendurance mileage of electric vehicles when a large numberof computation-intensive applications bring colossal energyconsumption to the vehicle To support resource-intensiveapplications running on the industrial Internet of things(IIOT) devices the authors in [20] presented a distributedgame-theoretic approach to achieving multihop cooperativecomputing offloading of the IIOT in the edge computingsystem












is the



(d1

i d2i dk

i ) dki





ci xij 1113936

Ni1 d

ki

1113936Ni1 1113936

Mj1 xij 1113936

Kk1 d

ki1113872 1113873


i1ci 1 (1)







(3)







pj

πj) where

qj

(q1lj q2lj qk

lj) and pj

(p1

j p2j pk

j) Moreoverqk




Edge computing

unit

Cloud server

Edgecomputing


Sell bidsBuy bids

Auctioneer






Mobile blockchain





can be expressed by

pkij

pkj hij le hprime

pkj

hij


⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(6)


pkj

1113936ni1 p

kij

n (7)






1113944

M



1113944N

i1xijd

ki le 1113944

2

l1q




Ui 1113944M

j1xij v








Uj pj minus 1113944

N

i1xij 1113944

K

k1d

ki middot p

kj minus 1113944

K

k1p


ki

⎛⎝ ⎞⎠

(13)


User 2

User 1

User i

C-ESPs

hij

bull bull bull



max 1113944

N

i1Ui + 1113944

M

j1Uj

⎛⎝ ⎞⎠

st 1113944M


st 1113944i1

i1xijd

ki le 1113944

2

l1q


(14)






bdj vjsj

1113968

sj 11139442

l11113944

K


klj

(15)


bdi visi

radic

si 1113944K

k1ωk middot d

ki

(16)







Table 1 Notation














vcgpi si




21113896 1113897 middot

si

radic (18)


pj xij 1113944

N

i1pi minus cj

⎛⎝ ⎞⎠ (19)









si

radic andvmax loser

smax loser





























































1357


0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

0

2

4

6

8

10

12

14

Tota

l util

ity

times104

R = 20 r = 004R = 20 r = 003

R = 5 r = 004R = 5 r = 003

(a)

03504

04505

05506

06507

07508

08509

095

Tota

l util

ity500 1000 1500 2000 2500 3000 3500 4000 4500 5000

User amount

R = 20 r = 004R = 20 r = 003

R = 5 r = 004R = 5 r = 003

(b)



times104

2

4

6

8

10

12

14

Tota

l util

ity

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(a)

055

06

065

07

075

08

085

09

Use

r win

ning

ratio

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(b)

0

01

02

03

04

05

06

07

08

09

1

VM

usa

ge ra

tio

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(c)


2

4

6

8

10

12

14times104

Tota

l util

ity

00

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

G-TRAPSTGASMGA

(a)

03504

04505

05506

06507

07508

08509

Use

r win

ning

ratio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

G-TRAPSTGASMGA

(b)

Figure 5 Continued






00

01

02

03

04

05

06

07

08

09

1

VM

usa

ge ra

tio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

G-TRAPSTGASMGA

(c)


035

04

045

05

055

06

065

07

075

08

085

09

Use

r win

ning

ratio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount



(a)

00

01

02

03

04

05

06

07

08

09

1

VM

usa

ge ra

tio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount



(b)



6 Conclusions



Data Availability





0

0002

0004

0006

0008

001

0012

0014

0016

0018

Exec

utio

n tim

e (s)

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(a)

0

50

100

150

200

250

300

350

400

Serv

ed u

sers

1 64 73 82 91

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01


(b)

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

Tota

l util

ity


a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(c)



Acknowledgments


References











































is the



(d1

i d2i dk

i ) dki





ci xij 1113936

Ni1 d

ki

1113936Ni1 1113936

Mj1 xij 1113936

Kk1 d

ki1113872 1113873


i1ci 1 (1)







(3)







pj

πj) where

qj

(q1lj q2lj qk

lj) and pj

(p1

j p2j pk

j) Moreoverqk




Edge computing

unit

Cloud server

Edgecomputing


Sell bidsBuy bids

Auctioneer






Mobile blockchain





can be expressed by

pkij

pkj hij le hprime

pkj

hij


⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(6)


pkj

1113936ni1 p

kij

n (7)






