Optimal multi-dimensional dynamic resource allocation in mobile cloud computing
- Shahin Vakilinia^{1}Email author,
- Dongyu Qiu^{1} and
- Mustafa Mehmet Ali^{1}
https://doi.org/10.1186/1687-1499-2014-201
© Vakilinia et al.; licensee Springer. 2014
Received: 16 July 2014
Accepted: 7 October 2014
Published: 28 November 2014
Abstract
In this paper, we propose a model for mobile application profiles, wireless interfaces, and cloud resources. First, an algorithm to allocate wireless interfaces and cloud resources has been introduced. The proposed model is based on the 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 finite state model and dynamic constraint programming method has been used to determine the appropriate transmission power, process power, cloud offloading and optimum QoS profiles. Numerical results show that the proposed algorithm saves the mobile battery life and guarantees both QoS and cost simultaneously. Moreover, it determines the best available cloud server resources and wireless interfaces for applications at the same time.
Keywords
Resource allocation Mobile cloud computing Wireless network cloud1 Introduction
Popularity of smartphones and related applications in various fields are increasing in everyday life significantly. These devices have a wide range of features (e.g., high-speed processors and supporting multiple wireless interfaces). Furthermore, due to increasing complexity of applications, smartphones require a significant computational capability. In addition, they have become a primary computing platform for many users due to the well-developed applications in realms such as mobile commerce, mobile learning, mobile health care, mobile computing, mobile gaming, and etc. As applications become more and more complex, mobile users experience shorter battery lifetime. Most of the smartphone applications are QoS-sensitive and computation-intensive to perform on a mobile system. Mobile cloud computing is a new concept in which mobile users access the cloud virtual resources via the Internet. It is beneficial to QoS and battery saving by means of mobile data offloading. Mobile computation offloading technique shares application code between the cloud server and the mobile. Most of the time, mobile users need to maintain a low level of power consumption and thus computation must be performed in the cloud which comes with cost. Therefore, mobile users always face 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 to cloud computing and shift the processing of base stations with different technologies to a virtual cloud network. Therefore, all wireless technologies is converging and is suitable for next generation wireless networks. WNC and cloud radio access network (C-RAN) [3] using similar software-defined radio (SDR) concept tend to decrease wireless network operating cost while enhancing the total network performance. Accordingly, without doubt, the next generation of wireless networks (5G) movement toward wireless clouds is irresistible [4, 5].
Despite flexibility and great potential applicability, resource allocation problem in heterogeneous wireless networks (HetNet) attributed with WNC and mobile cloud computing has received scarce attention as of today. Therefore, the prime contribution of the current research has been based on bridging HetNet with WNC and mobile cloud computing to better allocate resources to the end user. In addition, a multi-objective optimization problem considering cloud server power consumption, operating cost, and QoS followed by a detailed trade-off amongst user objectives have been studied.
In this paper, we propose a model including the operators, clouds, applications, and mobile profile parameters. Due to the fact that a part of the algorithm has to be conducted in smartphones, complexity order of the problem becomes a vital parameter. Estimation and approximation techniques have been used to linearly approximate the parameters to decrease complexity order of our algorithm. Using dynamic constraint programming [6, 7], event-based lexicographic multi-objective optimization method [8] and QoS-based resource allocation solutions [9, 10] with consideration to the resources and applications constraints, network, and mobile resources have been allocated to applications simultaneously.
It is worthy of note that the main objective of this paper concerns performance metrics of mobile devices and users, regardless of cloud computing centers and wireless operators related challenges, [11–16] which have not been considered in this paper.The rest of the paper is organized as follows: this study’s related works is discussed in Section 2, in Section 3, the system model will be defined, followed by the optimization algorithm in Section 4. Within Section 5, numerical results reveal performance of the proposed multi-dimensional algorithm. Finally, Section 6 concludes the paper.
2 Related works
Rahimi 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 challenges at the operational, user, and application levels have been discussed. They introduced MCC as the dominant computing model for mobile applications in the future.
