phased scheduling for resource-constrained mobile devices in mobile cloud computing

Wireless Pers CommunDOI 10.1007/s11277-014-1669-3

Phased Scheduling for Resource-Constrained MobileDevices in Mobile Cloud Computing

Chunlin Li · Layuan Li

© Springer Science+Business Media New York 2014

Abstract Mobile cloud computing combines wireless access service and cloud computingto improve the performance of mobile applications. Mobile cloud computing can balancethe application distribution between the mobile device and the cloud, in order to achievefaster interactions, battery savings and better resource utilization. To support mobile cloudcomputing, the paper proposes a phased scheduling model of mobile cloud such that mobiledevice’s users experience lower interaction times and extended battery life. The phasedscheduling optimization is solved by two subproblems: mobile device’s batch applicationoptimization and mobile device’s job level optimization. At the first stage, the mobile cloudglobal scheduling optimization implements the allocation of the cloud resources to the mobiledevice’s batch applications. At the second stage, mobile device’s job level optimization adjuststhe cloud resource usages to optimize the utility of single mobile device’s application. In thesimulations, compared with other algorithm, our proposed mobile cloud phased schedulingalgorithms achieve the better performance with acceptable overhead.

Keywords Cloud computing · Mobile cloud · Phased scheduling · Mobile device

1 Introduction

With the advances in technologies of wireless communications and portable devices, mobilecomputing has become integrated into our every day life. With increased mobility, users needto run stand-alone and/or to access remote mobile applications on mobile devices. Mobilecloud computing can accommodate complex applications which have been impractical to runsolely on smartphones, such as perception applications, vision, graphics and E-learning. Thereare three approaches to construct mobile cloud: 1) accessing cloud resources from mobile

C. Li (B) · L. LiDepartment of Computer Science, Wuhan University of Technology, Wuhan 430063,People’s Republic of Chinae-mail: [email protected]

L. Lie-mail: [email protected]

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devices; 2) enabling mobile devices to work collaboratively as cloud resource providers;3) augmenting the execution of mobile applications using cloud resources. Mobile devicesevolve from being mere intermediaries between the cloud and the end user into true intermedi-aries of cloud computing. Mobile cloud can facilitate the use of mobile devices to collect data,manipulate it and interact with scientific workflows running in the Cloud. By deploying data-intensive computation and data storage to the Cloud, the mobile cloud can release mobilesfrom heavy computational loads, thereby reducing mobile energy consumption, while usingthe cloud to increase processing power and storage capacity.

Dynamic resource provisioning and scheduling is one of most challenging problems inmobile cloud computing. Scheduling problem between resource-constrained devices andcloud resource provider in mobile cloud computing have attracted attention of the researchcommunity in the last years. However, little research focused on mobile cloud phased schedul-ing optimization for mobile device users and cloud resource providers, also on how theirinteractions are modeled to maximize their benefit.

The paper proposes a phased scheduling model of mobile cloud such that users experi-ence lower interaction times and extended battery life. The paper focuses batch processingapplications for mobile cloud computing environment. Our contributions have three aspects.

(1) The phased scheduling optimization is solved by two subproblems: mobile device’sbatch application optimization and mobile device’s job level optimization. At the firststage, the mobile cloud global scheduling optimization implements the allocation of thecloud resources to the mobile device’s batch applications. At the second stage, mobiledevice’s job level optimization adjusts the cloud resource usages to optimize the utilityof single mobile device’s application.

(2) We exploit a utility-driven approach solve interaction among mobile device users andcloud provider in mobile cloud. The paper presents an economics-based mobile cloudphased scheduling algorithm for balancing cost and benefits of mobile device users andcloud resource providers in mobile cloud.

(3) We demonstrate the efficiency of the proposed algorithm through extensive simulations.In the simulations, compared with other algorithm, our proposed mobile cloud phasedscheduling algorithms achieve the better performance with acceptable overhead.

The rest of the paper is structured as followings. Section 2 discusses the related works.Section 3 presents system model of phased scheduling in mobile cloud computing. Section 4presents the mathematic formulation and optimization solution. Section 5 presents mobilecloud phased scheduling algorithm. In Sect. 6 the experiments are conducted and discussed.Section 7 gives the conclusions to the paper.

2 Related Works

Recent research work has been focused on mobile cloud computing, which enables a newmodel of running applications between resource-constrained devices and Internet-basedCloud. Hoang et al. [1] study an admission control problem and adaptive resource allocationfor running mobile applications on a cloudlet. They formulate an optimization problem fordynamic resource sharing of mobile users in mobile cloud computing (MCC) hotspot witha cloudlet as a semi-Markov decision process (SMDP). Mishra et al. [2] propose a mobilecloud computing architecture to integrate mobile application with various cloud services.They aim at using cloud computing techniques for storage and processing of data on mobiledevices. Klein et al. [3] study intelligent access for mobile cloud. They exploit the specificinformation available by the Mobile Cloud Controller, i.e., the users’ location, context, and

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requested services, and significantly evolve the heterogeneous access management schemesdeveloped for the traditional heterogeneous access scenarios. Chun et al. [4] present thedesign and implementation of CloneCloud, a system that automatically transforms mobileapplications to benefit from the cloud. CloneCloud uses a combination of static analysis anddynamic profiling to partition applications automatically at a fine granularity while optimiz-ing execution time and energy use for a target computation and communication environment.Abolfazli et al. [5] propose a market-oriented architecture based on SOA to stimulate publish-ing, discovering, and hosting services on nearby mobiles, which reduces long WAN latencyand creates a business opportunity that encourages mobile owners to embrace service host-ing. Zhang et al. [6] propose a new elastic application model that enables seamless andtransparent use of cloud resources to augment the capability of resource-constrained mobiledevices.