1113944

M



1113944N

i1xijd

ki le 1113944

2

l1q




Ui 1113944M

j1xij v








Uj pj minus 1113944

N

i1xij 1113944

K

k1d

ki middot p

kj minus 1113944

K

k1p


ki

⎛⎝ ⎞⎠

(13)


User 2

User 1

User i

C-ESPs

hij

bull bull bull



max 1113944

N

i1Ui + 1113944

M

j1Uj

⎛⎝ ⎞⎠

st 1113944M


st 1113944i1

i1xijd

ki le 1113944

2

l1q


(14)






bdj vjsj

1113968

sj 11139442

l11113944

K


klj

(15)


bdi visi

radic

si 1113944K

k1ωk middot d

ki

(16)







Table 1 Notation














vcgpi si




21113896 1113897 middot

si

radic (18)


pj xij 1113944

N

i1pi minus cj

⎛⎝ ⎞⎠ (19)









si

radic andvmax loser

smax loser





























































1357


0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

0

2

4

6

8

10

12

14

Tota

l util

ity

times104

R = 20 r = 004R = 20 r = 003

R = 5 r = 004R = 5 r = 003

(a)

03504

04505

05506

06507

07508

08509

095

Tota

l util

ity500 1000 1500 2000 2500 3000 3500 4000 4500 5000

User amount

R = 20 r = 004R = 20 r = 003

R = 5 r = 004R = 5 r = 003

(b)



times104

2

4

6

8

10

12

14

Tota

l util

ity

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(a)

055

06

065

07

075

08

085

09

Use

r win

ning

ratio

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(b)

0

01

02

03

04

05

06

07

08

09

1

VM

usa

ge ra

tio

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(c)


2

4

6

8

10

12

14times104

Tota

l util

ity

00

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

G-TRAPSTGASMGA

(a)

03504

04505

05506

06507

07508

08509

Use

r win

ning

ratio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

G-TRAPSTGASMGA

(b)

Figure 5 Continued






00

01

02

03

04

05

06

07

08

09

1

VM

usa

ge ra

tio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

G-TRAPSTGASMGA

(c)


035

04

045

05

055

06

065

07

075

08

085

09

Use

r win

ning

ratio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount



(a)

00

01

02

03

04

05

06

07

08

09

1

VM

usa

ge ra

tio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount



(b)



6 Conclusions



Data Availability





0

0002

0004

0006

0008

001

0012

0014

0016

0018

Exec

utio

n tim

e (s)

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(a)

0

50

100

150

200

250

300

350

400

Serv

ed u

sers

1 64 73 82 91

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01


(b)

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

Tota

l util

ity


a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(c)



Acknowledgments


References


































(d1

i d2i dk

i ) dki





ci xij 1113936

Ni1 d

ki

1113936Ni1 1113936

Mj1 xij 1113936

Kk1 d

ki1113872 1113873


i1ci 1 (1)







(3)







pj

πj) where

qj

(q1lj q2lj qk

lj) and pj

(p1

j p2j pk

j) Moreoverqk




Edge computing

unit

Cloud server

Edgecomputing


Sell bidsBuy bids

Auctioneer






Mobile blockchain





can be expressed by

pkij

pkj hij le hprime

pkj

hij


⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(6)


pkj

1113936ni1 p

kij

n (7)






1113944

M



1113944N

i1xijd

ki le 1113944

2

l1q




Ui 1113944M

j1xij v








Uj pj minus 1113944

N

i1xij 1113944

K

k1d

ki middot p

kj minus 1113944

K

k1p


ki

⎛⎝ ⎞⎠

(13)


User 2

User 1

User i

C-ESPs

hij

bull bull bull



max 1113944

N

i1Ui + 1113944

M

j1Uj

⎛⎝ ⎞⎠

st 1113944M


st 1113944i1

i1xijd

ki le 1113944

2

l1q


(14)






bdj vjsj

1113968

sj 11139442

l11113944

K


klj

(15)


bdi visi

radic

si 1113944K

k1ωk middot d

ki

(16)







