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Vakilinia et al. EURASIP Journal onWireless Communications and Networking 2014, 2014:201http://jwcn.eurasipjournals.com/content/2014/1/201

RESEARCH Open Access

Optimal multi-dimensional dynamic resourceallocation in mobile cloud computingShahin Vakilinia*, Dongyu Qiu and Mustafa Mehmet Ali

Abstract

In this paper, we propose a model for mobile application profiles, wireless interfaces, and cloud resources. First, analgorithm to allocate wireless interfaces and cloud resources has been introduced. The proposed model is based onthe wireless network cloud (WNC) concept. Then, considering power consumption, application quality of service(QoS) profiles, and corresponding cost functions, a multi-objective optimization approach using an event-based finitestate model and dynamic constraint programming method has been used to determine the appropriate transmissionpower, process power, cloud offloading and optimum QoS profiles. Numerical results show that the proposedalgorithm saves the mobile battery life and guarantees both QoS and cost simultaneously. Moreover, it determinesthe best available cloud server resources and wireless interfaces for applications at the same time.

Keywords: Resource allocation; Mobile cloud computing; Wireless network cloud

1 IntroductionPopularity of smartphones and related applications in var-ious fields are increasing in everyday life significantly.These devices have a wide range of features (e.g., high-speed processors and supporting multiple wireless inter-faces). Furthermore, due to increasing complexity ofapplications, smartphones require a significant computa-tional capability. In addition, they have become a primarycomputing platform for many users due to the well-developed applications in realms such as mobile com-merce, mobile learning, mobile health care, mobile com-puting, mobile gaming, and etc. As applications becomemore and more complex, mobile users experience shorterbattery lifetime. Most of the smartphone applications areQoS-sensitive and computation-intensive to perform on amobile system. Mobile cloud computing is a new conceptin which mobile users access the cloud virtual resourcesvia the Internet. It is beneficial to QoS and battery savingby means of mobile data offloading. Mobile computationoffloading technique shares application code between thecloud server and the mobile. Most of the time, mobileusers need to maintain a low level of power consumptionand thus computation must be performed in the cloud

*Correspondence: [email protected] of Electrical and Computer Engineering, Concordia University,1455 De Maisonneuve, Montreal, H4B 1R6, Canada

which comes with cost. Therefore, mobile users alwaysface a trade-off between communication and computation[1].On the other hand, wireless network cloud (WNC) [2]

proposes an architecture to join wireless access systems tocloud computing and shift the processing of base stationswith different technologies to a virtual cloud network.Therefore, all wireless technologies is converging and issuitable for next generation wireless networks. WNC andcloud radio access network (C-RAN) [3] using similarsoftware-defined radio (SDR) concept tend to decreasewireless network operating cost while enhancing the totalnetwork performance. Accordingly, without doubt, thenext generation of wireless networks (5G) movementtoward wireless clouds is irresistible [4,5].Despite flexibility and great potential applicability,

resource allocation problem in heterogeneous wirelessnetworks (HetNet) attributed with WNC and mobilecloud computing has received scarce attention as of today.Therefore, the prime contribution of the current researchhas been based on bridgingHetNet withWNC andmobilecloud computing to better allocate resources to the enduser. In addition, a multi-objective optimization problemconsidering cloud server power consumption, operatingcost, and QoS followed by a detailed trade-off amongstuser objectives have been studied.

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Vakilinia et al. EURASIP Journal onWireless Communications and Networking 2014, 2014:201 of 14http://jwcn.eurasipjournals.com/content/2014/1/201

In this paper, we propose a model including the opera-tors, clouds, applications, and mobile profile parameters.Due to the fact that a part of the algorithm has to be con-ducted in smartphones, complexity order of the problembecomes a vital parameter. Estimation and approxima-tion techniques have been used to linearly approximatethe parameters to decrease complexity order of ouralgorithm. Using dynamic constraint programming [6,7],event-based lexicographic multi-objective optimizationmethod [8] and QoS-based resource allocation solutions[9,10] with consideration to the resources and applica-tions constraints, network, and mobile resources havebeen allocated to applications simultaneously.It is worthy of note that the main objective of this

paper concerns performance metrics of mobile devicesand users, regardless of cloud computing centers andwireless operators related challenges, [11-16] which havenot been considered in this paper.The rest of the paper is organized as follows: this study’srelated works is discussed in Section 2, in Section 3, thesystem model will be defined, followed by the optimiza-tion algorithm in Section 4. Within Section 5, numer-ical results reveal performance of the proposed multi-dimensional algorithm. Finally, Section 6 concludes thepaper.