Verbelen et al. [7] present a cloudlet architecture that not only provides fixed infrastruc-ture colocated with the WiFi access point, but also enables ad hoc discovery of devicesin the vicinity to share resources among each other. Park et al. [8] study mobile devicesas resources in mobile cloud environments. They propose a resource allocation techniquewhich offers reliable resource allocation considering the availability of mobile resources andmovement reliability of mobile resources. Flores et al. [9] design a middleware framework,Mobile Cloud Middleware (MCM), which handles the interoperability issues and eases theuse of process-intensive services from smartphones by extending the concept of mobile host.Ge et al. [10] propose a game-theoretic approach to optimize the overall energy in a mobilecloud computing system. They formulate the energy minimization problem as a conges-tion game, where each mobile device is a player and the strategy is to select one of theservers to offload the computation while minimizing the overall energy consumption. Songet al. [11] propose m-TMS (Mobile Trusted Monitoring System) that monitors the trustedstate of a computing environment. La et al. [12] present a framework for enabling context-aware mobile services. The framework enables tasks of capturing context, determining whatcontext-specific adaptation is needed. Niyato et al. [13] consider a mobile cloud computingenvironment in which the service providers can form a coalition to create a resource poolto support the mobile applications. The admission control mechanism is used to provideservices of mobile applications to the users given the available long-term reserved resourcesin a pool. For a given coalition of service providers, the revenue obtained from utilizing theresource pool has to be shared among the service providers. A coalitional game model isdeveloped for sharing the revenue. Ma et al. [14] migrate computation among mobile nodesand cloud nodes. Asynchronous migration technique is used to allow migrations to take placevirtually anywhere in the user codes.

Sanaei et al. [15] propose an arbitrated multi-tier infrastructure model named SAMI forMCC. The main strength of this architecture is in its multi-tier infrastructure layer whichleverages infrastructures from three main sources of Clouds, Mobile Network Operators(MNOs), and MNOs’ authorized dealers. Nguyen et al. [16] formulate the service imageplacement problem as an optimization problem by minimizing the cost function that is thecombination of composite cost and resource demand. Gu et al. [17] propose a deploymentscheme to offload expensive computational tasks from thin, mobile devices to powered,powerful devices on the cloud so that they could prolong battery life for mobile devices,meanwhile provide rich user experiences for such mobile applications. Yang et al. [18] studythe partitioning problem for mobile data stream applications, where the optimization is placedon achieving high throughput of processing the streaming data rather than minimizing themakespan of executions as in other applications. Lu et al. [19] introduce the concept ofan Internet-based Virtual Computing Environment (iVCE), which aims to provide Cloud

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Fig. 1 Mobile cloud environment

services by a dynamic combination of data centers and other multi-scale computing resourceson the Internet. Li et al. [20] propose Armada, an efficient range query processing schemeto support delay-bounded single-attribute and multiple-attribute range queries. Our previouswork [21] mainly dealt with resource allocation, QoS optimization in the grid computingenvironment. Reference [22] presents optimal resource provisioning for cloud computingenvironment.

The methods and contributions of this paper are different from above related works.The paper studies phased scheduling optimization in mobile cloud computing. The phasedscheduling optimization is solved by two subproblems: mobile device’s batch applicationoptimization and mobile device’s job level optimization.

3 System Model of Phased Scheduling in Mobile Cloud Computing

Figure 1 illustrates a mobile cloud system. The mobile cloud system consists of mobiledevices and cloud datacenter. The mobile device can access cloud datacenter by wirelesscommunication network. In wireless communication network, the mobile device connects toits base station (BS). The cloud datacenters and mobile cloud proxies run on wired networks,while mobile devices run on wireless network. Each mobile device communicates with thecloud datacenter through the mobile network. The mobile cloud proxy acts as an interme-diary that is hosted on the cloud datacenter which provides mobile devices access to cloudservices. The mobile cloud proxy improves interaction between mobile devices and cloudservices. When the mobile device’s application sends a request to the mobile cloud proxy, itimmediately gets a response that the transaction has been delegated to remote execution inthe cloud center. Once the process is finished at the cloud center, the notification about theresult of the task is sent back to the mobile device.

Figure 2 provides an overview of the architecture of mobile cloud service schedulingand provisioning, which consists of a mobile service interface that constructs service formobile device users, a cloud environment containing various services, and mobile cloudphase scheduling layer.

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Mobile cloud service interface

Mobile cloud phased scheduling optimization

mobile users

service provisioning

VM allocation

Cloud environment

Fig. 2 Architecture of mobile cloud service scheduling and provisioning

In order to achieve phased scheduling for data-intensive batch applications in mobilecloud, the phased scheduling optimization is deployed at two phases: mobile device’s batchapplication optimization and mobile device’s job level optimization. At the first phase, themobile cloud system scheduling implements the allocation of VMs to the mobile device’sbatch applications. The mobile device’s batch applications scheduling coordinate the deploy-ments of all mobile device’s applications that consume the VMs provided by mobile cloudcenters. At the second phase, mobile device’s job level scheduling adjusts the mobile cloudresource usages to maximize the utility of single mobile device’s application. The mobiledevice’s job level scheduling scheme attempts to greedily maximize the utility function. Foreach possible VM provisioning determined by the mobile cloud batch application scheduler,the mobile device job level scheduling scheme sends back the optimal payment for leasingVMs. The mobile device’s batch application scheduling scheme calculates the VMs alloca-tion that maximizes mobile cloud global utility. The information of VMs allocation is sentto each mobile device job level scheduler; the utility of the mobile device’s application willbe recalculated. For mobile device’s batch application optimization, mobile device’s batchapplications acquire VMs from the cloud resource provider.

