Cloud vs Edge Computing for Mobile Services: Delay-aware Decision Making to Minimize Energy Consumption
A promising technique to provide mobile applications with high computation resources is to offload the processing task to the cloud. Mobile cloud computing enables mobile devices with limited batteries to run resource hungry applications with the help of abundant processing capabilities of the clouds and to save power. However, it is not always true that cloud computing consumes less energy compared to mobile edge computing. It may take more energy for the mobile device to transmit a file to the cloud than running the task itself at the edge. This paper investigates the power minimization problem for the mobile devices by data offloading in multi-cell multi-user OFDMA mobile cloud computing networks. We consider the maximum acceptable delay and tolerable interference as QoS metrics to be satisfied in our network. We formulate the problem as a mixed integer nonlinear problem which is converted into a convex form using D.C. approximation. To solve the optimization problem, we have proposed centralized and distributed algorithms for joint power allocation and channel assignment together with decision making. Our simulation results illustrate that by utilizing the proposed algorithms, considerable power saving could be achieved e.g. about for short delays and large bitstream sizes in comparison with the baselines.
Swift growth in the development of resource hungry mobile applications has motivated users to use smart phones as a platform for running the applications. However mobile devices cannot always be considered as a platform for resource hungry applications due to their limited power and processing capacity. Moreover, one of the key concerns of users is the battery lifetime of mobile devices  while running the applications, knowing the fact that increasing the clock frequency of a CPU increases the power consumption . Therefore, there is a tension between the resource hungry applications and resource poor mobile devices. To tackle the aforementioned problem, one solution is to bridge the gap between available and required resources by offloading the burden from mobile devices to the cloud . Cloud computing with abundant processing resources has become an attractive solution in order to ease this pain for the storage and data processing. Cloud computing for mobile applications will enable new services for mobile users. It is true that cloud computing can potentially save energy for the mobile users , however this is not always true when the device consumes more energy to transmit the data to the cloud than to process that data itself . Because of the interference and radio channel conditions, the transmission of the data may consume more energy for the mobile device. However it is not trivial to decide after making a simple comparison of two energy figures for each device served by one base station since the decision may create interference and change the channel conditions for neighboring devices in the surrounding cells. There is also another important factor which has an impact on the decision: delay. A decision making procedure must consider the delay sensitivity of the applications to determine whether to choose local processing or offloading. Mobile devices consume more joules per bit as the delay requirement gets more stringent to process a certain task . Delay requirements from different mobile broadband services can be seen in Table I. In this paper, we investigate the energy saving potential of data offloading in mobile devices under multi-cell multi-user scenario and propose efficient algorithms to make decisions simultaneously for mobile devices to minimize the total energy consumption by meeting the delay requirements from the services. Channel assignment and power allocation problems are considered jointly with the offloading-decision.
|Service Type||Acceptable Delay [7, 8]|
|Third person avatar|
|First person avatar|
|Voice over IP|
|Video over IP|
|Non real-time services||Few seconds|
I-a Related Works
Mobile cloud computing (MCC) provides infrastructure, platform, and software as services to the mobile users . On the other hand, the interaction between cloud and mobile user is inevitable in MCC. Consequently, once users decide to offload data to the cloud, it is necessary to efficiently utilize the available resources. Otherwise, users can not benefit from the potential advantages of MCC. In other words, resource management schemes are the key techniques to guarantee the quality of service (QoS) in the MCC networks . The conducted surveys in  and , addressed the existing studies on the integrating mobile edge computing (MEC) to the mobile networks, the computation offloading schemes, resource management problems, and their current challenges. Accordingly, the main focus of  is to model the energy consumption of applications in the MCC networks. The authors also proposed an energy aware resource allocation algorithm and scheduling in the cloud. A framework for offloading the computation to the cloud is proposed in . They investigated an offloading infrastructure which eased the migration of the code to the cloud. The main goal of  is to study the mobile code offloading architecture. They illustrated that significant energy saving can be obtained by using their offloading methods. Task offloading for different applications for one user case is studied in . In , using experimental measurements, it is