2 Related worksRahimi et al., [17], Fernando et al., [18], and Dinh et al.,[19] give an overview of the mobile cloud computing(MCC) presenting definition, architecture, applications,and approaches, then, on the corresponding challengesat the operational, user, and application levels have beendiscussed. They introduced MCC as the dominant com-puting model for mobile applications in the future.Moreover, extensive research such as in [20-22] has

been done over wireless local area network (WLAN)/ cel-lular interworking mechanisms, which combines WLANsand cellular data networks into integrated wireless datanetworks featured with QoS capabilities. Liu et al. [23]suggest a new dynamic load balance (DLB) scheme toimprove communication performance focusing on under-lying users. In their proposed scheme, joint session admis-sion control is a basis for user mobility, cognition, andservice arrival awareness in integrated 3G/WLAN net-works. Gazis et al.and Luo et al. [24,25] recommend astandardization policy in the area of WLAN-cellular datanetwork integration for different interworking architec-tures. Proposing the generic interworking architecturesin the technical literature, [26] studies general aspectsof integrated WLAN-cellular data networks. Access net-work discovery and selection function (ANDSF) suggestsa function for selection of access network and controloffloading amongst 3rd generation partnership project(3GPP) and other access networks. Such selections are

based on the mobile battery saving, user preference, andoperator policies. However, ANDSF does not considerapplication preferences, selection optimality, and simulta-neous power allocation.In general, international standards and standardization

bodies such as WiMAX and 3GPP decide to move towardcreating a seamless integrated wireless technology enti-tled HetNet [27]. HetNet by its nature includes a varietyof wireless access technologies. Access networks are con-nected through a backbone which is a network core forall of them. Moreover, HetNet consists of both macro andmicro cells as well as low power nodes which have distinctor overlapped coverage areas. When a multi-interfacedevice moves within a HetNet environment, its defaultnetwork for every connection can be determined basedon a set of predetermined parameters of network naturesuch as QoS settings, signal strength, backbone utiliza-tion, speed preference, selected cost or service, andmobilenode’s remained battery life.Furthermore, some researchers have studied power con-

sumption in smartphones. Murmuria et al., [28] andCarroll and Heiser [29] measure, analyze, and modelpower usage of smartphones by characterizing their sub-systems power usages. Balasubramanian et al. [30] con-sider wireless interface selection problem as a statisticaldecision problem and propose an algorithm to selectthe wireless network interface considering the context ofthe mobile applications in order to improve the batterylifetime. Hence, the features of wireless access interfaceselection also has fundamental impact on the perfor-mance of mobile computing applications and their powerconsumption.There are some trade-offs amongst power consump-

tion, QoS parameters, and costs. These objectives aredependent on network parameters, applications profiles,and cloud resources. Cuervo et al. [31] aim to optimizeenergy consumption of a mobile device by estimation andevaluating the trade-off between the energy consumedby local processing versus the transmission of code anddata for cloud offloading. Decision process in [31] consid-ers information and complex characteristics of the mobileenvironment. A framework for smartphones is introducedin [32]. It shifts smartphone application processing intothe cloud centers. It is based on the concept of smart-phone virtualization in the cloud and addresses lack ofscalability by creating virtual machines of a completesmartphone system on the cloud. ThinkAir [32] provideson-demand resource allocation by dynamically manag-ing VMs in the cloud via using an execution controller.The execution controller handles decision-making andcommunication with the cloud server. It considers execu-tion time, energy, and cost to make decision in order toachieve optimum performance. With regard to the net-work profile parameters, device profile parameters, and


program profile parameters of the smartphone, ThinkAirdynamically allocates the available cloud resources to theprograms simultaneously. Kumar and Lu [33] suggestthat cloud computing can potentially save energy throughoffloading of applications processing with limited relia-bility and quality of service requirements. This reflectsthe fact that for some applications such as delay-sensitiveones, migrated offloading to the clouds could not sig-nificantly offer energy savings to the smartphones whilesatisfying QoS parameters.Trade-off between system throughput and energy con-

sumption of mobile devices has been addressed in [34].Based on the Lyapunov optimization approach, an onlinecontrol algorithm is designed to balance energy andthroughput. It maximizes a joint utility using stability-utility parameters while bounding the traffic queue length,via making instantaneous decisions to control the trans-mission pattern. The admission control algorithm dimin-ishes the need for statistical estimation of traffic arrivalsand link conditions.In order to allocate resources amongst the cloud users

efficiently, a communication framework amongst cloudusers and service providers has been designed in [35].There, authors propose a biding language in order toconvert cloud user demands into the organized requestswhich helps cloud providers to support heterogeneoususer demands while protecting the systems from selfishuser behavior. Moreover, online compatible online cloudauction (COCA) mechanism is implemented to makeusers incentive to reveal their honest valuations. Finally,they have considered the sum of all the valuations of theallocated resources as the benchmark.A QoS-aware resource-allocation multiple cooperative

subtasks of jobs in cloud-based computing and data storeservices are investigated in [36]. Defining the objectivefunction as a weighted sum of the expense and the jobcompletion time and job execution time deadlines andbudget constraints, game theory approach is used to solvethe scheduling problem. First, considering users as theirchosen strategy regardless of the others, a binary inte-ger programming method is proposed to obtain the initialindependent optimization solution. Then, an evolutionarystrategy is designed to achieve the optimal solution.Regarding the scalability advantage of public clouds