Mobile device’s batch applications’ optimization scheme dynamically reconfigures VMsallocation among the batch applications based on calculation of utility maximization. Itmanages the allocation of VMs among the mobile device’s batch applications. The mobiledevice’s batch applications’ scheduling can be viewed as an optimization problem where theinputs are the available resources in cloud datacenter and the requirements of the mobiledevice’s batch applications. The output of mobile device’s batch applications schedulingis the VMs allocation for each mobile device’s application. When allocating the available

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VMs among the mobile device’s batch applications, the mobile device’s batch applicationsscheduler computes what utility the mobile cloud system would attain. The goal of mobiledevice’s batch applications scheduling is to allocate VMs among mobile device’s applicationsfor maximizing the total utility of mobile device’s applications under the constraints.

4 Phased Scheduling in Mobile Cloud: Mathematic Formulation and Solutions

4.1 Mathematic Formulation

The notations used in the following sections are listed on Table 1.It is assumed that the mobile cloud system consists of multiple mobile cloud providers

and mobile device applications. It is assumed that the mobile cloud datacenter consistsof a set of physical machines which can host multiple virtual machines. It is hosted bymobile cloud provider who sells VMs using a pay-per-use payment model. Each mobilecloud provider may have different resource such as storage and compute power. LetV M = {vm1, vm2 . . . vm j ..vmn} denote n classes of VMs. Let v j

i denote the amount of VMsfor mobile device’s application i from mobile cloud provider j . Let C P = {cp1, cp2 . . . cp j }denote the set of mobile cloud providers. Each mobile cloud provider supplies a pool ofresources to host VM for the mobile device’s batch application. C j denotes the maximumnumber of VMs, which can be rented for the mobile device. M D = (M D1, M D2, . . . M Di )

denote the set of mobile devices. The mobile cloud provider provides the VMs for execut-ing mobile device’s batch applications. The mobile device application’ jobs are assumedto be computationally intensive. As soon as a job of the mobile device application arrives,it must be assigned to one VM for processing. Let a mobile device m has batch applica-tions A = {A1, A2 . . . Ai }. The set of all jobs generated by mobile device’s application iis denoted fi = { f 1

i , f 2i . . . f n

i }. Each mobile device application’s job can be described asf ni = (tn

i , qni ), in which tn

i stands for the time taken by the i-th mobile device application tocomplete n-th job, qn

i stands for the size of mobile device application’ s nth job.

Table 1 The description of notations

Notations Meanings

vji Provisioned VM for mobile device ’s application i from the mobile cloud provider j

Tk The deadline given by the mobile device’s batch application k

C j The maximum capacity of mobile cloud provider j

tni The time taken by the mobile device ’s application i to complete nth job

t ik The time taken by i th application in the mobile device’s batch application k

r ji The payments of the mobile device’s application i to mobile cloud provider j for running VM

Ek The budget of mobile device’s batch application k

Ti The deadline given by mobile device’s application i

en j The energy dissipation used by j th mobile cloud provider to support VMs

D j Limit of energy consumption of mobile cloud provider j

Bi The budget of mobile device’s application i

sni The payment of the nth job of mobile device’s application i

qni Computation task of i th mobile device’s application’s nth job

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In phased scheduling model of mobile cloud, the utility functions are used to evaluate thebenefits of mobile device’s batch applications and mobile cloud datacenters. UMCC is theutility of mobile cloud system which considers both mobile device’s batch applications andmobile cloud providers. UM Dbatchapp

(k) is the utility of mobile device’s batch application

k. Uiapp

(k)is the utility of i-th application of mobile device’s batch application k. Mobile

cloud system utility is sum of the mobile device’s batch application’s utility and mobile cloudprovider’ utility:

UMCC =K∑

k=1

UMDbatchapp(k) + UMC P (4.1)

The utility of mobile device’s batch application is defined as.

UMDbatchapp(k) =

I∑

i

U iapp

(k)(4.2)

UMDbatchapp(k) =

(Tk − K

I∑

i=1

t ik

)+

(Ek −

I∑

i=1

r ji

)(4.3)

UMDbatchapp(k) is aimed to maximize the mobile device’s batch applications’ benefit to pay

less money and complete all applications of the mobile device as soon as possible. UMC P

presents the benefit of mobile cloud provider. In UMC P , we could have chosen any otherform for the utility that increases with r j

i . But we chose the log function because the benefitincreases quickly from zero as the provisioned VMs increase from zero and then increasesslowly.

UMC P =N∑

i=1

r ji log v

ji − en j (4.4)

In phased scheduling model of mobile cloud, the objective of mobile device’s batch appli-cations optimization is to provision VMs for batch applications such that the mobile cloudutility UMCC is maximized subject to the resource constraints of mobile cloud datacenter andthe requirements of mobile device’s batch applications respectively. The problem of mobilecloud phased scheduling optimization is formulated as the follows:

MaxUMCC

s.tC j ≥ ∑i

vji , Tk ≥

I∑i=1

t ik, Ek ≥

I∑i=1

r ji , en j ≤ D j

(4.5)

Formula 4.5 is global optimization objective for mobile cloud system. Formula 4.5 representsthe global utility function, which is constructed by the mobile device’s batch application’sutility and mobile cloud provider’s utility. Formula 4.5 is the linear construction of all factorsthat includes specific constraints of mobile device’s application and mobile cloud providerwhich includes cost, time, energy constraints and resource capacity. The utility function ofFormula 4.5 takes a system view and combines the perspectives of mobile device’s appli-cation and mobile cloud provider. It aims to jointly optimize the benefit of mobile device’sapplication and mobile cloud provider.

vji is the VM for mobile device ’s application i from the mobile cloud provider j . The

constraint implies that the aggregate VMs can’t exceed the total number of VMs of mobilecloud provider j . Other constraints are related with mobile cloud applications. The objec-tive of mobile device’s batch applications is to complete a sequence of applications within

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specified deadline,Tk , while the total payment cannot exceed the budget Ek ,∑I

i=1 r ji are

the payments of the mobile device’s batch applications to the mobile cloud provider j forprovisioned VMs respectively.