shown that wireless access has an inevitable effect on the performance of MCC. The authors in , considered the problem of resource scheduling for multi-service multi-user MCC networks. Also in , a heuristic approach is adopted to minimize the energy consumption of all users while making decision on offloading and resource allocation for each task. The authors in , modeled the energy consumption of the mobile devices. They formulated an optimization problem to minimize the energy consumption of a single device by data offloading. A dynamic application’s task offloading algorithm using Lyapunov optimization is proposed in , aiming at minimizing the energy consumption of users with constraint on the maximum acceptable delay for the application. The authors in , presented a practical offloading framework in a cost aware Wi-Fi system considering the throughput-delay trade offs. In , a game theoretic approach is adopted to design an offloading mechanism for mobile devices. In their model, a multi-user case has been considered while the corresponding QoS as well as their effect on the other users are ignored. In , a decentralized offloading game is proposed to make decision among mobile devices in a simple single channel scenario. The partitioning problem for mobile data stream application is defined in . They have used genetic algorithm to solve the problem. They also reported that partitioning data can enhance the application performance in terms of throughput. The authors in , utilized the Markov decision process approach to solve the problem of task offloading. They have formulated a delay minimization problem to find the optimal task scheduling policy. In , the authors studied the problem of network energy minimization in C-RAN based, MCC system. In this study, the authors jointly optimized the beamforming design and power allocation with a decision making strategy. For energy consumption and latency minimization problem, partial computation offloading algorithm to optimize the computational speed of mobile devices and their transmit power is proposed in . In , the authors deal with the latency issue by means of cloudlet infrastructure, which is a data center to bring the cloud closer to the users. The authors in , proposed a model for the mobile device energy consumption. They have also derived an offloading policy considering delay and energy consumption under single stochastic wireless channel with only ”good” or ”bad” channel state. Their model is limited to single-user single-channel case and interference and users’ QoS is not addressed in their model. The authors in , considered a simple single-user mobile-edge computing system. They proposed an algorithm to optimize the power consumption and to minimize the delay. In this study, the interference analysis and its effect on the offloading decision is missing. The authors in , solved the offloading optimization problem to remove the processing burden from mobile devices without considering the resource allocation. The authors in , modeled the offloading decision as a competitive game where users try to minimize their energy consumptions. They did not consider the power allocation which has significant impact on the performance of the algorithms. In , to minimize the offloading energy consumption, the authors proposed the joint optimization of computing and radio resources considering the latency constraints in a cloud-edge computing network. In , we proposed joint power allocation, decision making and channel assignment (J-PAD) algorithm to perform the resource allocation considering interference and delay constraints.
There are still plenty of challenges to be tackled in the multi-cell multi-user and multi-channel MCC networks. To the best of our knowledge, the problem of resource allocation and decision making for data offloading in multi cell networks considering multi users has not been addressed in the literature. In this paper we aim at minimizing the power consumption of users while considering the user’s QoS in terms of delay and maximum tolerable interference on each channel. We formulate the resource allocation and offloading optimization problem. We show that the problem is mixed integer nonlinear problem (MINLP), where the optimal solution is intractable. To have a tractable solution, we convert the problem to the convex form and propose two algorithms called J-PAD and C-PAD to solve the problem in a polynomial time. The main contribution of this paper can be summarized as follows:
In the context of multi cellular multi user OFDMA MCC networks, we formulate the resource allocation and offloading problem that is aware of network status and users’ demand aiming at minimizing the total power consumption of all users subject to constraints on QoS of users and interference threshold.
We formulated the problem as a mixed integer nonlinear optimization problem (MINLP). To solve the problem, it is converted to the convex form using variable changing, DC approximation, adding penalty factor, and relaxing the binary constraints. Therefore the problem can be solved in a polynomial time.
We also propose two algorithms to solve the problem of resource allocation and decision making. The first algorithm is a centralized scheme, designed to be performed at the base station while the second one is a distributed scheme, which requires a partial information exchange, suitable to be performed at the user terminal. The complexity of these algorithms is also investigated.