Moreover, extensive research such as in [20–22] has been done over wireless local area network (WLAN)/ cellular interworking mechanisms, which combines WLANs and cellular data networks into integrated wireless data networks featured with QoS capabilities. Liu et al. [23] suggest a new dynamic load balance (DLB) scheme to improve communication performance focusing on underlying users. In their proposed scheme, joint session admission control is a basis for user mobility, cognition, and service arrival awareness in integrated 3G/WLAN networks. Gazis et al.and Luo et al. [24, 25] recommend a standardization policy in the area of WLAN-cellular data network integration for different interworking architectures. Proposing the generic interworking architectures in the technical literature, [26] studies general aspects of integrated WLAN-cellular data networks. Access network discovery and selection function (ANDSF) suggests a function for selection of access network and control offloading amongst 3rd generation partnership project (3GPP) and other access networks. Such selections are based on the mobile battery saving, user preference, and operator policies. However, ANDSF does not consider application preferences, selection optimality, and simultaneous power allocation.
In general, international standards and standardization bodies such as WiMAX and 3GPP decide to move toward creating a seamless integrated wireless technology entitled HetNet [27]. HetNet by its nature includes a variety of wireless access technologies. Access networks are connected through a backbone which is a network core for all of them. Moreover, HetNet consists of both macro and micro cells as well as low power nodes which have distinct or overlapped coverage areas. When a multi-interface device moves within a HetNet environment, its default network for every connection can be determined based on a set of predetermined parameters of network nature such as QoS settings, signal strength, backbone utilization, speed preference, selected cost or service, and mobile node’s remained battery life.
Furthermore, some researchers have studied power consumption in smartphones. Murmuria et al., [28] and Carroll and Heiser [29] measure, analyze, and model power usage of smartphones by characterizing their sub-systems power usages. Balasubramanian et al. [30] consider wireless interface selection problem as a statistical decision problem and propose an algorithm to select the wireless network interface considering the context of the mobile applications in order to improve the battery lifetime. Hence, the features of wireless access interface selection also has fundamental impact on the performance of mobile computing applications and their power consumption.
There are some trade-offs amongst power consumption, QoS parameters, and costs. These objectives are dependent on network parameters, applications profiles, and cloud resources. Cuervo et al. [31] aim to optimize energy consumption of a mobile device by estimation and evaluating the trade-off between the energy consumed by local processing versus the transmission of code and data for cloud offloading. Decision process in [31] considers information and complex characteristics of the mobile environment. A framework for smartphones is introduced in [32]. It shifts smartphone application processing into the cloud centers. It is based on the concept of smartphone virtualization in the cloud and addresses lack of scalability by creating virtual machines of a complete smartphone system on the cloud. ThinkAir [32] provides on-demand resource allocation by dynamically managing VMs in the cloud via using an execution controller. The execution controller handles decision-making and communication with the cloud server. It considers execution time, energy, and cost to make decision in order to achieve optimum performance. With regard to the network profile parameters, device profile parameters, and program profile parameters of the smartphone, ThinkAir dynamically allocates the available cloud resources to the programs simultaneously. Kumar and Lu [33] suggest that cloud computing can potentially save energy through offloading of applications processing with limited reliability and quality of service requirements. This reflects the fact that for some applications such as delay-sensitive ones, migrated offloading to the clouds could not significantly offer energy savings to the smartphones while satisfying QoS parameters.
Trade-off between system throughput and energy consumption of mobile devices has been addressed in [34]. Based on the Lyapunov optimization approach, an online control algorithm is designed to balance energy and throughput. It maximizes a joint utility using stability-utility parameters while bounding the traffic queue length, via making instantaneous decisions to control the transmission pattern. The admission control algorithm diminishes the need for statistical estimation of traffic arrivals and link conditions.
In order to allocate resources amongst the cloud users efficiently, a communication framework amongst cloud users and service providers has been designed in [35]. There, authors propose a biding language in order to convert cloud user demands into the organized requests which helps cloud providers to support heterogeneous user demands while protecting the systems from selfish user behavior. Moreover, online compatible online cloud auction (COCA) mechanism is implemented to make users incentive to reveal their honest valuations. Finally, they have considered the sum of all the valuations of the allocated resources as the benchmark.
A QoS-aware resource-allocation multiple cooperative subtasks of jobs in cloud-based computing and data store services are investigated in [36]. Defining the objective function as a weighted sum of the expense and the job completion time and job execution time deadlines and budget constraints, game theory approach is used to solve the scheduling problem. First, considering users as their chosen strategy regardless of the others, a binary integer programming method is proposed to obtain the initial independent optimization solution. Then, an evolutionary strategy is designed to achieve the optimal solution.