MaxUMCC =K∑

k=1

((Tk −

I∑

i=1

t ik

)+

(Ek −

I∑

i=1

r ji

))+

N∑

i=1

(r j

i log vji

)− en j

s.tC j ≥∑

i

vji , Tk ≥

I∑

i=1

t ik, Ek ≥

I∑

i=1

r ji , en j ≤ D j (4.6)

Let us consider the Lagrangian form of mobile cloud phased scheduling optimization prob-lem:

L =K∑

k=1

((Tk −

I∑

i=1

t ik

)+

(Ek −

I∑

i=1

r ji

))+

N∑

i=1

(r j

i log vji

)− en j

+ λ

(C j −

∑

i

vji

)+ β

(Tk −

I∑

i=1

t ik

)+ μ

(Ek −

I∑

i=1

r ji

)+ σ

(en j − D j

)(4.7)

Where λi is the Lagrangian multiplier. Solving the optimization function MaxUMCC requiresthe coordination of mobile device’s batch applications, but it is unrealistic for mobile cloud.In order to achieve a distributed solution, we must divide the mobile cloud phased schedulingoptimization into divisible subproblem.

Since the Lagrangian is separable, the maximization of the Lagrangian can be processed inparallel by mobile device’s batch applications and mobile cloud providers respectively. Themobile device’s batch application optimization problem leads to a decomposition of problemMaxUMCC into two subproblems MCP and MDBA, which are respectively conducted bymobile device’s batch applications and mobile cloud providers as follows:

MCP :MaxUMCP =

N∑i=1

(r j

i log vji

)− en j

s.tC j≥∑i

vji , en j ≤ D j

(4.8)

MDBA :MaxUM Dbatchapp =

K∑k=1

((Tk −

I∑i=1

t ik

)+

(Ek −

I∑i=1

r ji

))

s.tTk ≥I∑

i=1t ik, Ek ≥

I∑i=1

r ji

(4.9)

Subproblem MCP is conducted by the mobile cloud provider, different mobile cloudproviders compete for provisioning the VMs for mobile device’s batch applications and max-imizing the revenue. The mobile cloud providers attempt to maximize the benefit functionand minimize the payment of the mobile device’s batch applications and energy consumptionfor provisioning VMs. To provision VMs for mobile device’s batch applications, the mobilecloud provider has to pay for the energy cost depending on its electricity price. The mobilecloud provider need maximize the benefit function without exceeding maximal energy con-straints. Subproblem MDBA is conducted by the mobile device’s batch applications, the batchapplications calculate the optimal payment to mobile cloud providers under the constraintsto maximize mobile device’s batch applications’ satisfaction. Mobile device’s applications igives the payment r j

i to the mobile cloud provider j for running VMs. Ek − ∑Ii=1 r j

i repre-

sents the budget surpluses of mobile device’s batch applications.(

Tk − ∑Ii=1 t i

k

)represents

the deadline of mobile device’s batch applications subtracting actual spending time.

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In mobile cloud phased scheduling optimization model, for job-level optimization prob-lem, a mobile device’s application needs to complete a sequence of jobs within the deadline,Ti , while minimizing the cost occurred and processing time. We assume that each job ofmobile device’s application i submits sn

i for the VM. Mobile device’s jobs compete forthe resources of mobile cloud application i . The resources allocated to mobile device’sjobs depend on the relative payments sent by all jobs. The nth mobile device’s jobs receivemobile cloud resources proportional to its payment. Given the deadline Ti for mobile device’sapplicationi to complete all jobs, the job-level optimization scheduling in mobile cloud canbe formulated as:

MDJ : MaxUM D J ={(

Bi − ∑n

sni

)+

(Ti − ∑

ntni

)}

s.tTi ≥ ∑n

tni

(4.10)

4.1.1 Optimization Solutions

4.1.2 Mobile Device’s Batch Applications Scheduling Optimization

In mobile cloud phased scheduling optimization model, mobile device’s batch applicationoptimization in mobile cloud is aimed at provisioning VMs to mobile device’s batch applica-tions for high level optimization such as maximizing the mobile cloud global utility under theconstraints of mobile cloud provider and mobile device’s batch applications. Mobile cloudglobal optimization considers both mobile device’s batch applications and mobile cloudproviders. The mobile cloud global optimization is divided into two subproblems, which aresolved by the mobile cloud providers and mobile device’s batch applications. A mobile cloudprovider supports multiple VMs to run and complete the jobs for mobile device’s batch appli-cations, the mobile cloud provider has to pay for the energy consumption according to theelectricity price px j . The objective of mobile cloud provider optimization is to maximize therevenue of providing VMs for mobile device’s batch applications and minimize the energycost. For the mobile cloud provider’s optimization problem, different mobile cloud providerscompute VMs for maximizing the revenue.

In (4.8), Mobile cloud provider’s optimization aims at calculating the optimal VM vj∗i for

mobile device’s batch applications while maximizing the benefit function of mobile cloudprovider without exceeding the total number of VMs and upper payment of energy consump-tion. The VMs allocated to mobile device’s batch applications are constrained by the totalof capacity of mobile cloud providers. Total allocated VMs don’t exceed the total capacityC j . For the mobile cloud provider’s optimization problem, mobile cloud providers computeoptimal VMs to maximize the benefit function and minimize the payment for providing VMsto mobile device’s batch applications. The profits of mobile cloud provider are affected by thepayments of mobile device’s batch applications and energy payment of provisioning VMs. Sothe revenue of mobile cloud provider increases when the VMs leased to the mobile device’sbatch applications increase and the payments received from mobile devices increase, also thepayment for energy consumption decreases.