Through simulations, we show that there exists an offloading region for each user where offloading can help them to save more power. By comparing the cell edge user and normal user in the network, we show that the optimal region depends not only on delay threshold and bit stream size of users but also on the position and channel condition of the users.
The rest of the paper is organized as follows. In Section II, system model is presented. The problem formulation and the solution methodology are discussed in Section II-C. We propose our algorithms and corresponding complexity analysis in Section IV followed by the simulation results presented in Section V. Finally, we bring the concluding remarks in Section VI.
Ii System Model and Problem Formulation
Ii-a System Description
According to Fig.1, we consider a cellular network with base stations where mobile users (MUs) are uniformly distributed within a cell range. Each base station is equipped with a server which is responsible for the offloaded users’ data processing and we assume there is a centralized unit which exchanges the required information between base stations using backhaul.
Each cell can serve up to active users. We assume that the available bandwidth is divided to sub-channels. The sub-channel model is adopted from  and is composed of large scale fading, small scale fading, and shadow fading. Also, we consider OFDMA as an access method, hence users in the same cell cannot share same sub-channel with each other; however, each user might experience an interference from neighboring cells. In this model, user in cell has a bit stream of size . We have generated the users’ bit stream size with normal distribution with mean and variance . Users can process the data on their own or send it to the cloud. Users can not use both schemes, e.g. sending a portion of the data to the cloud and processing the remaining data locally. The data corresponds to the user in cell should be processed within the maximum acceptable delay (delay threshold), , generated with normal distribution with mean and variance . As we assume that the processed data is short, the response time delay can be neglected .
Ii-B Power Model
Ii-B1 Local Processing Power Model
When users are supposed to process the data locally, the CPU power consumption is dominant. It is composed of dynamic power, circuit power, and leakage power . The dynamic power as a dominating power in CPU, is function of required CPU cycles which depends on both delay threshold and input data size. Under the optimal value for CPU frequency, the minimum power consumption of CPU is proportional to the , where is the maximum acceptable delay and is the users’ bit stream size and is the scaling factor power . Consequently, we use the following model for local processing power consumption:
where is the local processing power consumption of user in cell and is a constant value that depends on the CPU and application parameters .
Ii-B2 Offloading Power Model
The transmission power, for sending data to the cloud is,
where denotes the transmission power consumption of user in cell and is a binary variable representing whether the corresponding sub-channel is assigned to the user or not. Therefore, the user’s total transmission power is
where is power amplifier coefficient and is a constant circuit power.
Ii-B3 Aggregated Power Model
Total power consumption of the active users in the network can be written as:
The integer variable takes the value of if user in cell uses its own processor and takes the value of if the user sends the data to the cloud. Therefore, the total power consumption can be written as:
Moreover, the signal to noise plus interference ratio at the base station in cell is given by:
where the channel gain from th MU of th cell is denoted by . The channel gain from user , in cell to the cell is denoted by . The first term in the denominator of (7) is the noise power and the second term is the interference from other cells on channel in cell which can be calculated as:
In our assumption, the users must utilize the whole duration. Considering fixed , power minimization is in line with energy minimization.
Ii-C Problem Formulation
In this section, we develop the mathematical formulation for decision making and resource allocation problem. The base station determines the offloading users and allocates sub-channels to its users and specifies the suitable power level on each sub-channel. The objective of the resource allocation is to minimize the aggregated power consumption of all users by allocating resources to the offloading users in a way that their delay requirement is satisfied. The optimization problem can be formulated as follows:
In (9), the objective is to minimize the total power consumption of all active MUs in the network. The constraint C1 indicates that the transmit power of each user is limited to . The constraint C2 states that for each base station , the interference arising from other cells on each sub-channel is restricted to be within a threshold. The constraint C3 restricts the maximum tolerable delay for user in the -th cell to if the aforementioned user sends its data to the cloud. If a user decides to process the data locally, then the CPU will be responsible for satisfying this constraint. In our analysis we assume that CPU uses the entire available time to reduce the power consumption. The constraint C4 addresses the processing limitation at the cloud. The constraint C5 guarantees the OFDMA assumption in each cell where each sub-channel is assigned to at most one user. The constraints C6 and C7 indicate that the sub-channel and data offloading indices are binary variables. It is worth mentioning that the constraint C3 can be written in an equivalent form. Using C3 we will have
Defining and noting that the left side of (10) is the total data rate of the -th user in the -th cell, we obtain the following equivalent constraint for C3:
In the rest of this paper, we consider the constraint C3 in the form presented in (11).