Regarding the scalability advantage of public clouds and better QoS especially delay and power consumption of local clouds, MAPCloud is proposed in [37]. This provided a means to select local and public clouds for mobile applications in order to increase the performance and scalability of the applications. Interestingly, for a fixed price, MAPCloud decreases 32% of the delay and power consumption while providing scalability. Then, cloud resource allocation for mobile applications (CRAM) using heuristic methods has been developed as a resource allocation module for mobile applications achieving 84% of the optimal power saving solutions for large amount of users.
Rahimi et al. [38] focused on modeling the mobile applications as location-time workflows (LTW) of task. 2D location map is used to locate mobile hosts and cloud resources. Moreover, trajectory has been associated with mobile users. Defining QoS as a function of delay, power, and price, an efficient heuristic algorithm called MuSIC is proposed to maximize the mobile utilities while ensuring high-application QoS.
Applying the game theory approach, coalition of the cloud service providers is addressed in [39] where the uncertainty of internal users from each provider has been taken into account. First, with respect to randomness of demand, a stochastic linear programming game model to study the resource and revenue sharing for cloud providers is developed. Then, using the Markov chain to model coalitional arrangement, the coalitional game for forming the cooperation to share resource and revenue are investigated.
In this paper, we address performance modeling of mobile applications using MCC and WNC. A resource allocation algorithm is proposed to allocate resources and mobile transmission power and process power.
3 System model
Table of parameters
Parameters | Indicator |
---|---|
${\lambda}_{\text{min}}^{i}$ | Minimum required incoming traffic rate of the i th |
application | |
${\lambda}_{\text{max}}^{i}$ | Maximum required incoming traffic rate of the i th |
application | |
λ _{ i } | Incoming traffic rate of the i th application |
S _{ i } | Effective processor speed (instructions per second) |
dedicated to the i th application in a mobile device | |
C _{ i } | Instructions of i th application per time slot |
${R}_{\text{min}}^{i}$ | Minimum required transmission rate of the i th application |
${R}_{\text{max}}^{i}$ | Maximum required transmission rate of the i th application |
R _{ i } | Transmission rate of the i th application |
γ _{ i } | Instructions have to be processed in cloud servers i th |
application | |
${\chi}_{i}^{\text{dep}}$ | Utilization factor of the i th application dependent on |
incoming traffic rate | |
${\chi}_{i}^{\text{indep}}$ | Utilization factor of the i th application independent from |
incoming traffic rate | |
${D}_{i}^{\mathit{\text{th}}}$ | Delay threshold of i th application traffic |
D _{ i } | Delay of i th application traffic |
η _{ i } | Mobile data offloading to clouds instructions of i th |
application | |
T D _{ i } | Uploading data of i th application |
${R}_{k}^{\text{max}}$ | Maximum achievable transmission rate using k th |
interface | |
H _{ k } | Channel quality indicator of the k th interface |
${\mathit{\text{Dw}}}_{k}^{\mathit{\text{th}}}$ | Achievable guaranteed downlink delay of k th interface |
D w _{ k } | Downlink delay of k th interface |
${\alpha}_{k}^{w}$ | Cost coefficient of k th wireless download rate |
(per instruction) | |
θ _{ k } | Downlink QoS exponent of k th interface |
μ _{ k } | Download rate of k th interface |
P_{maint}(k) | Connection power consumption of k th interface |
${P}_{\text{Error}}^{\mathit{\text{Th}}}$ | Error rate threshold |
${\beta}_{j}^{n}$ | Delay between the wireless cloud and j th cloud server at |
the n th time slot | |
$\widehat{{\beta}_{j}^{n}}$ | Estimation of the ${\beta}_{j}^{n}$ |
${S}_{j}^{{}^{\prime}}$ | Effective processor speed of j th cloud server |
${\alpha}_{j}^{\mathit{\text{DL}}}$ | Cost coefficient of downlink traffic of j th cloud server |
${\alpha}_{j}^{\mathit{\text{UL}}}$ | Cost coefficient of uplink traffic of j th cloud server |
${\alpha}_{j}^{\text{comp}}$ | Cost coefficient cloud computation of j th cloud |
P _{comp} | Process power consumption per processing speed unit |
E ^{ n } | n th moment |
ε(n) | Mobile energy level at the n th time slot |
B g(n) | Mobile budget fee at the n th time slot |
Moreover, there are some limitations and restrictions on resources and user profiles which are strictly dependent on the mobile application QoS requirements and network parameters. In the following subsections, the objective functions and constraints will be investigated. Traffic rate of the i th application is defined discretely between ${\lambda}_{\text{min}}^{i}$ and ${\lambda}_{\text{max}}^{i}$ where i belongs to {1,2,...,I}. Due to the bound limits, different functions of downlink traffics are linearly approximated using affine functions and the Taylor series. Such approximations decrease the complexity order in a dramatic way while errors remain small.