∑Ni=1(r

ji log v

ji ) presents the revenue obtained

by mobile cloud provider j from mobile device’s batch applications. The objective of mobilecloud provider is to maximize the revenue and minimize energy consumption en j .

Mobile device’s batch application adaptively submit the demand of VM based on thecurrent conditions of mobile cloud provider, while the mobile cloud provider adaptivelyallocates VMs required by the mobile device’s batch applications. The interaction betweenmobile device’s batch applications and mobile cloud provider is controlled through the use

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of the variable p j , which are the price charged from mobile device’s batch applications bymobile cloud provider and regulates the mobile device’s batch applications’ VM demand andthe VM supply of mobile cloud provider

en j = px j ∗N∑

i=1

ec ji (4.11)

In above equation, px j denote electricity price. The energy consumption rate of mobile cloudprovider for hosting VMs is denoted as ej. The energy consumption cost of mobile cloudprovider for hosting VMs can’t exceed more than D j , which is the maximal payment forenergy consumption.

The electrical energy consumption used by mobile cloud provider j to run VM for mobiledevice’s application i denoted as ec j

i can be written as following:

ec ji = e j ∗ v

ji (4.12)

We reformulate mobile cloud provider’s optimization problem as

Max∑(

r ji log v

ji

)− px j

N∑

i=1

e j ∗ vji (4.13)

The Lagrangian for UMC P (vji ) is

L(vji ) =

∑(r j

i log vji

)− px j

N∑

i=1

e j ∗ vji + λ

(C−

j

∑

i

vji

)+ η(D j − px j

N∑

i=1

e j∗vji )

(4.14)

Where λ, η are the Lagrangian constants. From Karush–Kuhn–Tucker Theorem we know

that the optimal solution is given ∂L(vji )

/∂v

ji = 0 for λ > 0.

∂L(vji )

/∂v

ji = r j

i

vji

− (1 + λ + η)px j e j (4.15)

Let

∂L(vji )

/∂v

ji = 0 v

ji = r j

i

(1 + λ + η)px j e j(4.16)

Using this result in the constraint equation, we can determine ω = 1 + η + λ as

D j = 1

ω

∑r j

i , ω =∑

r ji

D j,

We obtain

vj∗i = r j

i D j

px j e j∑

r j (cpu)i

(4.17)

It means that mobile cloud providers calculate optimal VM vj∗i to host VM for mobile device’s

application i while maximizing its benefit.

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The mobile device’s application i is the consumer of mobile cloud provider, which pro-vision VMs for mobile device’s application. We assume that mobile device’s application isubmits payment r j

i to the mobile cloud provider j for VM. Let r ji is the payment of the i th

mobile device’s application. N mobile device’s applications compete for the VMs. Mobilecloud provider’s VMs are allocated using a market mechanism, where the divisions dependon the relative payments sent by the mobile device’s batch applications.

Let’s consider the interactions of mobile device’s application i and mobile cloud providerin mobile cloud. We assume that mobile device’s application i is associated with the benefitfunction Ui

app . The benefit function for mobile device’s application i depends on provisioned

VMvji . For the mobile device’s batch application optimization problem, the mobile device’s

application i calculates the unique optimal payment to mobile cloud provider under theconstraints to maximize the mobile device’s batch application’s benefit. The payment accruedto buy or lease VMs cannot exceed the budget of mobile device’s batch application Ek .

The mobile device’s batch applications give the unique optimal payment to mobile cloudproviders under the constraints of the deadline and budget to maximize the set of mobiledevice’s batch applications’ benefits.

The time taken by the mobile device’s batch application to complete i th application is:

t ik = p j

C jrj

i

(4.18)

The mobile device’s batch application optimization problem can be reformulated as follows.

Max

(Tk − K

∑i

p j

C j rj

i

)+

(Ek − ∑

jr j

i

)

s.tTk ≥I∑

i=1t ik, Ek ≥

I∑i=1

r ji

(4.19)

Let the pricing policy, p = (p1, p2, . . . , p j ), denote the set of VM prices of all mobile cloudproviders. The mobile device’s application i receives the VMs according to its paymentrelative to the sum of the mobile cloud provider’s revenue.

The Lagrangian associated with problem UM Dbatchapp for the mobile device’s application

i’s utility is L(r ji )

L(r ji ) =

⎛

⎝Ek −∑

j

r ji

⎞

⎠ +⎛

⎝Tk − K∑

j

p j

C jrj

i

⎞

⎠

+β

⎛

⎝Ek −∑

j

r ji

⎞

⎠ + η

⎛

⎝Tk − K∑

j

p j

C jrj

i

⎞

⎠ (4.20)

Where β, η is the Lagrangian constant. From Karush–Kuhn–Tucker Theorem we know that

the optimal solution is given ∂L/

∂r ji = 0 for β > 0.

∂L(r ji )

/∂r j

i = −1 + Kp j

C j (rj

i )2− β + ηK

p j

C j (rj

i )2(4.21)

Let ∂L/

∂r ji = 0 to obtain

r j (cpu)i =

((kη + k)p j

(1 + β)C j

)1/2

(4.22)

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Using this result in the constraint equation, we can determine θ = (kη+k)(1+β)

as

(θ)−1/2 = Tk

∑Jj=1

(p jC j

)1/2 (4.23)

We substitute θ to obtain r j∗i

r j∗i =

(p j

C j

)1/2∑J

j=1

(p jC j

)1/2

Tk(4.24)

The mobile device’s application i wants to pay r j∗i to mobile cloud provider j for VMs.

