cooperative game-based virtual machine resource allocation

Research ArticleCooperative Game-Based Virtual Machine Resource AllocationAlgorithms in Cloud Data Centers

Sungwook Kim

Department of Computer Science Sogang University 35 Baekbeom-ro (Sinsu-dong) Mapo-gu Seoul 04107 Republic of Korea

Correspondence should be addressed to Sungwook Kim swkim01sogangackr

Received 10 December 2019 Revised 1 February 2020 Accepted 19 February 2020 Published 16 March 2020

Academic Editor Marco Picone

Copyright copy 2020 Sungwook Kim )is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

With the growing demand of cloud services cloud data centers (CDCs) can provide flexible resource provisioning in order toaccommodate the workload demand In CDCs the virtual machine (VM) resource allocation problem is an important andchallenging issue to provide efficient infrastructure services In this paper we propose a unified resource allocation scheme forVMs in the CDC system To provide a fair-efficient solution we concentrate on the basic concept of Shapley value and adopt itsvariations to effectively allocate CDC resources Based on the characteristics of value solutions we develop novel CPU memorystorage and bandwidth resource allocation algorithms To practically implement our algorithms application types are assumed ascooperative game players and different value solutions are applied to optimize the resource utilization )erefore our fourresource allocation algorithms are jointly combined as a novel fourfold game model and take various benefits in a rational waythrough the cascade interactions while solving comprehensively some control issues To ensure the growing demand of cloudservices this feature can leverage the full synergy of different value solutions To check the effectiveness and superiority of ourproposed scheme we conduct extensive simulations )e simulation results show that our algorithms have significant per-formance improvement compared to the existing state-of-the-art protocols Finally we summarize our cooperative game-basedapproach and discuss possible major research issues for the future challenges about the cloud-assisted DC resourceallocation paradigm

1 Introduction

Nowadays Internet of )ings (IoT) has created many ex-citing applications and they generate big volume of data)erefore there is a strong need to conduct analysis on thebig data to support various data-driven services To meet theever-increasing demand of applications and services cloudcomputing has recently been brought into focus in bothacademia and industry )e advent of cloud computing hasgiven rise to new and exciting prospects for individualssmall- and medium-sized enterprises and large organiza-tions who can flexibly lease processing storage and networkresources on-demand Due to their temporal needs of cloudservices we have witnessed the rapid growth of cloud datacenters (CDCs) in the past few years and expect the numberof CDCs will triple by 2020 [1 2]

To handle the rapid increment of computation re-quirements CDCs provide unparalleled large-scale com-putational capability and ubiquitous data accessibilitywhich can make service more acceptable ConventionallyCDCs are warehouses that host tens of thousands ofservers providing data-processing service and enablingcommunications among large amounts of computing re-sources )ese servers may be used to provide differentservices to individual users over the Internet and to benefitfrom economy of scale to reduce computational costs)erefore CDC infrastructures which are maintained andmanaged at scale by local as well as global operators such asAmazon Rackspace Microsoft and Google are widelyused to offer as-a-services such as data-intensive applica-tions including query web service and big data analytics[2 3]

HindawiMobile Information SystemsVolume 2020 Article ID 9840198 11 pageshttpsdoiorg10115520209840198

)e properties of CDCs and the mechanisms for limitedresource allocations largely define the operation and per-formance of the CDC system In order to be sustainable thesignificant capital outlay required for building a CDC makesmaximization of Return on Investment (RoI) crucial whichin turn necessitates efficient and adaptive CDC resourceusage Moreover the economic viability of a CDC greatlydepends on running the CDC at acceptable performancelevels and allowing users and applications to highly utilizeand share its infrastructure and resources In summary theperformance of CDCs is directly associated with how toimprove the resource usability However the average CDCresource utilization has found to be low typically rangingfrom 10 to 20 percent )erefore it is necessary to increasethe resource utilization for the CDC system efficiency[2 4 5]

Recently virtualization technology has been touted as arevolutionary technology to tackle the low-utilizationproblem in CDCs Initially virtualization began in the1960s as a method of creating a virtual version of some-thing including virtual computer hardware platformsstorage devices and computer network resources Sincethen the meaning of the term has broadened In CDCsdifferent physical resources are logically partitioned andmultiplexed among different applications )rough virtu-alization technology virtual machines (VMs) are createdaccording to usersrsquo demands and users execute their ap-plications on the VMs that are indeed running on physicalmachines (PMs) Usually multiple VMs can be created on aPM using the virtualization software )erefore PM re-source distribution for VMs is a hot research topic toimprove the PM utilization With multiple resource re-quests finding an optimal solution of PM resource dis-tribution problem will thus create a lot of challenges to theresearchers However under a complicated scenario tra-ditional resource allocation approach suffers from ex-tremely high computational complexity and controloverhead )erefore we need a new control paradigm toeffectively mediate between the implementation practi-cality and the system optimality [5 6]

11 Cooperative Game-Based Value Solutions Game theoryis a theoretical framework for conceiving situations amongcompeting players In some respects game theory is thescience of strategy or at least the optimal decision-making ofindependent and competing players in a strategic settingGame theory has two major subdivisions noncooperativeand cooperative game theory In cooperative game theoryrational players will find ways to commit themselves to theagreement and enjoy the benefits that arise from theagreement Indeed one possibility is that a group of playersmay cooperate to exploit another player or group of players)e value is a central solution concept in the cooperativegame theory In 1953 the basic concept of value was in-troduced by Shapley for the study of cooperative games Andthen the idea of value solutions has been extended in dif-ferent ways some of the most notable values solutions aredeveloped by Harsanyi and Shapley [7]

Recently value-based cooperative game approaches havebeen widely investigated to solve the resource allocationproblems In this study we design a new VM resource al-location scheme based on four value solutions Shapley value(SV) weighted Shapley value (WSV) proportional Shapleyvalue (PSV) and weighted-egalitarian Shapley value(WESV) )ey exhibit a number of interesting axiomaticproperties and can be supported from a game-theoreticperspective To effectively distribute four different CDCinfrastructure resources ie CPU memory storage andbandwidth these four solutions can be individually appliedto ensure mutual advantages and they are integrated into afourfold game model to reach an effective solution Duringthe resource allocation process CDC control agents maketheir control decisions to achieve a globally desirable systemperformance while effectively balancing between efficiencyand fairness

12 Main Research Objectives To provide a fair-efficientsolution for the VM resource allocation problem in the CDCsystem we concentrate on the cooperative game-based valuesolutions Our major research objectives are summarized asfollows

(i) According to the cooperative game theory we ex-plore the main concepts of value-based solutions tosolve the VM resource allocation problem in CDCs

(ii) By using the SV WSV PSV and WESV solutionswe develop novel CPU memory storage andbandwidth resource allocation algorithms for eachPM )erefore the CDCrsquos resource allocationproblem is divided into four component parts andour developed algorithms work together and actcooperatively with each other to enhance the systemperformance

(iii) We create a new collaborative fourfold game modelby jointly employing four different resource allo-cation algorithms Our integrated fourfold gameapproach can achieve mutual advantages throughattractive axiomatic properties

(iv) We can effectively strike the appropriate perfor-mance balance between contradictory requirementsbased on the synergy effect which is a consequenceof the reciprocal combination of different valuesolutions

(v) We conduct experiments on extensive simulationsand analyze empirical results to demonstrate theeffectiveness of our fourfold game approach Bydiscussing and analyzing the simulation results wecan confirm the superiority of our proposedscheme compared with the existing state-of-the-artprotocols

13 Organization )e remainder of this paper is organizedas follows In Section 2 we discuss and summarize therelated work followed by the objective of resource allocationsin CDCs Section 3 introduces the overall infrastructure of

2 Mobile Information Systems

CDCs and provides background preliminaries about the SVWSV PSV andWESV And then we outline the main stepsof proposed algorithms and formulate our fourfold gamemodel to design our CDC resource allocation schemeSection 4 presents the experimental setup simulation re-sults and performance evaluation To validate the effec-tiveness of our approach experiments are described whilecomparing our proposed scheme against the existing pro-tocols Finally we conclude this study and discuss the futureresearch directions in Section 5

2 Related Work

Different resource allocation in CDCs has become a com-pelling topic and has been widely studied in the literatureUntil now state-of-the-art literature studies have discussedthe CDC resource allocation problem in various aspectsincluding resource utilization cost scalability overheadand system performance In [8] authors propose two al-gorithms to enhance the multicast capacity Both algorithmsutilize the SDN-based controller system to handle multicastrouting )e key motivation for this paper is the transitionhappening in the uncompressed video transport technolo-gies from legacy non-IP format based on Serial DigitalInterface (SDI) to transport based on IP Major efforts areunderway in the standard bodies to define standards andrelevant encapsulations [8]

)e paper [9] proposes a network-aware VM relocationalgorithm which optimizes the distribution of the VMsrunning on the DC in order to conserve energy in bothservers and network switches It targets the communicatedVMs and places them closer to each other while reducing thetraffic overhead between any communicating VMs )isapproach also increases the VMs consolidation to someservers while leaving other servers idle [9] In [10] Wardatet al propose a new holistic view how to ensure the in-creasing demands for cloud services while guaranteeing themaximum revenue )ey include the power usage optimi-zation technique using a server consolidation approachthrough a formulation of the problem taking into accountthe need for DC expansion while reducing the total oper-ational cost )e server consolidation is achieved by pow-ering off the underutilized servers without impacting thesystem ability to satisfy the customersrsquo service requirements[10]