3.1 QoS utilization and constraints
where ${\chi}_{i}^{\text{dep}}({\lambda}_{i},{R}_{i})$ depends on the upload and download rate. Conversely, ${\chi}_{i}^{\text{indep}}$ is independent from the upload and download rate in the i th application utilization function.
3.2 Power consumption process
where W_{ k } represents the k th interface sub-channel bandwidth. h_{ mk } is the m th sub-channel quality indicator of k th interface. Γ_{ k } indicates coding gain of k th interface, n_{ mk } states the m th sub-channel noise of the k th interface, and M_{ k } represents the number of subcarriers of the k th interface.
In the rest of the paper, we use Equation (10) as the transmission power function. Connection maintenance power consumption has a linear relation with transmission time. According to central limit theorem, allocated processing power for applications is approximated by a Gaussian random variable. Then, mobile CPU process sharing feasibility is defined by $\mathit{\text{Pr}}\left(\sum _{i=1}^{I}{S}_{i}>S\right)\le p$ therefore, $\left(\sum _{i=1}^{I}{\mu}_{S\left(i\right)}+\zeta \sum _{i=1}^{I}{\sigma}_{S\left(i\right)}\right)<S$ where ζ=Φ^{-1}(1-p), Φ^{-1} is the inverse function of the CDF of normal distribution with μ_{S(i)} and σ_{S(i)} as the first and the second moments, respectively. For the proof, see [48].
3.3 Cost function
${\lambda}_{k}^{{}^{\u2033}}$ and ${R}_{k}^{{}^{\u2033}}$ denote the sum of incoming and outgoing traffic rates, respectively, of applications which the k th interface is assigned to them. Accordingly, the following characteristics for clouds and wireless network interfaces are proposed: ${\mathit{\text{CR}}}_{j}=\{{\alpha}_{j}^{\mathit{\text{UL}}},{\alpha}_{j}^{\mathit{\text{DL}}},{\beta}_{j},{S}_{j}^{{}^{\prime}}\}$ and ${\mathit{\text{WN}}}_{k}=\{{\alpha}_{k}^{w},{H}_{k},{R}_{k}^{\text{max}},{P}_{\mathit{\text{maint}}\left(k\right)}\}$ (See Table 1).
It is also possible to define objective functions and constraints with respect to application tasks instead of applications alone. Changing the scale from application to task increases resource allocation accuracy as well as complexity order of the algorithm.
4 Problem formulation and solution
4.1 Problem definition
Less power consumption, user satisfaction, and cost are of great interest to many mobile users. In this section, we propose a multi-objective dynamic resource allocation algorithm to optimize the aforementioned topics of interest in the form of objective function and processes with respect to the network resources and mobile and application constraints. Dynamic constraint programming and lexicographic-event-based optimization method [8] have been used to solve the multi-objective optimization problem. However, complexity order of the proposed algorithm also needs to be considered. Moreover, the previously highlighted measures of interest usually are not available in a closed form and are mostly obtained from numerical data. Henceforth, linear interpolation method for numerical data and the Taylor series for closed form function have been applied to approximate the input data or non-linear functions in a short interval, e.g., ${\lambda}_{i}\in [{\lambda}_{\text{min}}^{i},{\lambda}_{\text{max}}^{i}]$. However, as it will be explained shortly, the proposed protocol architecture design does not depend on linear functions of the system model. In fact, application of non-linear functions will not impact the complexity order drastically.
4.2 Problem formulation
- 1.
Best QoS strategy: in this state, we try to maximize user utilization while considering other objectives as constraint.
- 2.
Cost-effective mode: in this state, considering the QoS and power consumption constraints, the proposed resource allocation algorithm attempts to minimize the cost of the system.
- 3.