4.1.3 Mobile Device’s Job Level Optimization

In mobile cloud phased scheduling model, mobile device’s job level scheduling optimizationin mobile cloud is conducted by mobile device’s application; the mobile device’s applicationcalculates the payment to mobile cloud provider under the deadline to satisfy the mobile cloudapplication’s requirements. Bi −∑

n sni is the surplus of all jobs of mobile device’s application.∑

n tni represents the execution time for processing all mobile device application’s jobs. The

objective of job level scheduling optimization is to minimize the cost of mobile device’sapplications and complete all jobs as soon as possible. Under the constraint of the deadline,mobile device application i wants to complete all jobs. qn

i is the computation task of i th mobiledevice application’s nth job. The execution time taken by the i th mobile device applicationto complete nth job is:

tni = qn

i

vji sn

i

(4.25)

We reformulate (4.10)

Max

{(Bi −

∑

n

sni

)+

(Ti −

N∑

n=1

qni

vji sn

i

)}(4.26)

The Lagrangian for UM D J utility is L(sni ).

L(sni ) =

(Bi −

∑

n

sni

)+

(Ti −

N∑

n=1

qni

vji sn

i

)+ λ

(Ti −

N∑

n=1

tni

)(4.27)

Where λ is the Lagrangian constant. From Karush–Kuhn–Tucker Theorem we know that the

optimal solution is given ∂L(sni )

/∂sn

i = 0 for λ > 0.

Using this result in the constraint equation, we can determine θ = 1 + λ as

(θ)−1/2 = Ti

∑Nn=1

(qn

i

vji

)1/2 (4.28)

We substitute θ to qni obtain

sn∗i =

(qn

i

vji

)1/2∑N

n=1

(qn

i

vji

)1/2

Ti(4.29)

It means that nth job of mobile device’s application i want to pay sn∗i for the cloud resource.

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5 Phased Scheduling Algorithm for Data-Intensive Batch Applications in MobileCloud

The phased scheduling algorithms in mobile cloud include two algorithms: mobile device’sbatch application optimization algorithm and mobile device’s job level optimization algo-rithm respectively. In mobile device’s batch application optimization algorithm, the mobiledevice’s batch application solves the fees to pay for VMs, sends VM demands and notifiesthe mobile cloud providers about VMs demand. After the new VM demand is observed bythe mobile cloud providers, they publishes VM prices and sends the new prices to the mobiledevice’s batch application, and the cycle repeats. In mobile device’s job level optimizationalgorithm, the mobile device’s job in a mobile cloud application calculates the paymentto mobile cloud provider under the deadline constraint to maximize the mobile device’sbatch application’s utility. The proposed algorithm is used to describe mobile cloud phasedscheduling, which includes mobile device’s batch application optimization algorithm formobile cloud global utility and mobile device’s job level optimization algorithm for mobiledevice’s application.

6 Experiments

In this section, we evaluate the performance of proposed phased scheduling algorithm inmobile cloud (PSA). We simulate a mobile cloud environment with a 2 dimension areaof 500 m*500 m to study mobile device’s behavior. Each mobile device in the simulatedenvironment has a maximal radio range of 100 m, and moves following a random-walkingmobility model. The average speed of each mobile device is 5 m per second. The averagedistance between neighboring devices is 25 m. Mobile devices dynamically enter and leavethe mobile cloud. There are a number of parameters associated with each mobile device usersuch as the deadline, the budget and a two-dimension position value. In the experiments, thecost of cloud datacenter resource and the energy usage are expressed in dollar that can bedefined as unit resource or energy processing cost. The initial price of electrical energy forcloud datacenter is set from 1 to 100 dollars. The initial price of VM is set from 10 to 500dollars. There are 40 mobile devices and 12 cloud resource provider, all of which contributeresources to the mobile cloud environment. Mobile cloud proxy residing in WLANs, actingas the interface point between the mobile devices. All Wi-Fi interfaces operate at a rateof 11Mb/s. All Ethernet interfaces operate at a rate of 10 Gb/s. Jobs arrive at each cloudnode si , i = 1, 2, . . ., n according to a Poisson process with rate α. The energy cost can beexpressed in the dollar that can be defined as unit energy processing cost. Mobile device userssubmit their jobs with varying deadlines. The deadlines of mobile device user are chosenfrom 100 to 400 ms. The budgets of mobile device users are set from 100 to 1,500 dollars.Each experiment is repeated 6 times and 95 % confidence intervals are obtained. Simulationparameters are listed in Table 2.

The experiments aimed at comparing our phased scheduling algorithm in mobile cloud(PSA) with [13] proposed by Niyato et al. The authors consider a mobile cloud comput-ing environment in which the service providers can form a coalition to create a resourcepool to support the mobile applications. Choosing the reference [13] as the comparison hastwo reasons. The first reason is that the reference [13] also aims to solve the problem ofresource allocation in mobile cloud environment. The second reason is reference [13] alsouses economic method in mobile cloud.

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C. Li, L. Li

Niyato et al. [13] study multiple service providers cooperatively offer mobile services tothe users. Mobile applications are supported by the mobile cloud service providers in whichthe radio and computing resources in terms of bandwidth and servers are reserved for theusers. To improve the resource utilization and revenue, mobile service providers can cooperateto form a coalition and create a resource pool for the users running mobile applications. Theadmission control of this cooperative environment has been developed based on optimizationformulation. With a coalition, mobile cloud providers can optimize the capacity expansion,which determines the reserved bandwidth and servers to be contributed to a resource pool.The objective of mobile cloud provider is to maximize the profit from supporting mobileapplications through a resource pool. In [13], the author proposes distributed algorithm forcapacity expansion game of mobile cloud service providers, which is denoted as CEG in thispaper.