)e Two-Tiered Resource Allocation (TTRA) schemeproposes a two-tiered on-demand resource allocationmechanism to find a dynamic resource allocation solution[1] To solve the problem of on-demand resource provisionfor VMs the TTRA scheme is consisting of the local andglobal resource allocation methods to improve the efficiencyof CDCs On each server the local on-demand resourceallocation method optimizes the resource allocation to VMswhile considering the allocation threshold )e global on-demand resource allocation method optimizes the resource

allocation among applications at the macro level byadjusting the allocation threshold of each local resourceallocation Local and global resource schedulers reallocateresources by evaluating the arriving workloads To guide thedesign of the on-demand resource allocation algorithms theTTRA scheme dynamically allocates CDC resources to VMsaccording to the time-varying capacity demands and thequality requirements of applications [1]

In the paper [6] the Multiobjective Resource Allocation(MORA) scheme is a new Euclidean distance-based mul-tiobjective resource allocation method for CDCs [6] )isscheme mainly focuses on the key goals of multiobjectiveVM allocation on PMs in CDCs in terms of energy efficiencyand minimization of resource wastage In particular a hy-brid mechanism based on genetic algorithm (GA) particleswarm optimization (PSO) and Euclidean distance is de-veloped to achieve an optimal point of energy efficiency andresource utilization )e core idea of this scheme is to applythe GA for the generation of initial VMs allocation on PMsand then apply the PSO for the improvement of the initialsolution Finally the hybrid approach can get the near globaloptimal solution of the VM allocation problem )e mainobjectives of the MORA scheme are (i) to formulate the VMallocation problem as a multiobjective multidimensionalcombinatorial optimization problem and (ii) to adaptivelyallocate the multiple resources of VMs while minimizing theresource wastage at CDCs [6]

Dai et al propose the Virtual Scheduling-based ResourceAllocation (VSRA) scheme by considering the placement ofVMs onto the servers in CDCs intelligently [11] )e VMplacement problem is formulated as an integer program-ming problem and authors in [11] explore two greedyapproximation algorithms the minimum energy VMscheduling (MinES) algorithm and the minimum commu-nication VM scheduling (MinCS) algorithm )e main goalof MinES and MinCS is to achieve a good feasible solutionIn particular the MinES algorithm avoids powering up extraservers and networking devices by placing VMs on activeservers )e MinCS algorithm attempts to allocate the VMsto decrease the total energy consumption on both networkand servers Both algorithms start from the solution of therelaxed original integer program and attempt to round thesolution intelligently to achieve the minimum energy con-sumption )e search for the solution in both heuristic al-gorithms is guided by a relaxed version of the originalproblem [11]

)ere is also much work done on the resource allocationmethods related to the VM placement in CDCs Especiallythe TTRA MORA and VSRA schemes have attracted a lotof attentions recently they have introduced unique chal-lenges to efficiently solve the resource allocation problem inthe CDC system Compared to these existing schemes in[1 6 11] we demonstrate that our proposed scheme attains abetter performance during the CDC resource allocationoperations

Mobile Information Systems 3

3 Proposed CDC Resource Allocation Scheme

In this section we introduce the infrastructure of the CDCsystem Afterward the basic ideas of SV WSV PSV andWESV solutions are demonstrated to design our CDC re-source allocation scheme And then the proposed protocolis presented in detail based on the fourfold game modelFinally we describe concretely the proposed scheme in thenine-step procedures

31 Cloud-Based DC System Infrastructure )e CDC ar-chitecture is a well-known multitier system infrastructurewhich is composed of routers switches and a large numberof PMs P PM1 PM2 PMn1113864 1113865 Each PM has four dif-ferent resources and the resource of PM1leilen is characterizedby a tuple RPMi

rarr RC

PMiRM

PMiRS

PMiRB

PMi1113966 1113967 indicating the

available resource capacities of PMi in terms of CPU powercapacity (RC

PMi) memory size (RM

PMi) storage space (RS

PMi)

and communication bandwidth (RBPMi

) respectively Tomonitor the available resources an intelligent agent (IA) isdeployed in each PM and periodically adjusts its RPM

rarr Each

IA distributes its associated PMrsquos resources according to thecurrently updated RPM

rarrinformation [6 11 12]

To implement the CDCmanagement paradigm the timeaxis is partitioned into equal intervals of length unit_time(Δt) At each Δt application tasks are received in the CDCand VMs are generated to support the requested tasks Inthis study we assume four different application typesI II III IV Based on the application types execution ofVMs requires different resource amounts with diversifiedpreferences For a given VMj isin V VM1VM2 1113864 1113865the required resource specification and preference are

described by RVMj

rarr RC

VMjRM

VMjRS

VMjRB

VMj1113882 1113883 and

αVMj

rarr αC

TVMj

αMTVMj

αSTVMj

αBTVMj

1113882 1113883 respectively where

TVMjisin I II III IV is the application type of VMj

During the CDC operation |V | ⋟ |P| andRVMrarr

and αVMrarr are

differently decided for each VM )erefore multiple VMsare nested in each PM [6 11 12] )e utility function(UVMj

(RVMj

rarr αVMj

rarr)) of VMj is defined based on the al-

located resources of associated PM UVM(middot) maps servicequality of the target to a benefit value

UVMjRVMj

rarr αVMj

rarrTVMj

X) 1113944Xisin CMSB

αXTVMj

times1

1 + exp AXVMj

RXVMj

1113874 1113875

minus β⎛⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎠⎛⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎠⎛⎜⎜⎜⎜⎜⎜⎜⎜⎝ (1)

where ACVMj

AMVMj

ASVMj

and ABVMj

are the allocated CPUmemory storage and bandwidth resources respectivelyfrom the associated PM β is a control parameter to cal-culate the UVM(middot) When a new application is arrived at theCDC the corresponding VM is generated And then itshould be assigned a specific PM by the CDC controller Inthe proposed scheme we design a novel VM placement

method by considering the PMrsquos resource availabilityFrom a commonsense standpoint our VM placementapproach can be interpreted as a compromise solutionbetween the weighted proportionality and the utilitariansolution According to (2) the new VMj is matched theselected PMi isin M where the PMi is the most adaptable PMto nest the VMj

MAT VMjTVMjPMi1113874 1113875 ≔ max

PMiisinP1113944

Xisin CMSB

αXTVMj

times RXPMi

minus RXVMj

1113874 11138751113874 1113875⎛⎝ ⎞⎠ (2)

At each PM the IA monitors and distributes its re-sources for assigned VMs To effectively share the limitedresources we adopt the cooperative game approach In thispaper we assume that each PM has four different resourcesC M S B )erefore four different cooperative games aredeveloped individually and independently for each re-source distribution in a PM At each Δt these games are

executed in a dispersive and parallel manner )erefore wecan effectively reduce the computation complexity At eachgame model each application type (TVM isin I II III IV )

of VM is assumed as an individual game player ie PI PIIPIII and PIV and utility functions for players are formu-lated First in the PMi the utility functions for the CPUcapacity (C) ieUC

I UCIIU

CIII andU

CIV are defined as follows


UCI RVMk

rarr αVMk

rarr1113874 1113875 1113944

VMkisinPMi

log RCVMk

+ c1113872 1113873αCI timesRC

VMk1113872 1113873

1113888 1113889

UCII RVMk

rarr αVMk

rarr1113874 1113875 1113944

VMkisinPMi

log RCVMk

+ c1113872 1113873αCIItimesR

CVMk

1113872 11138731113888 1113889

UCIII RVMk

rarr αVMk

rarr1113874 1113875 1113944

VMkisinPMi

log RCVMk

+ c1113872 1113873αCIIItimesR

CVMk

1113872 11138731113888 1113889

UCIV RVMk

rarr αVMk

rarr) 1113944

VMkisinPMi

log RCVMk

+ c1113872 1113873αCIVtimesRC

VMk1113872 1113873

1113888 1113889⎛⎝

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)

where c is a control factor to calculate the UCIsim IV(middot) And

then as the same manner as the UCIsim IV utility functions for

other PM resources such as M S and B ie UMIsim IV U

SIsim IV

and UBIsim IV are defined respectively At each Δt UC

Isim IVUMIsim IVU

SIsim IV andU

BIsim IV are examined periodically by the IA

and the C M S and B resources in each individual PM aredistributed for its corresponding VMs

32 Main Concepts of Value-Based Cooperative SolutionsIn 1953 the concept of value in cooperative games wasintroduced by Shapley It is the most eminent allocationrule for cooperative games with transferable utility Hisinitial idea was to answer the question of what a player mayreasonably expect from playing a game As a normative toolto achieve efficiency and symmetry the SV has receivedconsiderable attention in numerous fields and applicationsMany axiomatic characterizations have helped to under-stand the mechanisms underlying the SV In 1959 theconcept of dividend was introduced by Harsanyi it can bedefined inductively )e dividend of the empty set is zeroand the dividend of any other possible coalition of a playerset equals the worth of the coalition minus the sum of alldividends of proper subsets of that coalition )erefore thedividend identifies the surplus that is created by a coalitionof players in a cooperative game and it can be interpretedas the pure contribution of cooperation in a game Harsanyishows that the SV coincides with the payoff that resultsfrom the equal division of dividends within each coalition[13 14]

In 1953 Shapley did consider the possibility for sym-metric players to be treated differently )is asymmetricversion of the SV is obtained by introducing exogenousweights in order to cover asymmetries )e concept of WSVwas introduced as an allocation rule based on weightedcontributions and it had been axiomatized by Kalai andSamet in 1987 Simply the SV splits equally the dividend ofeach coalition among its members but the WSV splits theHarsanyi dividends in proportional to the exogenously givenweights of its members Weights are given by the stand-alone worths of the players and the value associated withpositive weights turns out to result from a weighted divisionof dividendswithin each coalition)us it coincides with theSV whenever all such worths are equal [14]