and better QoS especially delay and power consump-tion of local clouds, MAPCloud is proposed in [37].This provided a means to select local and public cloudsfor mobile applications in order to increase the perfor-mance and scalability of the applications. Interestingly,for a fixed price, MAPCloud decreases 32% of the delayand power consumption while providing scalability. Then,cloud resource allocation for mobile applications (CRAM)using heuristic methods has been developed as a resourceallocation module for mobile applications achieving 84%

of the optimal power saving solutions for large amount ofusers.Rahimi et al. [38] focused onmodeling the mobile appli-

cations as location-time workflows (LTW) of task. 2Dlocation map is used to locate mobile hosts and cloudresources. Moreover, trajectory has been associated withmobile users. Defining QoS as a function of delay, power,and price, an efficient heuristic algorithm called MuSIC isproposed to maximize the mobile utilities while ensuringhigh-application QoS.Applying the game theory approach, coalition of the

cloud service providers is addressed in [39] where theuncertainty of internal users from each provider has beentaken into account. First, with respect to randomness ofdemand, a stochastic linear programming game modelto study the resource and revenue sharing for cloudproviders is developed. Then, using the Markov chain tomodel coalitional arrangement, the coalitional game forforming the cooperation to share resource and revenue areinvestigated.In this paper, we address performance modeling of

mobile applications using MCC and WNC. A resourceallocation algorithm is proposed to allocate resources andmobile transmission power and process power.

3 SystemmodelIn this section, we present a system model for opti-mum resource allocation. We assumed that mobile usersaccess application clouds via WNC and the Internet.Figure 1 shows the presumed topology based on [2] and[19]. However, as of today, smartphones just supportWLAN/cellular technologies simultaneously.We assume that there are a number of active appli-

cations on a mobile phone that support both WLANand cellular technologies. In order to achieve a bet-ter performance and improve power saving, a portionof the processing workload has to be offloaded to theclouds. As depicted in the Figure 2, each application mustchoose a proper wireless interface and a cloud networkto offload the processes to. However, the said selectionprocess depends on parameters such as battery lifetimeand required processing load. In addition, a feasible QoSprofile for the application needs to be determined.In order to conceive thismodel presumption, we defined

sets of variables according to application profiles, com-puting resource profiles, and network profiles. A ={1, 2, .., i, ..I} states a set of mobile applications, CR ={1, .., j, , ..J} states a set of available cloud computingresources, and WN = {WN1, ..,WNk , , ..WNK } repre-sents accessible wireless network interfaces collection.Note thatI, J, and K are the number of active applica-tions, available clouds, and wireless interfaces, respec-tively. Each collection element is a vector of characteristicswhich is related to the cost, power consumption, and


Figure 1 Network topology.

QoS. An operating point OPn = (Un,Pn,Cn) is definedto describe the mobile system behavior over the nth timeslot. Un shows the utilization associated with mobile usersatisfaction and is strictly related to the QoS indexesof applications. Pn represents mobile phone power con-sumption, and Cn demonstrates mobile phone cost func-tion. In this paper, appropriate j ∈ CR and k ∈ WN areassigned to the ith application in order for better formu-lation of controlling and optimizing the operating point.Therefore, operating point indicates important objectivesof mobile user such as mobile power consumption at eachtime slot. All parameters of the model are detailed inTable 1.Moreover, there are some limitations and restrictions on

resources and user profiles which are strictly dependent

on the mobile application QoS requirements and net-work parameters. In the following subsections, the objec-tive functions and constraints will be investigated. Trafficrate of the ith application is defined discretely betweenλimin and λimax where i belongs to {1,2,...,I}. Due to thebound limits, different functions of downlink trafficsare linearly approximated using affine functions and theTaylor series. Such approximations decrease the com-plexity order in a dramatic way while errors remainsmall.

3.1 QoS utilization and constraintsAs explained before, utilization function is related toapplication QoS characteristics. Objective utilizationfunction will be as follows:

Figure 2 Algorithm architecture.


Table 1 Table of parameters

Parameters Indicator

λimin Minimum required incoming traffic rate of the ithapplication

λimax Maximum required incoming traffic rate of the ithapplication

λi Incoming traffic rate of the ith applicationSi Effective processor speed (instructions per second)

dedicated to the ith application in a mobile deviceCi Instructions of ith application per time slotRimin Minimum required transmission rate of the ith applicationRimax Maximum required transmission rate of the ith applicationRi Transmission rate of the ith applicationγi Instructions have to be processed in cloud servers ith

applicationχdepi Utilization factor of the ith application dependent on

incoming traffic rateχindepi Utilization factor of the ith application independent from

incoming traffic rateDthi Delay threshold of ith application traffic

Di Delay of ith application trafficηi Mobile data offloading to clouds instructions of ith

applicationTDi Uploading data of ith applicationRmaxk Maximum achievable transmission rate using kth

interfaceHk Channel quality indicator of the kth interfaceDwth

k Achievable guaranteed downlink delay of kth interfaceDwk Downlink delay of kth interfaceαwk Cost coefficient of kth wireless download rate