To evaluate the performance of our phased scheduling algorithm in mobile cloud (PSA)against distributed algorithm for capacity expansion game of mobile cloud service providers

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Table 2 Simulation parameters Simulation Parameter Value

Total number of mobile device users 40

Total number of cloud providers 12

Mobility model Random-walking mobility

Average speed of mobile device 5 m/s

Initial price of VM [10, 500]

Deadline [100, 400]

Expense budget [100, 1500]

Electrical energy [0.1, 1.0]

Bandwidth [100, 1000]

Computing power [100, 1000]

RAM [100, 2000]

Energy price [1, 100]

Job arrival rate [0.1, 0.6]

Fig. 3 Processing time withvarying job size

0

200

400

600

800

1000

0.5 1 5 10 15 20

job size(Mb)

proc

essi

ng ti

me(

ms)

PSA CEG

Fig. 4 Resource allocationefficiency with varying job size

0

20

40

60

80

100

0.5 1 5 10 15 20

job size (Mb)

allo

catio

n ef

fici

ency

% PSA CEG

(CEG) [13], we adopt the metrics: processing time, resource allocation efficiency, revenueand payment. Resource allocation efficiency is the ratio of the consumed cloud resources tothe total cloud resources available as a percentage.

The impacts of the job size on processing time, resource allocation efficiency, revenue andpayment were illustrated in Figs. 3, 4, 5 and 6 respectively. The experiments are to comparethe performance of PSA and CEG under different job size. From the results in Fig. 3, whenthe computation task is 0.5Mb, the processing time of PSA is 27 % less than CEG. Whilethe job size increases, the processing time of PSA increases mildly. Increasing job size leadsto longer times to complete the job, so some jobs of mobile device user can’t be processedbefore the deadline. Considering the resource allocation efficiency, from the results in Fig.4, the resource allocation efficiency of PSA is higher than CEG. When the job size reaches

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C. Li, L. Li

Fig. 5 Payment with varying jobsize

0

100

200

300

400

500

600

0.5 1 5 10 15 20

job size (Mb)

paym

ent

PSA CEG

Fig. 6 Revenue with varying jobsize

0

200

400

600

800

1000

0.5 1 5 10 15 20

job size(Mb)

reve

nue

PSA CEG

Fig. 7 Payment under differentnumber of task

0

100

200

300

400

500

600

10 50 100 150 200 300

number of task

paym

ent

PSA CEG

20Mb, the resource allocation efficiency of PSA is 23 % less than when the job size is 0.5Mbs.PSA perform better than CEG. Figure 5 shows the effect of varying job size on the payment,the payment of PSA increases more sharply when the job size increases. When the job sizeis 20 (s = 20), the payment of PSA is 41 % more than s = 0.5. When increasing job size bys = 20, the payment of CEG is as much as 16 % more than PSA. Figure 6 shows the effect ofvarying job size on the revenue, the revenue of PSA increases when the job size increases. Alarger job size enables mobile device user to expense more time for transfer and computation.When the job size is large, the revenue is high. When the job size is 20Mbs, the revenue ofPSA is 39 % more than the revenue when the job size is 0.5Mbs. Under the same condition,CEG has better revenues than PSA.

Following experiments are to compare the performance of PSA and the method proposedby Niyato et al. [13] under different number of tasks in terms of processing time, resourceallocation efficiency, revenue and payment were illustrated in Figs. 7, 8, 9 and 10 respectively.Figure 7 shows that the payment increases quickly for CEG andPSA when the number oftask increases. The payment of our PSA increases more slowly, when the more tasks needto be completed, because CEG is only concerned with cost factor, the objective of PSA is tobalance both the payment and processing times. Figure 8 shows the effect of the number of

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Fig. 8 Allocation efficiencyunder different number of task

0

20

40

60

80

100

10 50 100 150 200 300

number of task

allo

catio

n ef

fici

ency

%

PSA CEG

Fig. 9 Processing time underdifferent number of task

0

100

200

300

400

500

10 50 100 150 200 300

number of task

proc

essi

ng ti

me(

ms)

PSA CEG

Fig. 10 Revenue under differentnumber of task

0

200

400

600

800

1000

10 50 100 150 200 300

number of task

reve

nue

PSA CEG

tasks on the allocation efficiency. CEG only takes care of cloud resource provider’s revenue,the objective of CEG is to maximize the revenue of mobile cloud provider. When the numberof task increases, CEG has lower resource allocation efficiency than PSA. When the numberof tasks is 200, allocation efficiency of PSA decreases to 72 %, resource allocation efficiencyof CEG decreases to 57 %. For processing time, Fig. 9 show that CEG need more processingtime when the number of task increases, because CEG is more concerned with the revenuethan processing time. The completion time of PSA increase more slowly, our PSA optimizeboth payment and processing time, so it outperforms CEG in term of processing time. Theperformance effect of varying the number of tasks on the revenue is shown in Fig. 10. Whenthe number of tasks increases, the revenue increases. When the number of tasks is 200, therevenue of PSA is 42 % more than the revenue when the number of tasks is 10. Under thesame condition, CEG has better revenues than PSA.