PSV is another value solution It is similar in spirit to theWSV )erefore the PSV inherits many of the properties ofthe WSV However contrary to the WSV the PSV reservesthe equal treatment property it is a well-defined solution forgames in which the worths of all singleton coalitions havethe same sign Based on the proportional principle the PSVsatisfies proportional aggregate monotonicity but does notsatisfy the classical axioms of linearity and consistency [13]

After the introduction of SV-related solutions manyother axiomatic foundations for the rule were intensivelystudied Usually the SV is an efficient rule that satisfiesstrong monotonicity and symmetry As redistribution rulesthese two properties focus on each playerrsquos contributions ina game to determine their rewards)erefore the SV can bethought of as an allocation rule completely based on eachplayerrsquos performance Recently we face the followingquestion what allocation rule reconciles performance-based evaluation with a solidarity principle and takesplayersrsquo heterogeneity into consideration To answer thisquestion a new solution called WESV was introducedbased on the combination of the SV and the weighteddivision )is solution satisfies weaker monotonicity thisproperty does not require each playerrsquos evaluation to de-pend only on his contribution but rather allows it to dependalso on the worth of the grand coalition to reflect a soli-darity principle [15]

To characterize the basic concepts of value-based solu-tions we preliminarily define some mathematical expres-sions R (R+R++) denote the set of all (nonnegativepositive) real numbers N will denote the set of positiveintegers LetU subeN be a fixed and infinite universe of playersDenote byU the set of all finite subsets ofU is denoted by UA cooperative game is a pair (N v) where N isin U andv 2N⟶ R such that v(empty) 0 For a game (N v) wewrite (S v) for the subgame of (N v) induced by SsubeN byrestricting v to 2S the real number v(S) is the worth of Swhich the members of the coalition S can distribute amongthemselves Let RN(RN

+ RN++) be the N-fold Cartesian

product of R (R+R++) A game (N v) is individuallypositive if v( i )gt 0 for all i isin N and individually negative ifv( i )lt 0 for all i isin N [13]

Define C as the class of all games with a finite player setN Let (N v) isin C and the Harsanyi dividends ΔNv(S)where SsubeN are defined inductively as follows [13 16]


ΔNv(S) v(S) minus 1113936

T sub S

ΔNv(T) if S isin 2N

0 if S empty

⎧⎪⎨

⎪⎩

st v(S) 1113944TsubeSΔNv(T)

(4)

)is formula shows that dividends uniquely determinethe characteristic function Another well-known formula ofthe dividends is given for all SsubeN and Sneempty by the followingequation [17]

ΔNv(S) 1113944TsubeS

(minus1)sminus t

times v(T)1113872 1113873ie

Δv( i ) v( i )

Δv( i j1113864 1113865) v( i j1113864 1113865) minus v( i ) minus v( j1113864 1113865)

Δv( i j k1113864 1113865) v( i j k1113864 1113865) minus v( i j1113864 1113865) minus v( i k ) minus v( j k1113864 1113865) + v( i ) + v( j1113864 1113865) + v( k )

⋮

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(5)

In terms of the distribution of the Harsanyi dividendsthe SV is the value ϕ on C defined as follows [13]

ϕi(N v) 1113944

Sisin2N

iisinS

1|S|

times ΔNv(S)1113888 1113889 stforall(N v) isin Cforalli isin N

(6)

)e WSV with weights w where w (wi isin R++)iisinN and1113936iisinNwi 1 is the value ϕw on C defined as follows [13]

ϕwi (N v) 1113944

Sisin2N

iisinS

wi

1113936jisinSwj

times Δv(S)1113888 1113889 stforall(N v) isin Cforalli isin N

(7)

)e PSV is the value ϕP on C defined as follows [13]

ϕPi (N v) 1113944

Sisin2N

iisinS

v( i )

1113936jisinSv( j1113864 1113865)times Δs(S)1113888 1113889

stforall(N v) isin Cforalli isin N

(8)

)eWESV is the value ϕwminus E on C defined as follows [15]

ϕwminusEi (N v) δ times ϕi(N v)( 1113857 + (1 minus δ) times wi times v(N)( 1113857

st forall(N v) isin Cforalli isin N δ isin [0 1] wiisinN isin R++(9)

If δ 1 the ϕwminusEi (N v) values coincides with the SV and

distributes the surplus v(N) based only on the playersrsquocontributions If δ 0 the ϕwminusE

i (N v) coincides with theweighted division [15]

All the value-based solutions are characterized by a col-lection of desirable axiomsmdashHomogeneity MonotonicityWeak Monotonicity Symmetry Balanced Contributions Effi-ciency Proportional Balanced Contributions w-BalancedContributions Dummy Player Out Ratio Invariance for NullPlayers Proportional Aggregate Monotonicity ProportionalStandardness Standardness Weak Linearity ConsistencyWeakConsistencyWeakDifferentialMarginality for Symmetric

Players and Nullity [13 15] To explain these axioms we needsome prior definitions A value onC is a functionf that assignsa payoff vector f(N v) isin RN to any (N v) isin C andS isin 2N empty Let QA denote the class of all quasiadditivegames In a quasiadditive game the worths of all coalitions areadditive except possibly for the grand coalition for which therecan be some surplus or loss compared to the sum of the stand-alone worths of its members Based on the S andf the reducedgame (S v

f

S ) is defined for all isin 2S [13]

vf

S (T) v(T cup (NS)) minus 1113944iisinNS

fi(T cup (NS) v) (10)

)e concept of the reduced game is used to define theaxiom consistency If f satisfies the axiom efficiency v

f

S (T)

1113936iisinTfi(Tcup (NS) v) [13]

(i) Homogeneity (H) for all (N v) isin C i isin N andα isin R we have fi(N αυ) αfi(N υ)

(ii) Monotonicity (M) for all(N v) isin C and i isin N such that

fi(υ)gefi υprime( 1113857

st υ(S) υprime(S) for S ⊊N

υ(S)ge υprime(S) for S N1113896

(11)

(iii) Weak Monotonicity (WM) for all(N v) (N vprime) isin C with v(N)ge vprime(N) ifv(S) minus v(S i )ge vprime(S) minus vprime(S i ) for all S subeN withi isin S then fi(v)gefi(vprime)

(iv) Symmetry (Sym) for all (N v) isin C and i j isin N

such that i and j are symmetric in (N υ) we havefi(N υ) fj(N υ)

(v) Balanced Contributions (BC) for all (N v) isin C andall i j isin N

fi(N v) minus fi(N j1113864 1113865 v) fj(N v) minus fj(N i v)

(12)

(vi) Efficiency (E) for all (N v) isin C we have1113936iisinNfi(N v) v(N)


(vii) Proportional Balanced Contributions (PBC) for all(N v) isin C and all i j isin N

fi(N v) minus fi(N j1113864 1113865 v)

v( i )

fj(N v) minus fj(N i v)

v( j1113864 1113865) (13)

(viii) w-Balanced Contributions (w-BC) for allw (wi)iisinU with wi isin R++ for all i isin U all(N v) isin C and all i j isin N

fi(N v) minus fi(N j1113864 1113865 v)

wi


wj

(14)

(ix) Dummy Player Out (DPO) for all (N v) isin C ifi isin N is a dummy player in (N v) then for allj isin N i fj(N v) fj(N i v)

(x) Ratio Invariance for Null Players (RIN) for all(N v) (N vprime) isin C and i j isin N such that i and j arenull players in v vprime we havefi(v) times fj(vprime) fi(vprime) times fj(v)

(xi) Proportional Aggregate Monotonicity (PAM) forall b isin R and all (N v) isin C such that nge 2 and alli j isin N

fi(N v) minus fi N v + buN( 1113857

v( i )

fj(N v) minus fj N v + buN( 1113857

v( j1113864 1113865)

(15)

(xii) Proportional Standardness (PS) for all( i j1113864 1113865 v) isin C

fi( i j1113864 1113865 v) v( i )

v( i ) + v( j1113864 1113865)1113888 1113889 times v( i j1113864 1113865) (16)

(xiii) Standardness (S) for all ( ij1113864 1113865v)isinC fi( ij1113864 1113865v)

v( i )+(12)(v( ij1113864 1113865)minusv( i )minusv( j1113864 1113865))

(xiv) Weak Linearity (WL) for all a isin RN++ all b isin R

and all (N v) (N w) isin C if (N bv + w) isin Cthen f(N bv + w) bf(N v) + f(N w)

(xv) Consistency (C) for all (N v) isin C all isin 2N andall i isin S fi(N v) fi(S v

f

S )(xvi) Weak Consistency (WC) for all (N v) isin QA all

S isin 2N such that (S vf

S ) isin QA and all i isin Sfi(N v) fi(S v

f

S )(xvii) Weak Differential Marginality for Symmetric

Players (WDMSP) for all (N v) (N vprime) isin C andi j isin N such that i and j are null players in v ifi j are symmetric in vprime and v(N) vprime(N) thenfi(v) minus fi(vprime) fj(v) minus fj(vprime)

(xviii) Nullity (NY) let Θ be the null game For anyi isin N fi(Θ) 0

)e main notable difference between PBC and w-BC isthat the weights are endogenous ie they can vary acrossgames )e consequence is that the system of equationsgenerated by PBC together with E is not linear Neverthelessit gives rise to a unique nonlinear value WL is combinedwith the axioms E and DPOWM states that a playerrsquos payoffweakly increases as his marginal contributions and the totalvalue weakly increase In contrast with M WM does notinsist that each playerrsquos evaluation totally depends on hiscontributions but rather allows that it can depend on thetotal value RIN requires that as long as some players say i j

and contribute zero in both games v and vprime the ratio of theirpayoffs fi(v)fj(v) does not vary N is a weak feasibilitycondition which requires that every player receives nothingif every coalitionrsquos worth is zero [13 15] In conclusion SVcan be characterized by axiomsmdashBC S Sym E C H MDPO WL and WC )e WSV can satisfy the axioms E HM w-BC DPO and WL for all possible weights w )e PSVis the unique value on C that satisfies E H M DPO PAMPS WL WC and PBC )e WESV satisfies the axioms ESym WM RIN WDMSP and N [13 15]