Table 1 Notation














vcgpi si




21113896 1113897 middot

si

radic (18)


pj xij 1113944

N

i1pi minus cj

⎛⎝ ⎞⎠ (19)









si

radic andvmax loser

smax loser





























































1357


0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

0

2

4

6

8

10

12

14

Tota

l util

ity

times104

R = 20 r = 004R = 20 r = 003

R = 5 r = 004R = 5 r = 003

(a)

03504

04505

05506

06507

07508

08509

095

Tota

l util

ity500 1000 1500 2000 2500 3000 3500 4000 4500 5000

User amount

R = 20 r = 004R = 20 r = 003

R = 5 r = 004R = 5 r = 003

(b)



times104

2

4

6

8

10

12

14

Tota

l util

ity

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(a)

055

06

065

07

075

08

085

09

Use

r win

ning

ratio

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(b)

0

01

02

03

04

05

06

07

08

09

1

VM

usa

ge ra

tio

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(c)


2

4

6

8

10

12

14times104

Tota

l util

ity

00

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

G-TRAPSTGASMGA

(a)

03504

04505

05506

06507

07508

08509

Use

r win

ning

ratio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

G-TRAPSTGASMGA

(b)

Figure 5 Continued






00

01

02

03

04

05

06

07

08

09

1

VM

usa

ge ra

tio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

G-TRAPSTGASMGA

(c)


035

04

045

05

055

06

065

07

075

08

085

09

Use

r win

ning

ratio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount



(a)

00

01

02

03

04

05

06

07

08

09

1

VM

usa

ge ra

tio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount



(b)



6 Conclusions



Data Availability





0

0002

0004

0006

0008

001

0012

0014

0016

0018

Exec

utio

n tim

e (s)

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(a)

0

50

100

150

200

250

300

350

400

Serv

ed u

sers

1 64 73 82 91

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01


(b)

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

Tota

l util

ity


a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(c)



Acknowledgments


References


































can be expressed by

pkij

pkj hij le hprime

pkj

hij


⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(6)


pkj

1113936ni1 p

kij

n (7)






1113944

M



1113944N

i1xijd

ki le 1113944

2

l1q




Ui 1113944M

j1xij v








Uj pj minus 1113944

N

i1xij 1113944

K

k1d

ki middot p

kj minus 1113944

K

k1p


ki

⎛⎝ ⎞⎠

(13)


User 2

User 1

User i

C-ESPs

hij

bull bull bull



max 1113944

N

i1Ui + 1113944

M

j1Uj

⎛⎝ ⎞⎠

st 1113944M


st 1113944i1

i1xijd

ki le 1113944

2

l1q


(14)






bdj vjsj

1113968

sj 11139442

l11113944

K


klj

(15)


bdi visi

radic

si 1113944K

k1ωk middot d

ki

(16)







Table 1 Notation














vcgpi si




21113896 1113897 middot

si

radic (18)


pj xij 1113944

N

i1pi minus cj

⎛⎝ ⎞⎠ (19)









si

radic andvmax loser

smax loser





























































1357


0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

0

2

4

6

8

10

12

14

Tota

l util

ity

times104

R = 20 r = 004R = 20 r = 003

R = 5 r = 004R = 5 r = 003

(a)

03504

04505

05506

06507

07508

08509

095

Tota

l util

ity500 1000 1500 2000 2500 3000 3500 4000 4500 5000

User amount

R = 20 r = 004R = 20 r = 003

R = 5 r = 004R = 5 r = 003

(b)



times104

2

4

6

8

10

12

14

Tota

l util

ity

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(a)

055

06

065

07

075

08

085

09

Use

r win

ning

ratio

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(b)

0

01

02

03

04

05

06

07

08

09

1

VM

usa

ge ra

tio

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(c)


2

4

6

8

10

12

14times104

Tota

l util

ity

00

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

G-TRAPSTGASMGA

(a)

03504

04505

05506

06507

07508

08509

Use

r win

ning

ratio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

G-TRAPSTGASMGA

(b)

Figure 5 Continued






00

01

02

03

04

05

06

07

08

09

1

VM

usa

ge ra

tio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

G-TRAPSTGASMGA

(c)