(per instruction)θk Downlink QoS exponent of kth interfaceμk Download rate of kth interfacePmaint(k) Connection power consumption of kth interfacePThError Error rate thresholdβnj Delay between the wireless cloud and jth cloud server at

the nth time slotβ̂nj Estimation of the βn

jS

′j Effective processor speed of jth cloud server

αDLj Cost coefficient of downlink traffic of jth cloud server

αULj Cost coefficient of uplink traffic of jth cloud server

αcompj Cost coefficient cloud computation of jth cloud

Pcomp Process power consumption per processing speed unitEn nth momentε(n) Mobile energy level at the nth time slotBg(n) Mobile budget fee at the nth time slot

U =I∑

i=1(χ

depi (λi,Ri) + χ

indepi ) (1)

where χdepi (λi,Ri) depends on the upload and download

rate. Conversely, χindepi is independent from the upload

and download rate in the ith application utilization func-tion.Delay process consists of two parts, namely process-

ing delay and communication delay. Also, communicationdelay includes two parts: wireless link delay and internetnetwork delay. Applications such as cloud mobile gam-ing (CMG) interact closely with cloud servers. Therefore,

uplink delay is a significant parameter as well. In addi-tion, effective capacity concept has been used to modeldownlink wireless link delay. Assuming that arrival ratesand service rates of the wireless links are all stationary andindependent, according to the Gartner-Ellis limits [40,41],wireless link delay violation probability of kth wirelessinterface is approximated by [42-44]:

pr(Dk > DThk ) ≈ e−θμkDTh

k (2)

Internet delay (delay between the wireless networkcloud and cloud servers) for interactive applications suchas CMGdenotes the round trip time delay, and for stream-ing applications denotes the one-way delay. Calculat-ing the Internet delay requires a complicated procedure.However, assuming that the mobile cloud computing cen-ters are near the wireless access network, Internet delaymay be considered as a Gaussian random variable. There-fore, linear estimator [45] based on adaptive algorithmproposed in [46] is used to predict the Internet delay:

β̂nj = βn−1

j +rσ n

βj

σ nβ̂j

(β̂n−1i − βn−1

j ) (3)

where r is equal to

r =√√√√ E2(βn

j − E(βnj ))(β̂n

j − E(β̂nj ))

(E(βnj − E(βn

j ))2)(E(β̂nj − E(β̂n

j ))2)(4)

βnj represents the Internet delay of the jth cloud server

with the application in the nth time slot. After cloud serverselection process, a cloud server is mapped to the ithapplication. Hereafter, we assume that the jth cloud serverand kth wireless interface are assigned to the ith appli-cation. Therefore, total delay of ith application could bewritten by

Di = processdelay + wirelessuplinkdelay + internetdelay+ cloudprocessdelay + wirelessdownlinkdelay

(5)

In Equation 5, the first part denotes the processing delayin the mobile phone related to the number of instructionsper time slot executed in the mobile phone. Mobile pro-cess delay is approximated by Ci−ηi

Si where ηi representsthe offloading instructions to the cloud and Si denoteseffective processor speed dedicated to ith application. Thesecond part denotes the uploading delay of smartphoneapproximated by TDi

Ri . The third part represents the net-work delay represented by βj. The forth part denotes theprocessing delay of the cloud server considered as ηi+γi

S′j.

Finally, the last part implies the downlink delay of the kthinterface represented by Dwk . Dwk is considered a ran-dom variable and its expected value is of great benefit to


decision-making. The expected delay has to be less thanthe application delay threshold. QoS characteristics of theith application could be written as follows:

Qi = {λimin, λimax, λi,Ri

min,Rimax,Ri,Di,DTh

i } (6)

3.2 Power consumption processPower consumption also consists of two main parts,namely transmission power consumption and processingpower consumption. The formulation will be as follows:

P = processing power + transmission power (7)

The first part indicates the processing power consump-tion, and the second part is the transmission power. Pro-cessing power may be approximated linearly as a functionof effective processor speed dedicated to the applications.

Processingpower =( I∑

i=1PcompSi

)(8)

Transmission power itself consists of connection main-tenance power consumption [47] and data transmissionpower consumption.

Transmissionpower =( K∑k=1

(Ptrk (Hk ,Rk) + Pmaint(k)))

(9)

Transmission power depends on the channel state infor-mation (CSI) and transmission rate of the mobile phone.Without a doubt, OFDM is the dominant technology inthe current and future transmission technologies. Withrespect to the CSI on the receiver side, ‘Water filling’ couldbe an optimum algorithm to allocate the transmissionpower to the sub-carriers. Considering a single antenna, itwill be equal to

Ptrk (Hk ,Rk) =Mk∑

mk=1

(eln2(

RkWk

−∑Mkmk=1 log2(

hmk�knmk

)) − hmk�knmk

)

(10)

where Wk represents the kth interface sub-channel band-width. hmk is the mth sub-channel quality indicator ofkth interface. �k indicates coding gain of kth interface,nmk states the mth sub-channel noise of the kth interface,and Mk represents the number of subcarriers of the kthinterface.In the rest of the paper, we use Equation (10) as the

transmission power function. Connection maintenancepower consumption has a linear relation with transmis-sion time. According to central limit theorem, allocatedprocessing power for applications is approximated by aGaussian random variable. Then, mobile CPU processsharing feasibility is defined by Pr

(∑Ii=1 Si > S

)≤ p

therefore,(∑I

i=1 μS(i) + ζ∑I

i=1 σS(i))

< S where ζ = −1(1−p), −1 is the inverse function of the CDF of nor-mal distribution with μS(i) and σS(i) as the first and thesecond moments, respectively. For the proof, see [48].