33 PM Resource Allocation Algorithms for VMs In generalthe limited CDC resource distribution problem mathe-matically corresponds to a bankruptcy game situation Astandard bankruptcy game is given by a finite game playerset N a real positive estate number E and a nonnegativeclaim vector d d1 dn1113864 1113865 isin RN while satisfying1113936iisinNdi ≽ E In the analysis of bankruptcy situation the mainobjective is to obtain a satisfactory mechanism for distrib-uting the estate while verifying two properties the estate hasto be completely distributed among the game players andeach player has to obtain a nonnegative quantity not greaterthan their demand A bankruptcy rule is a map f whichassigns to a payoff vector f(N E d) isin RN such that [18]

1113944iisinN

xi E st 0 ≼ xi ≼ di for all i isin N (17)

For the bankruptcy problem (N E d) a correspondingcooperative bankruptcy game (N vEd) can be defined asfollows [18]

vEd(S) max 0 E minus 1113944jnotinS

dj⎧⎪⎨

⎪⎩(18)

For the SV WSV PSV and WESV the above bank-ruptcy rule can be applied to calculate the characteristicfunction ] for the coalition S (](S)) From the viewpoint ofPMi the IA of PMi observes its resource distribution statusand adjusts its tuple RPMi

rarrat each Δt If the PMirsquos available

resources are not sufficient to support the correspondingVMsrsquo requests the limited resources must be shared intel-ligently taking into account differences of application types


In this study we adopt the value-based cooperativesolutions to design our PM resource allocation algorithmsFor each PM its RC

PMRMPMRS

PM and RBPM resources are

shared by game players PIsimIV which represent applicationtypes According to (3) each player has its own utilityfunction UX with X isin C M S B where UX represents theamount of satisfaction of a player toward the outcome ofresource distribution )e higher the value of the utility thehigher the satisfaction of the player for that outcome Tocalculate the characteristic function (v(S)) of each coalitionS we use the PIsimIVrsquo claim vector dX dX

I dXII dX

III dXIV1113864 1113865

where dXI UX

I (RVMrarr

αVMrarr

) dXII UX

II(RVMrarr

αVMrarr

)dXIII UX

III(RVMrarr

αVMrarr

) and dXIV UX

IV(RVMrarr

αVMrarr

)For the PMi we individually develop the

RCPMi

RMPMi

RSPMi

and RBPMi

resource allocation algorithmsFirst to design the RC

PMiresource allocation algorithm we

consider the features of CPU computation and emphasizethe characteristics of S and C axioms )erefore we adoptthe SV idea as a solution Based on the UC

I simIV(RVMrarr

αVMrarr

)the playersrsquo claim vector dC is defined and v(S) values areobtained using the bankruptcy rule And then the playersPIsimIV share the limited RC

PMiresource according to (6)

)erefore the RCPMi

is divided at the rate of ϕ values and theassigned RC

PMifor the PI(C

PMi

PI) is given by

CPMi

PI

ϕPI(N v)

1113936iisinN ϕi(N v)( 11138571113888 1113889 times R

CPMi

st N PI PII PIII PIV1113864 1113865 RCPM 1113944

iisinNCPMi

i

(19)

Finally the CPMi

PIshould be distributed to the type I VMs

in the PMi In our proposed algorithm the utilitarian idea istaken In the viewpoint of efficiency this idea attempts tomaximize the sum of VMsrsquo effectiveness

arg max AC

VMj1113876 1113877

1113944VMjisinPMi

UVMjRVMj

rarr αVMj

rarrTVMj

C1113874 1113875

⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭

st CPMi

PI 1113944

VMjisinPMi

ACVMj

(20)

To design the RMPM resource allocation algorithm we

consider the features of memory space and emphasize thecharacteristics of w-BC axiom)erefore we adopt theWSVidea as a solution to develop the RM

PM resource allocationalgorithm and the weight w of each player is assigned as hispreference αM

T And then the players PIsimIV share the limitedRM

PM resource according to (7) and the assigned RMPM for

each player is distributed among the same-type individualVMs by using the utilitarian idea as the same manner as theRC

PM resource allocation algorithmTo design the RS

PM resource allocation algorithm weconsider the features of PM storage and emphasize thecharacteristics of PAM PS and PBC axioms )erefore weadopt the PSV idea as a solution to develop theRS

PM resource

allocation algorithm)e playersPIsimIV share the limitedRSPM

resource according to (8) and the assigned RSPM for each

player is distributed among the same-type individual VMs asthe same manner as the RC

PM and RMPM resource allocation

algorithms To design the RBPM resource allocation algo-

rithm we consider the features of PM communicationbandwidth and emphasize the characteristics of RINWDMSP and N axioms )erefore we adopt the WESV ideaas a solution to develop theRB

PM resource allocation algorithmand the players PIsimIV share the limitedRB

PM resource accordingto (9) and the assigned RB

PM for each player is distributedamong the same-type individual VMs as the same manner asthe RC

PM RMPM and RS

PM resource allocation algorithms

34 Main Steps of the Proposed CDC Resource AllocationScheme )e advent of cloud computing is looking forwardto leasing out multiple instances of data centers In additionCDC resources can be shared amongst multiple users byusing the virtualization technology while preventing hardresource commitment and low system utilization VMs canbe dynamically allocated over a DC infrastructure in order toimprove application performance for the users and at thesame time efficiently utilize the CDCrsquos physical resources Inthis study we focus on the main ideas of SV WSV PSV andWESV solutions to solve the resource allocation problem forVMs in the CDC system As we have asserted throughoutthis study the proposed fourfold cooperative game approachis effectively advantageous under different and diversifiedCDC system situations

Our fourfold cooperative game approach can be ana-lyzed in two different ways From a theoretical point of vieweach solution for separate resource allocation process can befeatured by different axioms they characterize each solutionconcept and provide a sound theoretical basis From apractical point of view our main concern is to reduce thecomputation complexity Usually traditional optimal so-lutions need huge computational overheads according totheir complicated and complex computation formulas)erefore they are impractical in real-time process In ourgame model game players are not individual applicationsbut application types it can effectively reduce the compu-tational load )e principle novelties of our approach are ajudicious mixture of different value-based solutions and itsadaptability flexibility and practicality to current systemconditions of the CDC infrastructure )e main steps of theproposed scheme are described as follows

Step 1 at the initial time system factors and controlparameters are determined by a simulation scenario(refer to simulation assumptions and Table 1 in Section4)Step 2 at each Δt application tasks are received in theCDC and VMs are generated as one of four typesI II III IV Each VM has the resource specification

(RVMrarr

) and preference (αVMrarr

) )e utility function ofVM is defined according to (1)Step 3 using (2) the new VM is nested to the mostadaptable PM In each PM there are four resources


RCPMRM

PMRSPMRB

PM1113864 1113865 and multiple VMs are placed Todesign a game model VM types are assumed as playerswho compete with each other for the limited resourcesStep 4 each game playerrsquos utility functions for fourresources are defined based on equation (3) At each Δtthey are examined periodically by each individual IA ina dispersive and parallel mannerStep 5 for the RC

PM resource allocation the SV idea isadopted and the limited RC

PM is shared among gameplayers according to (6) By using (20) the assignedRC

PM for each player is distributed to the same-typeindividual VMs in the associated PMStep 6 for theRM

PM resource allocation theWSV idea isadopted and the limited RM

PM is shared among gameplayers according to (7) By using the same manner asthe RC

PM resource allocation algorithm the assignedRM

PM for each player is distributed to the same-typeindividual VMs in the associated PMStep 7 for the RS

PM resource allocation the PSV idea isadopted and the limited RS


PM and RMPM resource allocation algorithms the

assignedRSPM for each player is distributed to the same-

type individual VMs in the associated PMStep 8 for the RB

PM resource allocation the WESV ideais adopted and the limited RB

PM is shared among gameplayers according to (9) By using the same manner astheRC

PMRMPM andR

SPM resource allocation algorithms

the assigned RBPM for each player is distributed to the

same-type individual VMs in the associated PMStep 9 at each time period each PMrsquos RPM

rarrand utility

functions of VMs are dynamically estimated in anonline manner Constantly each IA in PM is self-monitoring and proceed to Step 2 for the next fourfoldcooperative game iteration

4 Simulation Results and Discussion

In this section the performance of our proposed scheme isevaluated via simulation and compared with that of theexisting TTRA MORA and VSRA schemes [1 6 11] First

of all we introduce the scenario setup of the simulation andsimulation parameters are listed in Table 1

(i) Simulated DC system consists of one DC controllerand n PMs )is structure can be extended hier-archically and recursively

(ii) In order to represent application tasks four dif-ferent applications types mdashI II III and IVmdashareassumed Application tasks are randomly receivedin the CDC system from these four types

(iii) Application tasks generate their correspondingVMs which have different resource requirementsRVMrarr

RCVMRM

VMRSVMRB

VM1113966 1113967 and their pref-erences αVM

rarr αC

TVM αM

TVM αS

TVM αB

TVM1113966 1113967 for four

PM resources(iv) Durations of VM execution are exponentially

distributed with different means for different ap-plication types

(v) )e arrival process for offered number of appli-cations (task generation rate) is Poisson process(ρ) )e offered rate range is varied from 0 to 3