035

04

045

05

055

06

065

07

075

08

085

09

Use

r win

ning

ratio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount



(a)

00

01

02

03

04

05

06

07

08

09

1

VM

usa

ge ra

tio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount



(b)



6 Conclusions



Data Availability





0

0002

0004

0006

0008

001

0012

0014

0016

0018

Exec

utio

n tim

e (s)

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(a)

0

50

100

150

200

250

300

350

400

Serv

ed u

sers

1 64 73 82 91

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01


(b)

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

Tota

l util

ity


a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(c)



Acknowledgments


References

































max 1113944

N

i1Ui + 1113944

M

j1Uj

⎛⎝ ⎞⎠

st 1113944M


st 1113944i1

i1xijd

ki le 1113944

2

l1q


(14)






bdj vjsj

1113968

sj 11139442

l11113944

K


klj

(15)


bdi visi

radic

si 1113944K

k1ωk middot d

ki

(16)







Table 1 Notation














vcgpi si




21113896 1113897 middot

si

radic (18)


pj xij 1113944

N

i1pi minus cj

⎛⎝ ⎞⎠ (19)









si

radic andvmax loser

smax loser





























































1357


0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

0

2

4

6

8

10

12

14

Tota

l util

ity

times104

R = 20 r = 004R = 20 r = 003

R = 5 r = 004R = 5 r = 003

(a)

03504

04505

05506

06507

07508

08509

095

Tota

l util

ity500 1000 1500 2000 2500 3000 3500 4000 4500 5000

User amount

R = 20 r = 004R = 20 r = 003

R = 5 r = 004R = 5 r = 003

(b)



times104

2

4

6

8

10

12

14

Tota

l util

ity

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(a)

055

06

065

07

075

08

085

09

Use

r win

ning

ratio

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(b)

0

01

02

03

04

05

06

07

08

09

1

VM

usa

ge ra

tio

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(c)


2

4

6

8

10

12

14times104

Tota

l util

ity

00

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

G-TRAPSTGASMGA

(a)

03504

04505

05506

06507

07508

08509

Use

r win

ning

ratio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

G-TRAPSTGASMGA

(b)

Figure 5 Continued






00

01

02

03

04

05

06

07

08

09

1

VM

usa

ge ra

tio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

G-TRAPSTGASMGA

(c)


035

04

045

05

055

06

065

07

075

08

085

09

Use

r win

ning

ratio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount



(a)

00

01

02

03

04

05

06

07

08

09

1

VM

usa

ge ra

tio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount



(b)



6 Conclusions



Data Availability





0

0002

0004

0006

0008

001

0012

0014

0016

0018

Exec

utio

n tim

e (s)

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(a)

0

50

100

150

200

250

300

350

400

Serv

ed u

sers

1 64 73 82 91

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01


(b)

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

Tota

l util

ity


a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(c)



Acknowledgments


References


































vcgpi si




21113896 1113897 middot

si

radic (18)


pj xij 1113944

N

i1pi minus cj

⎛⎝ ⎞⎠ (19)









si

radic andvmax loser

smax loser





























































1357


0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

0

2

4

6

8

10

12

14

Tota

l util

ity

times104

R = 20 r = 004R = 20 r = 003

R = 5 r = 004R = 5 r = 003

(a)

03504

04505

05506

06507

07508

08509

095

Tota

l util

ity500 1000 1500 2000 2500 3000 3500 4000 4500 5000

User amount

R = 20 r = 004R = 20 r = 003

R = 5 r = 004R = 5 r = 003

(b)



times104

2

4

6

8

10

12

14

Tota

l util

ity

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(a)

055

06

065

07

075

08

085

09

Use

r win

ning

ratio

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(b)

0

01

02

03

04

05

06

07

08

09

1

VM

usa

ge ra

tio

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(c)


2

4

6

8

10

12

14times104

Tota

l util

ity

00

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

G-TRAPSTGASMGA

(a)

03504

04505

05506

06507

07508

08509

Use

r win

ning

ratio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

G-TRAPSTGASMGA

(b)

Figure 5 Continued






00

01

02

03

04

05

06

07

08

09

1

VM

usa

ge ra

tio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

G-TRAPSTGASMGA

(c)