3.3 Cost functionThe cost function consists of the following two parts:

Cost = wirelessoperatorcosts + cloudservicecosts(11)

We assumed that each active application receives servicefrom a specific cloud server and a wireless interface isselected for communication of each application. Based onthe proposed cost model in [49], the mobile cloud servicecost function could be written as follows:

cloud service costs=J∑

j=1

(αcomp(γj + ηj)+αUL

j Rj+αDLj λ

′j

)

(12)

where λ′j denotes the sum of the incoming traffic rates

of applications which the jth cloud server is assignedto them. We assumed that each application is linkedto a cloud server. First part indicates the computationcost while the second and the third parts represent thecost associated with data upload and download to cloudservers, respectively. Wireless access network costs alsocould be approximated linearly by

wirelessoperatorcosts =K∑

k=1αwk λ

′′k + σw

k R′′k (13)

λ′′k and R′′

k denote the sum of incoming and outgoingtraffic rates, respectively, of applications which the kthinterface is assigned to them. Accordingly, the follow-ing characteristics for clouds and wireless network inter-faces are proposed: CRj = {αUL

j ,αDLj ,βj, S

′j} and WNk =

{αwk ,Hk ,Rmax

k ,Pmaint(k)} (See Table 1).It is also possible to define objective functions and

constraints with respect to application tasks instead ofapplications alone. Changing the scale from applicationto task increases resource allocation accuracy as well ascomplexity order of the algorithm.

4 Problem formulation and solution4.1 Problem definitionLess power consumption, user satisfaction, and cost areof great interest to many mobile users. In this section,we propose a multi-objective dynamic resource allocationalgorithm to optimize the aforementioned topics of inter-est in the form of objective function and processes withrespect to the network resources and mobile and appli-cation constraints. Dynamic constraint programming and


lexicographic-event-based optimization method [8] havebeen used to solve the multi-objective optimization prob-lem. However, complexity order of the proposed algo-rithm also needs to be considered. Moreover, the pre-viously highlighted measures of interest usually are notavailable in a closed form and are mostly obtained fromnumerical data. Henceforth, linear interpolation methodfor numerical data and the Taylor series for closed formfunction have been applied to approximate the input dataor non-linear functions in a short interval, e.g., λi ∈[ λimin, λimax]. However, as it will be explained shortly, theproposed protocol architecture design does not dependon linear functions of the system model. In fact, applica-tion of non-linear functions will not impact the complex-ity order drastically.Figure 3 shows the overall structure of the proposed

algorithm. The algorithm takes the parameters of cloudprofiles, wireless access networks, mobile devices, andmobile applications as its input. In addition, it linearlyapproximates inputs such as cloud server delay based onwhich the state and corresponding events are selected.In the next level, optimum wireless network interface,best available cloud servers, offloading coefficients of

Figure 3 The proposed algorithm structure.

applications, processing power and transmission powerof the mobile phone and optimum QoS profile willbe selected. Obtaining an optimum offloading solution,the execution controller introduced in [32] manages theshared process between the mobile phone and cloudservers.

4.2 Problem formulationObjective processes could be written as follows:

FI1(n) = −U(n) (14)

FI2(n) = P(n) (15)

FI3(n) = cost(n) (16)

Here, we used negative utilization factor to convertthe maximization problem to a minimization problem.Mobile device and resources constraints are ∀i ∈ A

0 ≤ ηi(n) ≤ Ci(n) (17)

�Ii=1(μSi(n) + ζσSi(n)) < S (18)

λ′′k(n) ≤ μk(n) (19)

Application QoS profile constraints (Qmin < Qi < Qmax)are considered as follows: ∀i ∈ A

E{Di(n)} ≤ Dthi (20)

λimin ≤ λi(n) ≤ λimax (21)

Rimin ≤ Ri(n) ≤ Ri

max (22)The current delay model approximates the real delay

scenarios. To accommodate a more complicated type of

Figure 4 FSM structure.


Figure 5 Algorithm architecture.

delay, Equation (20) can be replaced by arbitrary complexconstraints.We use lexicographic optimization method to solve the

proposed multi-objective optimization problem. Objec-tive functions are prioritized based on the state of thesystem. In fact, only one objective function is selectedin each state and others are considered as constraints.The state of the system depends on the next occurringevent. A finite state model (FSM) is proposed for optimalresource allocation while considering different events totransit amongst the states. Figure 4 shows the proposedFSM structure.The states are as follows:

1. Best QoS strategy: in this state, we try to maximizeuser utilization while considering other objectives asconstraint.

2. Cost-effective mode: in this state, considering theQoS and power consumption constraints, theproposed resource allocation algorithm attempts tominimize the cost of the system.