(vi) Each PMrsquos initial resources are 100 THz for RCPM

100GMB for RMPM 1 PMB for RS

PM and 15Gbpsfor RB

PM(vii) )e CDC system performance measures obtained

on the basis of 100 simulation runs are plotted asfunctions of the offered task generation rate (ρ)

According to the simulation metrics the CDC systemthroughput normalized application payoff and average CDCresource utilization are mainly evaluated to demonstrate thevalidity of the proposed approach)e simulation parameters arepresented in Table 1 Each parameter has its own characteristics

In Figure 1 we compare the system throughput in theCDC environment In this study system throughput is therate of successful VM execution in the CDC system Typ-ically throughput is a measure of how many tasks a systemcan process in a given amount of time From the viewpointof the system operator it is a main criterion on the per-formance evaluation In Figure 1 it is observed that ourproposed approach performs better at all levels of task

Table 1 System parameters used in the simulation experiments

Type RC RM RS RB αCI αM

II αSIII αB

IV1113864 1113865 Execution duration averageI 12GHz 350MB 15GB 35Mbps 03 03 02 02 120 unit_time (Δt)

II 18GHz 250MB 20GB 30Mbps 02 04 03 01 200 unit_time (Δt)

III 25GHz 150MB 10GB 45Mbps 01 02 03 04 150 unit_time (Δt)

IV 33GHz 100MB 12GB 25Mbps 04 01 02 03 250 unit_time (Δt)

Parameter Value Descriptionn 12 Number of PMs in the CDC systemβ 05 A control parameter to calculate the UVM(middot)

c 1 A control factor to calculate the UC(middot)

δ 05 A control parameter to calculate the ϕwminus E(middot)

RCPM 100 THz Initial CPU capacity for each PM

RMPM 100GMB Initial memory size for each PM

RSPM 1 PMB Initial storage space for each PM

RBPM 15Gbps Initial communication bandwidth for each PM


generation rate although the gain is very little profit at lowertask rates Note that our fourfold cooperative gamemodel caneffectively allocate the four different CDC resources whileimproving the system throughput )erefore it is easy toconfirm that we can accommodate the increased applicationtasks in the CDC system and maintains the stable perfor-mance superiority under different task load intensitiescompared to the existing TTRA MORA and VSRA schemes

Figure 2 shows the normalized application payoff withdifferent task generation rates From the viewpoint of endusers it is a major factor in the performance analysisUsually as the task generation rate increases the VM executiondelay may occur )erefore normalized application payoff de-creases gradually However in our proposed scheme each IA inPM periodically monitors its available resources and adaptivelydistributes the limited PM resources based on the value-basedsolutions In our fourfold game approach each resource is in-telligently shared among different-type VMswhile attempting tomaximize the sum of same-type VMsrsquo effectiveness )ereforewe can exhibit consistently better performance in applicationpayoff compared to the existing schemes

Figure 3 presents a comparison of performances for theaverage CDC resource utilization As can be observed allschemes have many similarities with the performance ofsystem throughput Traditionally resource utilization isstrongly related to system throughput When the offeredapplication load increases the utilization of PM resources alsoincreases It is intuitively correct In the proposed schemeeach IA adaptively intervenes to maximize the resourceutilization according to the viewpoint of utilitarian idea anddifferent application types reach binding commitments foreach PM resource distribution )erefore individual PMrsquosresources are strategically distributed in the step-by-stepinteractive online manner while satisfying desirable featureswhich are defined as axioms of value-based solutions

)e simulation results displayed in Figures 1ndash3 dem-onstrate that the actual outcome of our scheme is fairly dealt

out compared to the existing schemes and our fourfoldgame approach can attain an appropriate performancebalance between the viewpoints of system operator and endusers conversely the TTRA MORA and VSRA schemescannot offer such an attractive outcome under widely dif-ferent CDC application load intensities

5 Summary and Conclusions

Modern CDCs need to tackle efficiently the increasing de-mand for different resources and address the system effi-ciency challenge)erefore it is essential to develop efficientresource allocation policies that are aware of VM charac-teristics and applicable in dynamic scenarios )is studyhighlights the value-based cooperative game approach andformulates the CDC resource allocation algorithms based on

0 05 1 15 2 25 30

05

1

15

Offered number of applications (task generation rate)

The proposed schemeThe TTRA scheme

The MORA schemeThe VSRA scheme

Ave

rage

CD

C re

sour

ce u

tiliz

atio

n

Figure 3 Average CDC resource utilization

0 05 1 15 2 25 30

01

02

03

04

05

06

07

08

09

1




CDC

syste

m th

roug

hput

Figure 1 CDC system throughput

05 1 15 2 25 30

05

1

15




Nor

mal

ized

appl

icat

ion

payo

ff

Figure 2 Normalized application payoff


the SV WSV PSV and WESV solutions To effectivelydistribute the CPU memory storage and bandwidth re-sources individual cooperative game models are designedseparately )ey exhibit a number of interesting axiomaticproperties and can be supported from a game-theoreticperspective According to the developed fourfold gamemodel different resources in each PM are assigned forcorresponding VMs to achieve a ldquowin-winrdquo situation underdynamic CDC environments Compared to the existingprotocols the extensive simulations show that our proposedscheme delivers near-optimal CDC resource efficiency withvarious different application demands while other TTRAMORA and VSRA schemes cannot provide such a well-balanced system performance

Given the extensiveness of the CDC resource allocationmethods it is also concluded that more rigorous investi-gations are required with greater attentions )erefore therewill be different open issues and practical challenges for thefuture study First we will further explore the VMmigrationissue among PMs in CDCs and moreover we will developmore metrics to measure the quality of related algorithmsSecond we will also investigate the network topology ofCDCs and the different network capabilities among themAnother important factor is the network topology RunningVMs may need to communicate with each other due to theworkload dependencies )erefore by monitoring the VMrsquoscommunications we will develop an efficient VM allocationmethod to decrease the overhead of data communicationsLast but not least we are keen to implement our protocol toreal test-bed and analyze the CDC performance which ishopeful to achieve valuable experience for practitioners

Data Availability

)e data used to support the findings of the study areavailable from the corresponding author upon request(swkim01sogangackr)

Conflicts of Interest

)e author declares that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

)is research was supported by the MSIT (Ministry ofScience and ICT) Korea under the ITRC (InformationTechnology Research Center) support program (IITP-2019-2018-0-01799) supervised by the IITP (Institute for Infor-mation amp communications Technology Planning amp Evalu-ation) and was supported by Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Education (NRF-2018R1D1A1A09081759)

References

[1] Y Song Y Sun and W Shi ldquoA two-tiered on-demand re-source allocation mechanism for VM-based data centersrdquo

IEEE Transactions on Services Computing vol 6 no 1pp 116ndash129 2013

[2] R Cziva S Jouet D Stapleton F P Tso and D P PezarosldquoSDN-based virtual machine management for cloud datacentersrdquo IEEE Transactions on Network and Service Man-agement vol 13 no 2 pp 212ndash225 2016

[3] K Wang Q Zhou S Guo and J Luo ldquoCluster frameworksfor efficient scheduling and resource allocation in data centernetworks a surveyrdquo IEEE Communications Surveys amp Tuto-rials vol 20 no 4 pp 3560ndash3580 2018

[4] R Rojas-Cessa Y Kaymak and Z Dong ldquoSchemes for fasttransmission of flows in data center networksrdquo IEEE Com-munications Surveys amp Tutorials vol 17 no 3 pp 1391ndash14222015

[5] R Xie YWen X Jia andH Xie ldquoSupporting seamless virtualmachine migration via named data networking in cloud datacenterrdquo IEEE Transactions on Parallel and Distributed Sys-tems vol 26 no 12 pp 3485ndash3497 2015

[6] N K Sharma and G R M Reddy ldquoMulti-objective energyefficient virtual machines allocation at the cloud data centerrdquoIEEE Transactions on Services Computing vol 12 no 1pp 158ndash171 2019

[7] S Kim Game Ceory Applications in Network Design IGIGlobal Hershey PA USA 2014

[8] A Latif P Kathail S Vishwarupe S Dhesikan A Khreishahand Y Jararweh ldquoMulticast optimization for CLOS fabric inmedia data centersrdquo IEEE Transactions on Network andService Management vol 16 no 4 pp 1855ndash1868 2019

[9] O Al-Jarrah Z Al-Zoubi and Y Jararweh ldquoIntegratednetwork and hosts energy management for cloud data cen-tersrdquo Transactions on Emerging Telecommunications Tech-nologies vol 30 no 9 pp 1ndash22 2019

[10] M Wardat M Al-Ayyoub Y Jararweh and A A KhreishahldquoCloud data centers revenue maximization using serverconsolidation modeling and evaluationrdquo Proceedings of theIEEE International Conference on Computer Communicationspp 172ndash177 Honolulu HI USA April 2018

[11] X Dai J M Wang and B Bensaou ldquoEnergy-efficient virtualmachines scheduling in multi-tenant data centersrdquo IEEETransactions on Cloud Computing vol 4 no 2 pp 210ndash2212016

[12] F-H Tseng X Wang L-D Chou H-C Chao andV C M Leung ldquoDynamic resource prediction and allocationfor cloud data center using the multiobjective genetic algo-rithmrdquo IEEE Systems Journal vol 12 no 2 pp1688ndash1699 2018

[13] S Beal S Ferrieres E Remila and P Solal ldquo)e proportionalShapley value and applicationsrdquo Games and Economic Be-havior vol 108 pp 93ndash112 2018

[14] P Dehez ldquoOn Harsanyi dividends and asymmetric valuesrdquoInternational Game Ceory Review vol 19 no 3 pp 1ndash362017