The impacts of the of mobile device users on processing time, allocation efficiency, revenueand payment were illustrated in Figs. 11, 12, 13 and 14 respectively. Figure 11 shows as thenumber of mobile device users increases, the resource allocation efficiency decreases. WhenN = 55, the resource utilization of PSA is as 34 % less than the allocation efficiency by

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C. Li, L. Li

Fig. 11 Allocation efficiencyversus number of mobile cloudusers

0

0.2

0.4

0.6

0.8

1

10 15 20 25 30 40 50 55 60

number of mobile cloud users

allo

catio

n ef

fici

ency

PSA CEG

Fig. 12 Processing time versusnumber of mobile cloud users

0

50

100

150

200

250

300

10 15 20 25 30 40 50 55 60


proc

essi

ng ti

me

(ms)

PSA CEG

N = 20. When the number of mobile device users was very large, many jobs will be sentto system, mobile cloud resources are busier. Compared with PSA, the resource allocationefficiency of PSA decreases slowly than PSA when the number of mobile device usersincreases. When the number of mobile device users is 60 (N = 60), allocation efficiency ofPSA decreases to 61 %, resource allocation efficiency of CEG decreases to 50 %. Figure 12describes the impact of number of mobile device users on processing time, It can be seenfrom Fig. 12 that PSA use less time to complete tasks when compared to CEG especiallyunder larger number of mobile device users. After the number of mobile device user reach60, the response time using PSA can be as much as 29 % shorter than that using theCEG.The reason is that at small number of mobile device users, the task entering the mobilecloud is less than mobile cloud resource available. In such case, the task of mobile deviceusers can be accepted and executed when they are submitted. However, under larger numberof mobile device users, PSA can optimize the utility of mobile cloud users and select thebest available resource for a task, which executes the job on time. Figure 13 shows whenthe number of mobile device users increases (N = 50), the payment of PSA is as muchas 37 % more than that with N = 10. The payment is larger when the number of mobiledevice users is larger. When number of mobile device users increases, system load increases;some mobile device users’ requirements can’t be processed on time. If the jobs need to becompleted before deadline; they will pay more for cloud resource. Compared with CEG, thepayment of PSA decreases slowly when the number of mobile device users decreases. Whenthe number of mobile device users is 60 (N = 60), the payment of PSA decreases to 49 %than CEG. Figure 14 shows the effect of the number of mobile device users on the revenue.The revenue increases as the number of mobile device users increases. The mobile cloudresources are enough to be allocated to the mobile device users, so the price of the mobilecloud resource is cheap, more mobile device user can choose resources to complete tasks, sothe mobile cloud resource providers will get more revenue from mobile device users. PSAjointly considers both mobile device users and mobile cloud resource provider; CEG mainlyoptimize the revenues of mobile cloud provider, it has better revenues than PSA.

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Fig. 13 Payment versus numberof mobile cloud users

0

100

200

300

400

500

600

10 15 20 25 30 40 50 55 60


paym

ent

PSA CEG

Fig. 14 Revenue versus numberof mobile cloud users

0

200

400

600

800

1000

10 15 20 25 30 40 50 55 60


reve

nue

PSA CEG

From above comparison results, we can get some conclusions. Our proposed our phasedscheduling algorithm in mobile cloud (PSA) is solved by two subproblems: mobile device’sbatch application optimization and mobile device’s job level optimization. The objectiveof PSA is to satisfy mobile device users’ needs, as well as optimize the profit of mobilecloud provider. Distributed algorithm for capacity expansion game of mobile cloud serviceproviders (CEG) [13] mainly considers revenue of mobile cloud service provider and don’tconsider the mobile device user’s utility. Processing time and payment are the performancemetrics for mobile device users. So from above simulation results, processing time, paymentand resource allocation efficiency of PSA are better than CEG. The revenue of CEG is betterthan PSA.

7 Conclusions

The paper studies scheduling of batch applications for mobile cloud computing environment,and proposes a phased scheduling model of mobile cloud such that users experience lowerinteraction times and extended battery life. The phased scheduling optimization is solvedby two subproblems: mobile device’s batch application optimization and mobile device’sjob level optimization. At the first stage, the mobile cloud global scheduling optimizationimplements the allocation of the cloud resources to the mobile device’s batch applications.At the second stage, mobile device’s job level optimization adjusts the cloud resource usagesto optimize the utility of single mobile device’s application. In the simulations, comparedwith other algorithm, our proposed mobile cloud phased scheduling algorithms achieve thebetter performance with acceptable overhead.

Acknowledgments The authors thank the editors and the anonymous reviewers for their helpful commentsand suggestions. The work was supported by the National Natural Science Foundation (NSF) under grants (No.61171075), National Key Basic Research Program of China (973 Program) under Grant No. 2011CB302601,

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C. Li, L. Li

Special Fund for Fast Sharing of Science Paper in Net Era by CSTD (FSSP) No. 20130143110021, Programfor the High-end Talents of Hubei Province, Specialized Research Fund for the Doctoral Program of HigherEducation under Grant No. 20120143110014 and the Open Fund of the State Key Laboratory of SoftwareDevelopment Environment (SKLSDE-2013KF). Any opinions, findings, and conclusions are those of theauthors and do not necessarily reflect the views of the above agencies.

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Chunlin Li is a Professor of Computer Science in Wuhan Universityof Technology. She received the ME in Computer Science from WuhanTransportation University in 2000, and Ph.D. in Computer Softwareand Theory from Huazhong University of Science and Technology in2003. Her research interests include cloud computing and distributedcomputing.

Layuan Li is a Professor of Computer Science in the Wuhan Uni-versity of Technology. He received the BE from Harbin Institute ofMilitary Engineering, in 1970 and the ME from Huazhong Universityof Science and Technology, in 1982. He academically visited Massa-chusetts Institute of Technology, in 1985 and 1999. His research inter-ests include high-speed computer networks, and protocol engineering.He has published over 150 papers and is the author of six books. Hewas awarded the National Special Prize by the Chinese Government in1993.

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phased scheduling for resource-constrained mobile devices in mobile cloud computing

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