3. Energy-saving mode: in this state, the proposedalgorithm minimizes the power consumption of thesystem considering QoS and cost constraints.

The transition events take place as detailed below:� occurs when ε(n) ≤ ε(nth) where ε(n) and ε(nth)

denote the mobile energy in the nth time slot and itsthreshold, respectively. It shows that mobile energy is in

a critical situation. �́ occurs when: ε(n) ≤ ε(nth) and β

happens when ε(n) ≥ ε(n−1)meaning that mobile deviceis being charged and is not in a critical situation energywise. φ happens when Bg(n) ≤ Bgth where Bg and Bgthdenotes the mobile budget fee in the nth time slot andits threshold, respectively, reflecting the fact that mobileuser budget is approaching levels lower than its threshold.Also, φ́ occurs when Bg(n) ≥ Bgth. QoS-sensitive state isconsidered as the initial state. According to the occurringevents, dynamic constraint programming is applied tofind the optimal solution. The state of the system is shownby x, where x belongs to the set of states; X = {1, 2, 3}. Ineach state, we solve the following optimization problem:

Argmin WN ,CR,η,λ,R,SFIx�x

ST : FIx́�x ≤ Fth

x́ ∀x́ ∈ X, x́ �= x(17), (18), (19), (20), (21), (22)

where Equations (17), (18), (19) and Equations (20),(21), (22) are the resources and the mobile applicationsconstraints, respectively, and

λ = {λ1, ....λi, ...λI}η = {η1, ....ηi, ...ηI}R = {R1, ....Ri, ...RI}S = {S1, ....Si, ...SI}

Not only proper mobile cloud computing center andinterface should be selected for the applications but also

Table 2 Numerical validation parameters

Parameters Indicator

λimin iid rv between 10 and 384 kbps with uniform distributionλimax iid rv between 100 and 2Mbps with uniform distributionS 800 MHzCi iid rv between 100 and 107 with uniform distributionRmini iid rv between 0 and 100 kbps with uniform distributionRmaxi iid rv between 10 and 250 kbps with uniform distribution

χdepi iid rv between 0 and 1 with uniform distribution

χindepi iid rv between 0 and 1 with uniform distribution

Dthi iid rv between 50ms and 20 s with uniform distribution

TDi iid rv between 0 and 100 KB with uniform distributionRmaxk Maximum achievable transmission rate through using kth

interfaceDwth

k 50ms interfaceDwk iid rv between 10 and 250 kbps with uniform distributionαwk iid rv between 10 and 250 kbps with uniform distribution

μk kth iid rv between 100 kbps and 2Mbps with uniformdistribution

βnj iid rv between 20ms and 5 s with uniform distribution

αDLj Cost coefficient of downlink traffic of jth cloud server

αULj Cost coefficient of uplink traffic of jth cloud server

αcompj Cost coefficient cloud computation of jth cloud

Pmaint(k) iid rv between 120 and 400mw with uniform distribution forWiFi interfaces and iid rv between 500 and 800mW

Pcomp 2.34 × 10−10W/Hertz


40

50

60

70

80

90

10040

5060

7080

90

60

65

70

75

80

85

90

95

100

Power Consumption Indicator

Cost Indicator

Util

izat

ion

Indi

cato

r

Figure 6 Operating point tracking on the time.

offloading, downloading, and uploading rates also shouldbe determined in order to optimize the objective functionsconsidering the constraints.For instance, considering x = 2, the optimization

problem will be as follows:

Argminη,λ,R,S(∑I

i=1 PcompSi)+

(∑Kk=1(Ptk(Hk ,Rk)+Pmaint(k))

)ST :

∑Ii=1

(χdepi,λ (λi) + χ

depi,R (Ri) + χ

indepi

)≤ Uth∑J

j=1

(αcomp(γj + ηj) + αUL

j Rj + αDLj λ

′j

)+∑K

k=1(αwk λ"k + σw

k R"k) ≤ Costth

E{Di(n)} ≤ Dthi ∀i ∈ A

Rimin ≤ Ri(n) ≤ Ri

max ∀i ∈ A0 ≤ ηi(n) ≤ Ci(n) ∀i ∈ A�I

i=1(μSi (n) + ζσSi (n)) < Sλimin ≤ λi(n) ≤ λimax ∀i ∈ Aλ

′′k(n) ≤ μk(n) ∀k ∈ WN

Here, first the best possible wireless network interfaceand cloud have to be selected for each active application.Next, process offloading, and variables such as down-load/upload rate and effective processor speed dedicatedto the applications with the goal of minimizing the powerconsumption of the device will be calculated.