[15] T Abe and S Nakada ldquo)e weighted-egalitarian Shapleyvaluesrdquo Social Choice and Welfare vol 52 no 2 pp 197ndash2132019

[16] R van den Brink R Levınsky and M Zeleny ldquo)e Shapleyvalue the proper Shapley value and sharing rules for co-operative venturesrdquoOperations Research Letters vol 48 no 1pp 55ndash60 2020

[17] M Besner ldquoAxiomatizations of the proportional Shapleyvaluerdquo Ceory and Decision vol 86 no 2 pp 161ndash183 2019

[18] M Pulido J Sanchez-Soriano and N Llorca ldquoGame theorytechniques for university management an extended bank-ruptcy modelrdquo Annals of Operations Research vol 109no 1ndash4 pp 129ndash142 2002


)e properties of CDCs and the mechanisms for limitedresource allocations largely define the operation and per-formance of the CDC system In order to be sustainable thesignificant capital outlay required for building a CDC makesmaximization of Return on Investment (RoI) crucial whichin turn necessitates efficient and adaptive CDC resourceusage Moreover the economic viability of a CDC greatlydepends on running the CDC at acceptable performancelevels and allowing users and applications to highly utilizeand share its infrastructure and resources In summary theperformance of CDCs is directly associated with how toimprove the resource usability However the average CDCresource utilization has found to be low typically rangingfrom 10 to 20 percent )erefore it is necessary to increasethe resource utilization for the CDC system efficiency[2 4 5]

Recently virtualization technology has been touted as arevolutionary technology to tackle the low-utilizationproblem in CDCs Initially virtualization began in the1960s as a method of creating a virtual version of some-thing including virtual computer hardware platformsstorage devices and computer network resources Sincethen the meaning of the term has broadened In CDCsdifferent physical resources are logically partitioned andmultiplexed among different applications )rough virtu-alization technology virtual machines (VMs) are createdaccording to usersrsquo demands and users execute their ap-plications on the VMs that are indeed running on physicalmachines (PMs) Usually multiple VMs can be created on aPM using the virtualization software )erefore PM re-source distribution for VMs is a hot research topic toimprove the PM utilization With multiple resource re-quests finding an optimal solution of PM resource dis-tribution problem will thus create a lot of challenges to theresearchers However under a complicated scenario tra-ditional resource allocation approach suffers from ex-tremely high computational complexity and controloverhead )erefore we need a new control paradigm toeffectively mediate between the implementation practi-cality and the system optimality [5 6]

11 Cooperative Game-Based Value Solutions Game theoryis a theoretical framework for conceiving situations amongcompeting players In some respects game theory is thescience of strategy or at least the optimal decision-making ofindependent and competing players in a strategic settingGame theory has two major subdivisions noncooperativeand cooperative game theory In cooperative game theoryrational players will find ways to commit themselves to theagreement and enjoy the benefits that arise from theagreement Indeed one possibility is that a group of playersmay cooperate to exploit another player or group of players)e value is a central solution concept in the cooperativegame theory In 1953 the basic concept of value was in-troduced by Shapley for the study of cooperative games Andthen the idea of value solutions has been extended in dif-ferent ways some of the most notable values solutions aredeveloped by Harsanyi and Shapley [7]

Recently value-based cooperative game approaches havebeen widely investigated to solve the resource allocationproblems In this study we design a new VM resource al-location scheme based on four value solutions Shapley value(SV) weighted Shapley value (WSV) proportional Shapleyvalue (PSV) and weighted-egalitarian Shapley value(WESV) )ey exhibit a number of interesting axiomaticproperties and can be supported from a game-theoreticperspective To effectively distribute four different CDCinfrastructure resources ie CPU memory storage andbandwidth these four solutions can be individually appliedto ensure mutual advantages and they are integrated into afourfold game model to reach an effective solution Duringthe resource allocation process CDC control agents maketheir control decisions to achieve a globally desirable systemperformance while effectively balancing between efficiencyand fairness

12 Main Research Objectives To provide a fair-efficientsolution for the VM resource allocation problem in the CDCsystem we concentrate on the cooperative game-based valuesolutions Our major research objectives are summarized asfollows

(i) According to the cooperative game theory we ex-plore the main concepts of value-based solutions tosolve the VM resource allocation problem in CDCs

(ii) By using the SV WSV PSV and WESV solutionswe develop novel CPU memory storage andbandwidth resource allocation algorithms for eachPM )erefore the CDCrsquos resource allocationproblem is divided into four component parts andour developed algorithms work together and actcooperatively with each other to enhance the systemperformance

(iii) We create a new collaborative fourfold game modelby jointly employing four different resource allo-cation algorithms Our integrated fourfold gameapproach can achieve mutual advantages throughattractive axiomatic properties

(iv) We can effectively strike the appropriate perfor-mance balance between contradictory requirementsbased on the synergy effect which is a consequenceof the reciprocal combination of different valuesolutions

(v) We conduct experiments on extensive simulationsand analyze empirical results to demonstrate theeffectiveness of our fourfold game approach Bydiscussing and analyzing the simulation results wecan confirm the superiority of our proposedscheme compared with the existing state-of-the-artprotocols

13 Organization )e remainder of this paper is organizedas follows In Section 2 we discuss and summarize therelated work followed by the objective of resource allocationsin CDCs Section 3 introduces the overall infrastructure of



2 Related Work












rarr RC

PMiRM

PMiRS

PMiRB





PMi)



rarr Each




described by RVMj

rarr RC

VMjRM

VMjRS

VMjRB

VMj1113882 1113883 and

αVMj

rarr αC

TVMj

αMTVMj

αSTVMj

αBTVMj




and αVMrarr are


(RVMj

rarr αVMj



UVMjRVMj

rarr αVMj

rarrTVMj


αXTVMj

times1

1 + exp AXVMj

RXVMj

1113874 1113875

minus β⎛⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎠⎛⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎠⎛⎜⎜⎜⎜⎜⎜⎜⎜⎝ (1)

where ACVMj

AMVMj

ASVMj

and ABVMj




PMiisinP1113944

Xisin CMSB

αXTVMj

times RXPMi

minus RXVMj

1113874 11138751113874 1113875⎛⎝ ⎞⎠ (2)




I UCIIU

CIII andU



UCI RVMk

rarr αVMk

rarr1113874 1113875 1113944

VMkisinPMi

log RCVMk

+ c1113872 1113873αCI timesRC

VMk1113872 1113873

1113888 1113889

UCII RVMk

rarr αVMk

rarr1113874 1113875 1113944

VMkisinPMi

log RCVMk

+ c1113872 1113873αCIItimesR

CVMk

1113872 11138731113888 1113889

UCIII RVMk

rarr αVMk

rarr1113874 1113875 1113944

VMkisinPMi

log RCVMk


CVMk

1113872 11138731113888 1113889

UCIV RVMk

rarr αVMk

rarr) 1113944

VMkisinPMi

log RCVMk


VMk1113872 1113873

1113888 1113889⎛⎝

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)




SIsim IV


Isim IVUMIsim IVU

SIsim IV andU













T sub S


0 if S empty

⎧⎪⎨

⎪⎩


(4)



(minus1)sminus t

times v(T)1113872 1113873ie

Δv( i ) v( i )



⋮

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(5)


ϕi(N v) 1113944

Sisin2N

iisinS

1|S|


(6)


ϕwi (N v) 1113944

Sisin2N

iisinS

wi

1113936jisinSwj


(7)


ϕPi (N v) 1113944

Sisin2N

iisinS

v( i )



(8)









f


vf




f

S (T)







(11)






(12)




fi(N v) minus fi(N j1113864 1113865 v)

v( i )


v( j1113864 1113865) (13)


fi(N v) minus fi(N j1113864 1113865 v)

wi


wj

(14)





v( i )


v( j1113864 1113865)

(15)


fi( i j1113864 1113865 v) v( i )

v( i ) + v( j1113864 1113865)1113888 1113889 times v( i j1113864 1113865) (16)






f




f







1113944iisinN




dj⎧⎪⎨

⎪⎩(18)






PMRMPMRS



I dXII dX

III dXIV1113864 1113865

where dXI UX

I (RVMrarr

αVMrarr

) dXII UX

II(RVMrarr

αVMrarr

)dXIII UX

III(RVMrarr

αVMrarr

) and dXIV UX

IV(RVMrarr

αVMrarr


RCPMi

RMPMi

RSPMi

and RBPMi




I simIV(RVMrarr

αVMrarr



)erefore the RCPMi


PMifor the PI(C

PMi

PI) is given by

CPMi

PI

ϕPI(N v)


CPMi


iisinNCPMi

i

(19)

Finally the CPMi



arg max AC

VMj1113876 1113877

1113944VMjisinPMi

UVMjRVMj

rarr αVMj

rarrTVMj

C1113874 1113875

⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭

st CPMi

PI 1113944

VMjisinPMi

ACVMj

(20)









PM resource










PM RMPM and RS





(RVMrarr




RCPMRM

PMRSPMRB
















PMRMPM andR




rarrand utility








RCVMRM

VMRSVMRB


rarr αC

TVM αM

TVM αS

TVM αB

TVM1113966 1113967 for four






PM and 15Gbpsfor RB







II αSIII αB




















0 05 1 15 2 25 30

05

1

15




Ave

rage

CD

C re

sour

ce u

tiliz

atio

n


0 05 1 15 2 25 30

01

02

03

04

05

06

07

08

09

1




CDC

syste

m th

roug

hput


05 1 15 2 25 30

05

1

15




Nor

mal

ized

appl

icat

ion

payo

ff





Data Availability




Acknowledgments


References






















2 Related Work












rarr RC

PMiRM

PMiRS

PMiRB





PMi)



rarr Each




described by RVMj

rarr RC

VMjRM

VMjRS

VMjRB

VMj1113882 1113883 and

αVMj

rarr αC

TVMj

αMTVMj

αSTVMj

αBTVMj




and αVMrarr are


(RVMj

rarr αVMj



UVMjRVMj

rarr αVMj

rarrTVMj


αXTVMj

times1

1 + exp AXVMj

RXVMj

1113874 1113875

minus β⎛⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎠⎛⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎠⎛⎜⎜⎜⎜⎜⎜⎜⎜⎝ (1)

where ACVMj

AMVMj

ASVMj

and ABVMj




PMiisinP1113944

Xisin CMSB

αXTVMj

times RXPMi

minus RXVMj

1113874 11138751113874 1113875⎛⎝ ⎞⎠ (2)