Energy-saving mode: in this state, the proposed algorithm minimizes the power consumption of the system considering QoS and cost constraints.
The transition events take place as detailed below:
Not only proper mobile cloud computing center and interface should be selected for the applications but also offloading, downloading, and uploading rates also should be determined in order to optimize the objective functions considering the constraints.
Here, first the best possible wireless network interface and cloud have to be selected for each active application. Next, process offloading, and variables such as download/upload rate and effective processor speed dedicated to the applications with the goal of minimizing the power consumption of the device will be calculated.
4.3 Problem solution
where ${Y}_{{\mathit{\text{TD}}}_{i}}$ and ${Z}_{{\mathit{\text{TD}}}_{i}}$ are coefficients used in linear approximation of the uploading data of i th application in terms of offloading computation. ${Y}_{{C}_{i}}$ is the incoming traffic dependent part of the i th application process while ${Z}_{{C}_{i}}$ is its independent part.
where u_{lin},u_{nonlin} represent linear and non-linear control variables, respectively. Therefore, master problem is divided into sub-problems. Using column generation techniques, two sub-optimization problems are minimized simultaneously. Integration of the two aforementioned linear and non-linear subproblems restricts the optimization feasible region and despite of the increasing complexity, it converges to an optimal solution.
5 Numerical results
Numerical validation parameters
Parameters | Indicator |
---|---|
${\lambda}_{\text{min}}^{i}$ | iid rv between 10 and 384 k b p s with uniform distribution |
${\lambda}_{\text{max}}^{i}$ | iid rv between 100 and 2 M b p s with uniform distribution |
S | 800 MHz |
C _{ i } | iid rv between 100 and 10^{7} with uniform distribution |
${R}_{i}^{\text{min}}$ | iid rv between 0 and 100 k b p s with uniform distribution |
${R}_{i}^{\text{max}}$ | iid rv between 10 and 250 k b p s with uniform distribution |
${\chi}_{i}^{\text{dep}}$ | iid rv between 0 and 1 with uniform distribution |
${\chi}_{i}^{\text{indep}}$ | iid rv between 0 and 1 with uniform distribution |
${D}_{i}^{\text{th}}$ | iid rv between 50 m s and 20 s with uniform distribution |
T D _{ i } | iid rv between 0 and 100 K B with uniform distribution |
${R}_{k}^{\text{max}}$ | Maximum achievable transmission rate through using k th |
interface | |
${\mathit{\text{Dw}}}_{k}^{\text{th}}$ | 50 m s interface |
D w _{ k } | iid rv between 10 and 250 k b p s with uniform distribution |
${\alpha}_{k}^{w}$ | iid rv between 10 and 250 k b p s with uniform distribution |
μ _{ k } | k^{th} iid rv between 100 k b p s and 2 M b p s with uniform |
distribution | |
${\beta}_{j}^{n}$ | iid rv between 20 m s and 5 s with uniform distribution |
${\alpha}_{j}^{\mathit{\text{DL}}}$ | Cost coefficient of downlink traffic of j th cloud server |
${\alpha}_{j}^{\mathit{\text{UL}}}$ | Cost coefficient of uplink traffic of j th cloud server |
${\alpha}_{j}^{\text{comp}}$ | Cost coefficient cloud computation of j th cloud |
P_{maint}(k) | iid rv between 120 and 400 m w with uniform distribution for |
WiFi interfaces and iid rv between 500 and 800 m W | |
P _{comp} | 2.34×10^{-10}W/H e r t z |
6 Conclusions
In this paper, based on WNC concept, a system model for next generation of mobile communication has been considered. Cost, QoS, and power consumption functions are defined based on the system model. Next, a multi-dimensional optimization algorithm is proposed to optimize the objectives of a mobile user. The proposed multi-dimensional optimization algorithm takes network parameters, mobile device, and application constraints as input to optimally select the network resources and applications QoS profiles with optimum offloading coefficients. The proposed algorithm is established on event-based lexicographic optimization method and dynamic constraint programming. Numerical results for different environmental variables revealed that the proposed algorithm could be dynamically adaptive to environmental parameters variation. We have solved the optimization problem assuming particular linear approximations which may not be always valid. The next step could be extending the current work to the case of nonlinear functions and processes. In addition to the objectives of mobile users, performance metrics of cloud computing data centers and wireless operators can be considered as well.
Declarations
Authors’ Affiliations
References
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