The optimization problem defined in (9) is a mixed integer nonlinear problem (MINLP) and finding the optimal solution is NP-hard and cannot be solved in a polynomial time. The non-convexity is coming from three reasons in the problem. The first and second reasons are the binary inherent of decision making variable, constraint C7, and the combinatorial nature of sub-channel allocation, constraint C6. The third one is due to the constraints C3 and C4 and existence of the power allocation variable in the denominator of SINR formula defined in (7). In the following section, we address how to deal with these variables and solve the problem by converting it into a convex form.
Iii Solution Methodology
In this section, we aim to transform the primary problem defined in Section II-C into a canonical convex form. In this regard, we classify the challenges into two categories, binary variables and non convex functions.
To resolve the challenges caused by the binary variables, one approach is to relax the troublesome constraints, sub-channel allocation for instance, to shape the problem into a convex form and then making hard decision in the end as we did in . An alternative approach is to add auxiliary constraints to enforce the solution to be in our desired form as we will describe later. Another approach is to break the problem into sub-problems so that one could successively first solve the problem for the annoying binary variable and consequently, given this variable, solve the rest of the problem.
To deal with the non-convex functions, we utilize a theory of optimization for a superclass of convex functions, called Difference of Convex (D.C.) functions . Later we demonstrate that our problem can be written in form of D.C. functions. In the end, applying Taylor approximation enables us to solve the last stage of converting the primary problem defined in (9), into a convex form. Having all these powerful approaches available, we tackle the problem, as follows.
In the first step, we break down the problem into two sub-problems and then solve them successively. The first sub-problem is to determine the channel assignment for each user in each cell. The second sub-problem is to find out the decision variable and power allocation. We use the solution of the first sub-problem as an input to the second sub-problem. Also, the results of second sub-problem is used to update the solution for the first sub-problem and this process continues until the convergence. Furthermore, we apply two approaches to solve the second sub-problem. The overview of two utilized approaches to solve the problem can be seen in equations (III) and (III).
In the first approach, after separating the sub-channel assignment, the problem can be solved jointly for other variables e.g. power allocation and decision variable as follows:
In the second approach, we separate sub-channel assignment, power allocation, and decision variable from each other as follows:
The main difference between these two approaches is that in the former, we jointly solve the problem of power allocation and decision making; However, in the latter, we divide the second sub-problem into two steps and solve each sub-problem individually. In the following subsections, first we deal with solving the first sub-problem followed by solving the second sub-problem by converting it into a convex from.
Iii-a Sub-Problem One: Optimal Sub-channel Assignment
Given the power allocation vector , the optimal sub-channel assignment for further power allocation and offloading in the next iteration is as follows:
Given the power vector, minimum power consumption is attained when each sub-channel in each cell is assigned to the MU with the highest effective interference on that sub-channel.
Because the problem is power minimization and also minimum data rate requirement of users should be satisfied, the minimum power is consumed when the inequality of minimum required rate becomes the equality. Now let us assume that all users are given the best possible channel to reach their data rate with minimum power consumption. Also, let a user have a channel with effective interference value lower than a highest value and the user has data rate on that channel. Thus, the consumed power on that channel is
where here is a constant value. Also from our assumption, we know that the effective interference in a denominator of (15), e.g. , is not the highest possible value. Hence, if we assign the highest effective interference value to this user, the total power consumption will be lower and this is in contrast with the assumption of minimum power consumption. Therefore, minimum power is consumed when maximum effective interference is the criterion for the channel allocation. In other words, with higher effective interference, less power is consumed to satisfy the minimum required rate. ∎
Let denotes the effective interference vector of a user on the channel . High effective interference in a channel means that the MU is experiencing a good channel condition with a low interference from other cells. Therefore, the decision for channel allocation will be made based on the following criterion:
Thus, a channel allocation matrix at time , can be formed with the elements obtained from the equation (16).