I UCIIU

CIII andU



UCI RVMk

rarr αVMk

rarr1113874 1113875 1113944

VMkisinPMi

log RCVMk

+ c1113872 1113873αCI timesRC

VMk1113872 1113873

1113888 1113889

UCII RVMk

rarr αVMk

rarr1113874 1113875 1113944

VMkisinPMi

log RCVMk

+ c1113872 1113873αCIItimesR

CVMk

1113872 11138731113888 1113889

UCIII RVMk

rarr αVMk

rarr1113874 1113875 1113944

VMkisinPMi

log RCVMk


CVMk

1113872 11138731113888 1113889

UCIV RVMk

rarr αVMk

rarr) 1113944

VMkisinPMi

log RCVMk


VMk1113872 1113873

1113888 1113889⎛⎝

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)




SIsim IV


Isim IVUMIsim IVU

SIsim IV andU













T sub S


0 if S empty

⎧⎪⎨

⎪⎩


(4)



(minus1)sminus t

times v(T)1113872 1113873ie

Δv( i ) v( i )



⋮

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(5)


ϕi(N v) 1113944

Sisin2N

iisinS

1|S|


(6)


ϕwi (N v) 1113944

Sisin2N

iisinS

wi

1113936jisinSwj


(7)


ϕPi (N v) 1113944

Sisin2N

iisinS

v( i )



(8)









f


vf




f

S (T)







(11)






(12)




fi(N v) minus fi(N j1113864 1113865 v)

v( i )


v( j1113864 1113865) (13)


fi(N v) minus fi(N j1113864 1113865 v)

wi


wj

(14)





v( i )


v( j1113864 1113865)

(15)


fi( i j1113864 1113865 v) v( i )

v( i ) + v( j1113864 1113865)1113888 1113889 times v( i j1113864 1113865) (16)






f




f







1113944iisinN




dj⎧⎪⎨

⎪⎩(18)






PMRMPMRS



I dXII dX

III dXIV1113864 1113865

where dXI UX

I (RVMrarr

αVMrarr

) dXII UX

II(RVMrarr

αVMrarr

)dXIII UX

III(RVMrarr

αVMrarr

) and dXIV UX

IV(RVMrarr

αVMrarr


RCPMi

RMPMi

RSPMi

and RBPMi




I simIV(RVMrarr

αVMrarr



)erefore the RCPMi


PMifor the PI(C

PMi

PI) is given by

CPMi

PI

ϕPI(N v)


CPMi


iisinNCPMi

i

(19)

Finally the CPMi



arg max AC

VMj1113876 1113877

1113944VMjisinPMi

UVMjRVMj

rarr αVMj

rarrTVMj

C1113874 1113875

⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭

st CPMi

PI 1113944

VMjisinPMi

ACVMj

(20)









PM resource










PM RMPM and RS





(RVMrarr




RCPMRM

PMRSPMRB
















PMRMPM andR




rarrand utility








RCVMRM

VMRSVMRB


rarr αC

TVM αM

TVM αS

TVM αB

TVM1113966 1113967 for four






PM and 15Gbpsfor RB







II αSIII αB




















0 05 1 15 2 25 30

05

1

15




Ave

rage

CD

C re

sour

ce u

tiliz

atio

n


0 05 1 15 2 25 30

01

02

03

04

05

06

07

08

09

1




CDC

syste

m th

roug

hput


05 1 15 2 25 30

05

1

15




Nor

mal

ized

appl

icat

ion

payo

ff





Data Availability




Acknowledgments


References
























rarr RC

PMiRM

PMiRS

PMiRB





PMi)



rarr Each




described by RVMj

rarr RC

VMjRM

VMjRS

VMjRB

VMj1113882 1113883 and

αVMj

rarr αC

TVMj

αMTVMj

αSTVMj

αBTVMj




and αVMrarr are


(RVMj

rarr αVMj



UVMjRVMj

rarr αVMj

rarrTVMj


αXTVMj

times1

1 + exp AXVMj

RXVMj

1113874 1113875

minus β⎛⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎠⎛⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎠⎛⎜⎜⎜⎜⎜⎜⎜⎜⎝ (1)

where ACVMj

AMVMj

ASVMj

and ABVMj




PMiisinP1113944

Xisin CMSB

αXTVMj

times RXPMi

minus RXVMj

1113874 11138751113874 1113875⎛⎝ ⎞⎠ (2)




I UCIIU

CIII andU



UCI RVMk

rarr αVMk

rarr1113874 1113875 1113944

VMkisinPMi

log RCVMk

+ c1113872 1113873αCI timesRC

VMk1113872 1113873

1113888 1113889

UCII RVMk

rarr αVMk

rarr1113874 1113875 1113944

VMkisinPMi

log RCVMk

+ c1113872 1113873αCIItimesR

CVMk

1113872 11138731113888 1113889

UCIII RVMk

rarr αVMk

rarr1113874 1113875 1113944

VMkisinPMi

log RCVMk


CVMk

1113872 11138731113888 1113889

UCIV RVMk

rarr αVMk

rarr) 1113944

VMkisinPMi

log RCVMk


VMk1113872 1113873

1113888 1113889⎛⎝

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)




SIsim IV


Isim IVUMIsim IVU

SIsim IV andU













T sub S


0 if S empty

⎧⎪⎨

⎪⎩


(4)



(minus1)sminus t

times v(T)1113872 1113873ie

Δv( i ) v( i )



⋮

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(5)


ϕi(N v) 1113944

Sisin2N

iisinS

1|S|


(6)


ϕwi (N v) 1113944

Sisin2N

iisinS

wi

1113936jisinSwj


(7)


ϕPi (N v) 1113944

Sisin2N

iisinS

v( i )



(8)









f


vf




f

S (T)







(11)






(12)




fi(N v) minus fi(N j1113864 1113865 v)

v( i )


v( j1113864 1113865) (13)


fi(N v) minus fi(N j1113864 1113865 v)

wi


wj

(14)





v( i )


v( j1113864 1113865)

(15)


fi( i j1113864 1113865 v) v( i )

v( i ) + v( j1113864 1113865)1113888 1113889 times v( i j1113864 1113865) (16)






f




f







1113944iisinN




dj⎧⎪⎨

⎪⎩(18)






PMRMPMRS



I dXII dX

III dXIV1113864 1113865

where dXI UX

I (RVMrarr

αVMrarr

) dXII UX

II(RVMrarr

αVMrarr

)dXIII UX

III(RVMrarr

αVMrarr

) and dXIV UX

IV(RVMrarr

αVMrarr


RCPMi

RMPMi

RSPMi

and RBPMi




I simIV(RVMrarr

αVMrarr



)erefore the RCPMi


PMifor the PI(C

PMi

PI) is given by

CPMi

PI

ϕPI(N v)


CPMi


iisinNCPMi

i

(19)

Finally the CPMi



arg max AC

VMj1113876 1113877

1113944VMjisinPMi

UVMjRVMj

rarr αVMj

rarrTVMj

C1113874 1113875

⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭

st CPMi

PI 1113944

VMjisinPMi

ACVMj

(20)









PM resource










PM RMPM and RS





(RVMrarr




RCPMRM

PMRSPMRB
















PMRMPM andR




rarrand utility








RCVMRM

VMRSVMRB


rarr αC

TVM αM

TVM αS

TVM αB

TVM1113966 1113967 for four






PM and 15Gbpsfor RB







II αSIII αB




















0 05 1 15 2 25 30

05

1

15




Ave

rage

CD

C re

sour

ce u

tiliz

atio

n


0 05 1 15 2 25 30

01

02

03

04

05

06

07

08

09

1




CDC

syste

m th

roug

hput


05 1 15 2 25 30

05

1

15




Nor

mal

ized

appl

icat

ion

payo

ff





Data Availability




Acknowledgments


References





















UCI RVMk

rarr αVMk

rarr1113874 1113875 1113944

VMkisinPMi

log RCVMk

+ c1113872 1113873αCI timesRC

VMk1113872 1113873

1113888 1113889

UCII RVMk

rarr αVMk

rarr1113874 1113875 1113944

VMkisinPMi

log RCVMk

+ c1113872 1113873αCIItimesR

CVMk

1113872 11138731113888 1113889

UCIII RVMk

rarr αVMk

rarr1113874 1113875 1113944

VMkisinPMi

log RCVMk


CVMk

1113872 11138731113888 1113889

UCIV RVMk

rarr αVMk

rarr) 1113944

VMkisinPMi

log RCVMk


VMk1113872 1113873

1113888 1113889⎛⎝

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)




SIsim IV


Isim IVUMIsim IVU

SIsim IV andU













T sub S


0 if S empty

⎧⎪⎨

⎪⎩


(4)



(minus1)sminus t

times v(T)1113872 1113873ie

Δv( i ) v( i )



⋮

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(5)


ϕi(N v) 1113944

Sisin2N

iisinS

1|S|


(6)