4.3 Problem solutionwix is considered as the input of the proposed algorithm

corresponding to the ith application such as WN , CRcollections in the x state. uix also is considered as the con-trol variable vector related to the ith application such asoffloading factor and ith application incoming traffic rateat the x state. uix is selected from a predetermined set U .U ⊂ RI is restricted to Equations (17), (18), (19), and(21). We assumed that si is non-zero in all applications,because all applications need some process in a mobilephone. After multiplying Equation (5) by si, all constraintsand objective functions will be linear in terms of η ,λ, andS. The only non-linear variable is power transmission rate.Bender decomposition method [7] is used to decomposethe problem into functions linear in variables (i.e., η, λ,and S) and non-linear in variable R. Minimum amount ofRi could be easily found through Equations (5) and (20) asfollows:

Rimin =

Dthi − (β̂j + Ci−ηi

Si + ηi+γiS′j

) − E{Dwi}TDi

(23)


24

68

10

500

1000

1500

2000

2500

50

55

60

65

70

75

80

85

no of applications Power Consumption Threshold

Util

izat

ion

Indi

cato

r

50

55

60

65

70

75

80

85

Figure 7 Utilization indicator for different power thresholds and different number of applications.

Then, Ri could be found by

Ri = Rimin + εR(i) (24)

where εR(i) is dependent on the objective function andobjective constraints. In order to find the εR(i), simpleincremental selection algorithm [50] is used. It rangesfrom 0 to Ri

max−Rimin. However, if the transmission power

consumption is linearly approximated in terms of trans-mission rate [30], then optimization problem will be sim-plified to a bilinear matrix inequality problemwhich couldbe solved with less complexity. f ix́(u

ix,wi

x(j, k) | x) showsthe x́th objective function derived from the ith applica-tion. Therefore, cost to go function could be written asbelow:

FIx�x = f Ix�x(u

Ix,wI

x(j, k) | x) +I−1∑i=1

fx�x(uix,wix(j, k) | x) (25)

Thus,

FIx�x = f Ix�x(u

Ix,wI

x(j, k) | x) + FI−1x�x (26)

Also, the following constraint should be satisfied for thesuccessive objective functions:

FIx́�x = f Ix́�x(u

Ix,wI

x(j, k) | x) + FI−1x́�x ≤ Fth

x́�x ∀x́ ∈ X, x́ �= x(27)

Optimal solution to this problem could be found usingdynamic programming (DP). It should be noted that appli-cations are sorted according to their priorities and impor-tance. Hence, the initial value of the objective is relatedto the most prioritized application. However, due to theconstraints, computation complexity is much higher thana usual dynamic programming problem with brute-forcesearch. A diagram based on [9] is proposed to find theoptimal solution.Moreover, amethod of learning from themistakes [7] is used to restrict the feasible optimizationregion. Figure 5 shows the proposed algorithm structure.Using DP, the network and cloud resources are selected.In each DP step, linear programming output determinescontrol variables of the system uix. In order to decrease thecomplexity order, instead of brute-force search in resourceand network selection, a policy is developed to assignthe resources with the lowest objective values consideringthe application and resources constraints. The algorithmpseudo code is shown in Algorithm 1.To improve modeling, TDi and Ci could be approxi-

mated linearly by ηi and λi

TDi = YTDiηi + ZTDi ,Ci = YCiλi + ZCi (28)


Algorithm 1: Dynamic constraint programmingData: CR,WN,Qmin,QmaxResult: η , Q , Fx

1 events and states initialization;2 while ∀(u,w) ∈ {Valid}FI

x(u∗,w∗) = minFIx(u,w) do

3 for i = 1 → I do4 for j ∈ CR, k ∈ WN do5 wi

x = Argminj,k(f ix | Qmin)

6 end for7 uix = LPoptimization(wi

x � x)//Argminuix f (w

ix,uix � x)

8 if Q(i) /∈ (Qmin(i),Qmax(i)) then9 update the valid region

10 BREAK11 end if12 f ∗(wi

x,uix) = f (wix,uix)

13 ∀x ∈ X, Fix(u∗,w∗) =

Fi−1x (u∗,w∗) + f ∗

x (wix,uix)

14 end for15 if ∀x́ ∈ X, x́ �= x FI

x(u∗,w∗) ≤ Fthx then

16 update the valid region17 BREAK18 end if19 end while

where YTDi and ZTDi are coefficients used in linearapproximation of the uploading data of ith application interms of offloading computation. YCi is the incoming traf-fic dependent part of the ith application process while ZCiis its independent part.For more precise resource allocation under some con-

ditions, it is possible to approximate the functions byhigher order of the Taylor series or other functions (e.g.,exponential family). The proposed algorithm, using ben-der decomposition method, always breaks the optimiza-tion method into two different parts, namely linear andnon-linear optimization part.

Argminug(unonlin) + pulinST : z(unonlin) + qulin ≤ G

resource constraintsapplications constraints

(29)

where ulin,unonlin represent linear and non-linear con-trol variables, respectively. Therefore, master problemis divided into sub-problems. Using column generationtechniques, two sub-optimization problems are min-imized simultaneously. Integration of the two afore-mentioned linear and non-linear subproblems restrictsthe optimization feasible region and despite of the

increasing complexity, it converges to an optimalsolution.