035

04

045

05

055

06

065

07

075

08

085

09

Use

r win

ning

ratio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount



(a)

00

01

02

03

04

05

06

07

08

09

1

VM

usa

ge ra

tio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount



(b)



6 Conclusions



Data Availability





0

0002

0004

0006

0008

001

0012

0014

0016

0018

Exec

utio

n tim

e (s)

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(a)

0

50

100

150

200

250

300

350

400

Serv

ed u

sers

1 64 73 82 91

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01


(b)

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

Tota

l util

ity


a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(c)



Acknowledgments


References



















































































1357


0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

0

2

4

6

8

10

12

14

Tota

l util

ity

times104

R = 20 r = 004R = 20 r = 003

R = 5 r = 004R = 5 r = 003

(a)

03504

04505

05506

06507

07508

08509

095

Tota

l util

ity500 1000 1500 2000 2500 3000 3500 4000 4500 5000

User amount

R = 20 r = 004R = 20 r = 003

R = 5 r = 004R = 5 r = 003

(b)



times104

2

4

6

8

10

12

14

Tota

l util

ity

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(a)

055

06

065

07

075

08

085

09

Use

r win

ning

ratio

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(b)

0

01

02

03

04

05

06

07

08

09

1

VM

usa

ge ra

tio

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(c)


2

4

6

8

10

12

14times104

Tota

l util

ity

00

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

G-TRAPSTGASMGA

(a)

03504

04505

05506

06507

07508

08509

Use

r win

ning

ratio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

G-TRAPSTGASMGA

(b)

Figure 5 Continued






00

01

02

03

04

05

06

07

08

09

1

VM

usa

ge ra

tio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

G-TRAPSTGASMGA

(c)


035

04

045

05

055

06

065

07

075

08

085

09

Use

r win

ning

ratio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount



(a)

00

01

02

03

04

05

06

07

08

09

1

VM

usa

ge ra

tio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount



(b)



6 Conclusions



Data Availability





0

0002

0004

0006

0008

001

0012

0014

0016

0018

Exec

utio

n tim

e (s)

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(a)

0

50

100

150

200

250

300

350

400

Serv

ed u

sers

1 64 73 82 91

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01


(b)

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

Tota

l util

ity


a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(c)



Acknowledgments


References

































































1357


0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

0

2

4

6

8

10

12

14

Tota

l util

ity

times104

R = 20 r = 004R = 20 r = 003

R = 5 r = 004R = 5 r = 003

(a)

03504

04505

05506

06507

07508

08509

095

Tota

l util

ity500 1000 1500 2000 2500 3000 3500 4000 4500 5000

User amount

R = 20 r = 004R = 20 r = 003

R = 5 r = 004R = 5 r = 003

(b)



times104

2

4

6

8

10

12

14

Tota

l util

ity

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(a)

055

06

065

07

075

08

085

09

Use

r win

ning

ratio

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(b)

0

01

02

03

04

05

06

07

08

09

1

VM

usa

ge ra

tio

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(c)


2

4

6

8

10

12

14times104

Tota

l util

ity

00

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

G-TRAPSTGASMGA

(a)

03504

04505

05506

06507

07508

08509

Use

r win

ning

ratio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

G-TRAPSTGASMGA

(b)

Figure 5 Continued






00

01

02

03

04

05

06

07

08

09

1

VM

usa

ge ra

tio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

G-TRAPSTGASMGA

(c)


035

04

045

05

055

06

065

07

075

08

085

09

Use

r win

ning

ratio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount



(a)

00

01

02

03

04

05

06

07

08

09

1

VM

usa

ge ra

tio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount



(b)



6 Conclusions



Data Availability





0

0002

0004

0006

0008

001

0012

0014

0016

0018

Exec

utio

n tim

e (s)

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(a)

0

50

100

150

200

250

300

350

400

Serv

ed u

sers

1 64 73 82 91

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01


(b)

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

Tota

l util

ity


a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(c)



Acknowledgments


References










































1357


0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

0

2

4

6

8

10

12

14

Tota

l util

ity

times104

R = 20 r = 004R = 20 r = 003

R = 5 r = 004R = 5 r = 003

(a)