ϕwi (N v) 1113944

Sisin2N

iisinS

wi

1113936jisinSwj


(7)


ϕPi (N v) 1113944

Sisin2N

iisinS

v( i )



(8)









f


vf




f

S (T)







(11)






(12)




fi(N v) minus fi(N j1113864 1113865 v)

v( i )


v( j1113864 1113865) (13)


fi(N v) minus fi(N j1113864 1113865 v)

wi


wj

(14)





v( i )


v( j1113864 1113865)

(15)


fi( i j1113864 1113865 v) v( i )

v( i ) + v( j1113864 1113865)1113888 1113889 times v( i j1113864 1113865) (16)






f




f







1113944iisinN




dj⎧⎪⎨

⎪⎩(18)






PMRMPMRS



I dXII dX

III dXIV1113864 1113865

where dXI UX

I (RVMrarr

αVMrarr

) dXII UX

II(RVMrarr

αVMrarr

)dXIII UX

III(RVMrarr

αVMrarr

) and dXIV UX

IV(RVMrarr

αVMrarr


RCPMi

RMPMi

RSPMi

and RBPMi




I simIV(RVMrarr

αVMrarr



)erefore the RCPMi


PMifor the PI(C

PMi

PI) is given by

CPMi

PI

ϕPI(N v)


CPMi


iisinNCPMi

i

(19)

Finally the CPMi



arg max AC

VMj1113876 1113877

1113944VMjisinPMi

UVMjRVMj

rarr αVMj

rarrTVMj

C1113874 1113875

⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭

st CPMi

PI 1113944

VMjisinPMi

ACVMj

(20)









PM resource










PM RMPM and RS





(RVMrarr




RCPMRM

PMRSPMRB
















PMRMPM andR




rarrand utility








RCVMRM

VMRSVMRB


rarr αC

TVM αM

TVM αS

TVM αB

TVM1113966 1113967 for four






PM and 15Gbpsfor RB







II αSIII αB




















0 05 1 15 2 25 30

05

1

15




Ave

rage

CD

C re

sour

ce u

tiliz

atio

n


0 05 1 15 2 25 30

01

02

03

04

05

06

07

08

09

1




CDC

syste

m th

roug

hput


05 1 15 2 25 30

05

1

15




Nor

mal

ized

appl

icat

ion

payo

ff





Data Availability




Acknowledgments


References






















T sub S


0 if S empty

⎧⎪⎨

⎪⎩


(4)



(minus1)sminus t

times v(T)1113872 1113873ie

Δv( i ) v( i )



⋮

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(5)


ϕi(N v) 1113944

Sisin2N

iisinS

1|S|


(6)


ϕwi (N v) 1113944

Sisin2N

iisinS

wi

1113936jisinSwj


(7)


ϕPi (N v) 1113944

Sisin2N

iisinS

v( i )



(8)









f


vf




f

S (T)







(11)






(12)




fi(N v) minus fi(N j1113864 1113865 v)

v( i )


v( j1113864 1113865) (13)


fi(N v) minus fi(N j1113864 1113865 v)

wi


wj

(14)





v( i )


v( j1113864 1113865)

(15)


fi( i j1113864 1113865 v) v( i )

v( i ) + v( j1113864 1113865)1113888 1113889 times v( i j1113864 1113865) (16)






f




f







1113944iisinN




dj⎧⎪⎨

⎪⎩(18)






PMRMPMRS



I dXII dX

III dXIV1113864 1113865

where dXI UX

I (RVMrarr

αVMrarr

) dXII UX

II(RVMrarr

αVMrarr

)dXIII UX

III(RVMrarr

αVMrarr

) and dXIV UX

IV(RVMrarr

αVMrarr


RCPMi

RMPMi

RSPMi

and RBPMi




I simIV(RVMrarr

αVMrarr



)erefore the RCPMi


PMifor the PI(C

PMi

PI) is given by

CPMi

PI

ϕPI(N v)


CPMi


iisinNCPMi

i

(19)

Finally the CPMi



arg max AC

VMj1113876 1113877

1113944VMjisinPMi

UVMjRVMj

rarr αVMj

rarrTVMj

C1113874 1113875

⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭

st CPMi

PI 1113944

VMjisinPMi

ACVMj

(20)









PM resource










PM RMPM and RS





(RVMrarr




RCPMRM

PMRSPMRB
















PMRMPM andR




rarrand utility








RCVMRM

VMRSVMRB


rarr αC

TVM αM

TVM αS

TVM αB

TVM1113966 1113967 for four






PM and 15Gbpsfor RB







II αSIII αB




















0 05 1 15 2 25 30

05

1

15




Ave

rage

CD

C re

sour

ce u

tiliz

atio

n


0 05 1 15 2 25 30

01

02

03

04

05

06

07

08

09

1




CDC

syste

m th

roug

hput


05 1 15 2 25 30

05

1

15




Nor

mal

ized

appl

icat

ion

payo

ff





Data Availability




Acknowledgments


References






















fi(N v) minus fi(N j1113864 1113865 v)

v( i )


v( j1113864 1113865) (13)


fi(N v) minus fi(N j1113864 1113865 v)

wi


wj

(14)





v( i )


v( j1113864 1113865)

(15)


fi( i j1113864 1113865 v) v( i )

v( i ) + v( j1113864 1113865)1113888 1113889 times v( i j1113864 1113865) (16)






f




f







1113944iisinN




dj⎧⎪⎨

⎪⎩(18)






PMRMPMRS



I dXII dX

III dXIV1113864 1113865

where dXI UX

I (RVMrarr

αVMrarr

) dXII UX

II(RVMrarr

αVMrarr

)dXIII UX

III(RVMrarr

αVMrarr

) and dXIV UX

IV(RVMrarr

αVMrarr


RCPMi

RMPMi

RSPMi

and RBPMi




I simIV(RVMrarr

αVMrarr



)erefore the RCPMi


PMifor the PI(C

PMi

PI) is given by

CPMi

PI

ϕPI(N v)


CPMi


iisinNCPMi

i

(19)

Finally the CPMi



arg max AC

VMj1113876 1113877

1113944VMjisinPMi

UVMjRVMj

rarr αVMj

rarrTVMj

C1113874 1113875

⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭

st CPMi

PI 1113944

VMjisinPMi

ACVMj

(20)









PM resource










PM RMPM and RS





(RVMrarr




RCPMRM

PMRSPMRB
















PMRMPM andR




rarrand utility








RCVMRM

VMRSVMRB


rarr αC

TVM αM

TVM αS

TVM αB

TVM1113966 1113967 for four






PM and 15Gbpsfor RB







II αSIII αB




















0 05 1 15 2 25 30

05

1

15




Ave

rage

CD

C re

sour

ce u

tiliz

atio

n


0 05 1 15 2 25 30

01

02

03

04

05

06

07

08

09

1




CDC

syste

m th

roug

hput


05 1 15 2 25 30

05

1

15




Nor

mal

ized

appl

icat

ion

payo

ff





Data Availability




Acknowledgments


References






















PMRMPMRS



I dXII dX

III dXIV1113864 1113865

where dXI UX

I (RVMrarr

αVMrarr

) dXII UX

II(RVMrarr

αVMrarr

)dXIII UX

III(RVMrarr

αVMrarr

) and dXIV UX

IV(RVMrarr

αVMrarr


RCPMi

RMPMi

RSPMi

and RBPMi




I simIV(RVMrarr

αVMrarr



)erefore the RCPMi


PMifor the PI(C

PMi

PI) is given by

CPMi

PI

ϕPI(N v)


CPMi


iisinNCPMi

i

(19)

Finally the CPMi



arg max AC

VMj1113876 1113877

1113944VMjisinPMi

UVMjRVMj

rarr αVMj

rarrTVMj

C1113874 1113875

⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭

st CPMi

PI 1113944

VMjisinPMi

ACVMj

(20)









PM resource










PM RMPM and RS





(RVMrarr




RCPMRM

PMRSPMRB
















PMRMPM andR




rarrand utility








RCVMRM

VMRSVMRB


rarr αC

TVM αM

TVM αS

TVM αB

TVM1113966 1113967 for four






PM and 15Gbpsfor RB







II αSIII αB




















0 05 1 15 2 25 30

05

1

15




Ave

rage

CD

C re

sour

ce u

tiliz

atio

n


0 05 1 15 2 25 30

01

02

03

04

05

06

07

08

09

1




CDC

syste

m th

roug

hput


05 1 15 2 25 30

05

1

15




Nor

mal

ized

appl

icat

ion

payo

ff





Data Availability




Acknowledgments


References





















RCPMRM

PMRSPMRB
















PMRMPM andR




rarrand utility








RCVMRM

VMRSVMRB


rarr αC

TVM αM

TVM αS

TVM αB

TVM1113966 1113967 for four






PM and 15Gbpsfor RB







II αSIII αB




















0 05 1 15 2 25 30

05

1

15




Ave

rage

CD

C re

sour

ce u

tiliz

atio

n


0 05 1 15 2 25 30

01

02

03

04

05

06

07

08

09

1




CDC

syste

m th

roug

hput


05 1 15 2 25 30

05

1

15




Nor

mal

ized

appl

icat

ion

payo

ff





Data Availability




Acknowledgments


References




























0 05 1 15 2 25 30

05

1

15




Ave

rage

CD

C re

sour

ce u

tiliz

atio

n


0 05 1 15 2 25 30

01

02

03

04

05

06

07

08

09

1




CDC

syste

m th

roug

hput


05 1 15 2 25 30

05

1

15




Nor

mal

ized

appl

icat

ion

payo

ff





Data Availability




Acknowledgments


References























Data Availability




Acknowledgments


References





















cooperative game-based virtual machine resource allocation

Documents