5 Numerical resultsIn this section, some numerical results are presentedto verify analysis of the previous section. Resourcesand application constraints are usually based on [28-30].The resource characteristics considered in the numeri-cal results are shown on Table 2. In the studied problem,we assumed that a main application such as CMG, videocall, or media streaming is always present within thenetwork, while considering presence of others as minorapplications such as online social networks, health mon-itoring, or file and application download (I is considereda random variable between 2; 10 over the time). Fiftydifferent cloud service providers with different character-istics have been considered in the network. The numberof available WiFis is a random variable between 0 to 4.However, the number of available cellular networks variesfrom 1 to 5. If available resources are not enough forall applications, then the proposed algorithm allocatesresources in order to maximize the objective functionignoring applications with less weight in the objectivefunction. Connection maintenance power consumptionincludes elements such as receiving data power consump-tion. Receiving power consumption itself depends on sev-eral transmission parameters such as network contention[51].Objective indicators are defined as follows:

uindicator(n) = u(n)umax(n)

× 100, Pindicator(n) = pmin(n)p(n)

× 100and costindicator(n) = costmin(n)

cost(n)× 100 where umax(n),

pmin(n), and costmin(n) represent the extremum achiev-able utilization, cost, and power consumption withoutconsidering the constraints of the mobile device at thenth time slot. Figure 6 shows the mobile device perfor-mance with respect to the time. As demonstrated, themobile device had started with the best QoS strategy stateand had a large utilization factor. After budget reductionstate changed to cost effective mode, the algorithm min-imized the cost of the mobile usage. Finally, when theremaining battery energy went lower than the thresh-old (10%) the state was changed to energy-saving modewhich minimizes the device power consumption. Blueline shows the average tracking of the operating pointthrough the time. Red points are the operating pointsamples during different time slots. Figure 7 shows powerefficiency factor for different number of applications anddifferent power consumption thresholds. As it is shownin Figure 7, generally with higher power consumptionthresholds and more applications, utilization functiontends to increase. However, for higher levels in number ofapplications with low power consumption threshold, uti-lization function is lower in comparison with applications


2

4

6

8

10

30405060708090100

30

40

50

60

70

80

90

Time (Hour)

β(ms)

Pow

er E

ffici

ency

30

40

50

60

70

80

90

Figure 8 Power efficiency track over the time domain and different β parameters.

65

70

75

80

852

46

810

12

x 10−3

0.5

0.6

0.7

0.8

0.9

1

Cost Threshold

Utilization Threshold

Pow

er E

ffici

ency

0.5

0.6

0.7

0.8

0.9

1

Figure 9 Power efficiency.


Figure 10 Complexity comparison.

1with the same power threshold limit due to larger num-ber of constraints. Figure 8 depicts the system powerefficiency over the time domain for different averagenetwork delays. Value of power efficiency function showsthe state transition from the best QoS strategy or cost-effective mode to energy-effective mode. Figure 8 showsthat state transition takes place earlier for larger amountsof E(β). This indicates flexibility of the network in theproposed algorithm. However, for large values of E(β),algorithm could not find a feasible optimum pointsatisfying all the constrains. In addition, power efficiencydecreased in a dramatic way. Also, Figure 9 shows thepower efficiency in terms of different utilization thresh-olds and cost thresholds. It is obvious that with decreasein average utilization threshold, while average costthreshold increases, power efficiency increases as well.The complexity order of the proposed optimization

algorithm is less than the complexity of brute-force searchmethod. As depicted in Figure 10, the programming effortrequired which is defined by logarithm of the syntax linesto code the algorithm for the proposed dynamic constantprogramming is much less than the brute-force search.

6 ConclusionsIn this paper, based on WNC concept, a system modelfor next generation of mobile communication has beenconsidered. Cost, QoS, and power consumption func-tions are defined based on the system model. Next, amulti-dimensional optimization algorithm is proposed tooptimize the objectives of a mobile user. The proposedmulti-dimensional optimization algorithm takes networkparameters, mobile device, and application constraintsas input to optimally select the network resources andapplications QoS profiles with optimum offloading coef-ficients. The proposed algorithm is established on event-based lexicographic optimization method and dynamicconstraint programming. Numerical results for differentenvironmental variables revealed that the proposed algo-rithm could be dynamically adaptive to environmental

parameters variation. We have solved the optimizationproblem assuming particular linear approximations whichmay not be always valid. The next step could be extend-ing the current work to the case of nonlinear func-tions and processes. In addition to the objectives ofmobile users, performance metrics of cloud computingdata centers and wireless operators can be considered aswell.

Competing interestsThe authors declare that they have no competing interests.

Received: 16 July 2014 Accepted: 7 October 2014Published: 28 November 2014

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doi:10.1186/1687-1499-2014-201Cite this article as: Vakilinia et al.: Optimal multi-dimensional dynamicresource allocation in mobile cloud computing. EURASIP Journal onWirelessCommunications and Networking 2014 2014:201.

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