Iii-B Sub-Problem Two: Power Allocation, and Decision Making
In the previous subsection we have solved the problem of sub-channel assignment and therefore one of the challenges of the primary problem (9) is resolved. The results of previous subsection will be used in this section to solve the sub-problem of power allocation and decision making. As in (III) and (III), two approaches are applied to tackle the challenges. These approaches are discussed in the following subsections.
Iii-B1 Joint Power Allocation and Decision Making (J-PAD)
Given a sub-channel assignment, the problem of joint power allocation and data offloading can be rewritten as:
To solve (17), we first reformulate it to a more mathematically tractable form. Since is a binary variable, we can write . Moreover, the problem consists of the product terms of . We use the following change of variable
to recast the optimization problem. Also, the optimization problem includes integer variable . Hence to convert s into continuous variables, we can express the constraint C7 as the intersection of the following regions:
Hence, we can write the optimization problem of (17) as follows
The problem of (III-B1) is a continuous optimization problem with respect to all variables. However, we aim to find integer solutions for ’s. To attain this goal, we add a penalty function to the objective function of (III-B1) to penalize it if the values of ’s are not integer. Thus, the problem can be modified to
where is the penalty factor which should be . It can be shown that, for sufficiently large values of , the optimization problem of (III-B1) is equivalent to (III-B1) and attains the same optimal value .
We start with this point that the optimization problem of (III-B1) can be expressed as and its dual problem can be written as . Suppose that , , and denote the optimal solution and the optimal value of of the optimization problem of (III-B1), respectively, i.e.
Then, we will have
Recall that for , we have
In other words, is an increasing function in and according to (III-B1), is bounded by the optimal value of problem (III-B1). If for some , , then is feasible for the main problem, too. As a result, we will have
since is a monotonically increasing function with respect to , for we have
At the optimal point and for the second case where we have , goes to because of the monotonicity of the with respect to the . This contradicts the max-min inequality which states that is bounded from above. Thus, the term should be zero, and the results of the first case hold. ∎
Now, the optimization problem can be converted to the following problem
where . We can write the objective function in (III-B1) as , where , and are two convex functions. In a similar way, for , we define and as
then, we can write constraints C3 and C4 as follows
where , , , and are concave functions. Therefore, the problem is in the form of the difference of two convex (concave) functions (D.C. programming) . In D.C. programming, we start from a feasible initial point and iteratively solve the optimization problem. Let denote the iteration number. At the -th iteration, to make the problem convex, using the first order Taylor approximation for , and as follows
where and are the solutions of the problem at -th iteration and denotes the gradient operation with respect to . Thus, at the -th iteration, instead of dealing with the problem of (17), we solve the following convex problem
It can be shown that the D.C. programming results in a sequence of feasible solutions that iteratively achieves better solutions than previous iteration until it converges.
The D.C. programming results in a sequence of feasible solutions that iteratively decrease the total power consumption of the network.
To show that our solutions are feasible for the original problem, first, we notice that the solution of the approximated problem in the -th iteration must satisfy the constraint C3 and C4, i.e.,
On the other hand, since and are two concave functions with respect to , due to the first order condition for the concave functions , we have
Thus, the solution for the approximated problem is feasible for the original problem too. Now, we show that the total power consumption of the network will decrease iteratively. Since is a convex function, due to the first order condition for the convex functions , we have
Thus, the total power consumption of the network decreases as iterations continue. ∎
Iii-B2 Channel assignment, Power Allocation, and Decision Making (C-PAD)
Applying the first order Taylor approximation, the optimization problem can be written as
Given sub-channel assignment and power consumption vectors, offloading decisions can be made by users. Recall the power consumption of user in cell in (1) and (3). Each user can compare offloading and local processing power consumption to make the decision as follows: