The limited energy and computational resources in small-scale smart devices impede the expansion of the range of applications that those devices can support, especially to applications with tight latency constraints. Mobile edge computing is a promising framework that provides shared computational resources in the access points in the network and provides devices in that network with the opportunity to offload (a portion of) their computational tasks to the access points. To effectively capture that opportunity in an offloading system with multiple devices, the available communication and computation resources must be efficiently allocated. The main focus of this thesis is on the optimal allocation of communication resources in a K-user offloading system. The resource allocation problem that is considered in this thesis captures minimizing the total energy consumption of users while the requirements of the users, and their computational tasks, are met. That problem is addressed for two of the most widely-considered classes of computational tasks in the literature, namely, indivisible tasks (binary offloading) and divisible tasks (partial offloading).
This thesis begins with an exploration of the impact of the choice of multiple access scheme that is employed by the system on the total energy consumption of the users. In particular, the problem of minimizing the total energy consumption of a two-user
binary offloading system is tackled under various multiple access schemes, namely time division multiple access (TDMA), sequential decoding without time sharing, independent decoding, and multiple access schemes that can exploit the full capabilities of the channel, which are referred to as full multiple access schemes (FullMA) in this thesis. Using a decomposition-based approach, closed-form solutions to the resource allocation problem are obtained. Those expressions show that by exploiting the full capabilities of the channel, a FullMA scheme can significantly reduce the total energy consumption of the users as compared to the other schemes. The closed-form expressions also show that when the channel gains of the two users are equal, the TDMA scheme can achieve the optimal energy consumption. For the case of partial offloading, an analogous analysis leads to a reduced-dimension design problem and an extension to the optimally result for TDMA. In the next step of the development, the insights obtained from the decomposition-based analysis of the two-user case are used to tackle the communication resource allocation problem for a K-user offloading system in which the users are assumed to be served over a single time slot. Based on their performance in the two-user case, FullMA and TDMA schemes are considered. The mixed-integer optimization problem that arises in the binary offloading case is addressed by employing a decomposition approach with a closed-form expression obtained for the optimal resource allocation for given offloading decisions, and a tailored pruned greedy search algorithm developed herein for the offloading decisions. By exploiting the maximum allowable latency of each individual user, the proposed algorithm is able to significantly reduce the energy consumption of the users in comparison to the existing algorithms in the literature that assume equal latency constraints for all users. Furthermore, with the closed-form optimal solution to the resource allocation problem obtained for given offloading decisions, the proposed algorithm has a significantly lower computational cost compared to the existing algorithms. In the partial offloading case, a quasi-closed- form solution is obtained for the resource allocation problem.
Finally, a time-slotted signalling structure is proposed as an optimal transmission structure for a generic K-user offloading system. Furthermore, an optimal times-lotted structure that requires only K time slots is developed for a K-user offloading system that employs a FullMA scheme. The proposed time-slotted structure not only exploits the maximum latency constraint of each user, it also exploits the differences between the latency constraints of the users by taking advantage of the interference reduction that arises when a user finishes offloading. The proposed time-slotted FullMA signalling structure significantly reduces the energy consumption of the users compared to some existing methods that employ the TDMA scheme, and compared to those with FullMA, but sub-optimal single-time-slot signalling structures. Moreover, the computational cost of the proposed time-slotted algorithm is significantly lower than that of the existing algorithms in the literature.