03504

04505

05506

06507

07508

08509

095

Tota

l util

ity500 1000 1500 2000 2500 3000 3500 4000 4500 5000

User amount

R = 20 r = 004R = 20 r = 003

R = 5 r = 004R = 5 r = 003

(b)



times104

2

4

6

8

10

12

14

Tota

l util

ity

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(a)

055

06

065

07

075

08

085

09

Use

r win

ning

ratio

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(b)

0

01

02

03

04

05

06

07

08

09

1

VM

usa

ge ra

tio

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(c)


2

4

6

8

10

12

14times104

Tota

l util

ity

00

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

G-TRAPSTGASMGA

(a)

03504

04505

05506

06507

07508

08509

Use

r win

ning

ratio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

G-TRAPSTGASMGA

(b)

Figure 5 Continued






00

01

02

03

04

05

06

07

08

09

1

VM

usa

ge ra

tio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

G-TRAPSTGASMGA

(c)


035

04

045

05

055

06

065

07

075

08

085

09

Use

r win

ning

ratio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount



(a)

00

01

02

03

04

05

06

07

08

09

1

VM

usa

ge ra

tio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount



(b)



6 Conclusions



Data Availability





0

0002

0004

0006

0008

001

0012

0014

0016

0018

Exec

utio

n tim

e (s)

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(a)

0

50

100

150

200

250

300

350

400

Serv

ed u

sers

1 64 73 82 91

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01


(b)

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

Tota

l util

ity


a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(c)



Acknowledgments


References

































times104

2

4

6

8

10

12

14

Tota

l util

ity

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(a)

055

06

065

07

075

08

085

09

Use

r win

ning

ratio

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(b)

0

01

02

03

04

05

06

07

08

09

1

VM

usa

ge ra

tio

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(c)


2

4

6

8

10

12

14times104

Tota

l util

ity

00

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

G-TRAPSTGASMGA

(a)

03504

04505

05506

06507

07508

08509

Use

r win

ning

ratio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

G-TRAPSTGASMGA

(b)

Figure 5 Continued






00

01

02

03

04

05

06

07

08

09

1

VM

usa

ge ra

tio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

G-TRAPSTGASMGA

(c)


035

04

045

05

055

06

065

07

075

08

085

09

Use

r win

ning

ratio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount



(a)

00

01

02

03

04

05

06

07

08

09

1

VM

usa

ge ra

tio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount



(b)



6 Conclusions



Data Availability





0

0002

0004

0006

0008

001

0012

0014

0016

0018

Exec

utio

n tim

e (s)

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(a)

0

50

100

150

200

250

300

350

400

Serv

ed u

sers

1 64 73 82 91

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01


(b)

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

Tota

l util

ity


a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(c)



Acknowledgments


References





































00

01

02

03

04

05

06

07

08

09

1

VM

usa

ge ra

tio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount

G-TRAPSTGASMGA

(c)


035

04

045

05

055

06

065

07

075

08

085

09

Use

r win

ning

ratio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount



(a)

00

01

02

03

04

05

06

07

08

09

1

VM

usa

ge ra

tio

500 1000 1500 2000 2500 3000 3500 4000 4500 5000User amount



(b)



6 Conclusions



Data Availability





0

0002

0004

0006

0008

001

0012

0014

0016

0018

Exec

utio

n tim

e (s)

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(a)

0

50

100

150

200

250

300

350

400

Serv

ed u

sers

1 64 73 82 91

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01


(b)

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

Tota

l util

ity


a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(c)



Acknowledgments


References

































6 Conclusions



Data Availability





0

0002

0004

0006

0008

001

0012

0014

0016

0018

Exec

utio

n tim

e (s)

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(a)

0

50

100

150

200

250

300

350

400

Serv

ed u

sers

1 64 73 82 91

a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01


(b)

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

Tota

l util

ity


a1 = 02 a2 = 08a1 = 04 a2 = 06

a1 = 07 a2 = 03a1 = 09 a2 = 01

(c)



Acknowledgments


References

































Acknowledgments


References




































Documents

Double Auction-Based Two-Level Resource Allocation