Mobile computation offloading (MCO) is a way of improving mobile device (MD) performance by offloading certain task executions to a more resourceful edge server (ES), rather than running them locally on the MD. This thesis first considers the problem of assigning the wireless communication bandwidth and the ES capacity needed for this remote task execution, so that task completion time constraints are satisfied. The objective is to minimize the average power consumption of the MDs, subject to a cost budget constraint on communication and computation resources. The thesis includes contributions for both soft and hard task completion deadline constraints. The soft deadline case aims to create assignments so that the probability of task completion time deadline violation does not exceed a given violation threshold. In the hard deadline case, it creates resource assignments where task completion time deadlines are always satisfied. The problems are first formulated as mixed integer nonlinear programs. Approximate solutions are then obtained by decomposing the problems into a collection of convex subproblems that can be efficiently solved. Results are presented that demonstrate the quality of the proposed solutions, which can achieve near optimum performance over a wide range of system parameters.

The thesis then introduces algorithms for static task class partitioning in MCO. The objective is to partition a given set of task classes into two sets that are either executed locally or those classes that are permitted to contend for remote ES execution. The goal is to find the task class partition that gives the minimum mean MD power consumption subject to task completion deadlines. The thesis generates these partitions for both soft and hard task completion deadlines. Two variations of the problem are considered. The first assumes that the wireless and computational capacities are given and the second generates both capacity assignments subject to an additional resource cost budget constraint. Two class ordering methods are introduced, one based on a task latency criterion, and another that first sorts and groups classes based on a mean power consumption criterion and then orders the task classes within each group based on a task completion time criterion. A variety of simulation results are presented that demonstrate the excellent performance of the proposed solutions.

The thesis then considers the use of digital twins (DTs) to offload physical system (PS) activity. Each DT periodically communicates with its PS, and uses these updates to implement features that reflect the real behaviour of the device. A given feature can be implemented using different models that create the feature with differing levels of system accuracy. The objective is to maximize the minimum feature accuracy for the requested features by making appropriate model selections subject to wireless channel and ES resource availability. The model selection problem is first formulated as an NP-complete integer program. It is then decomposed into multiple subproblems, each consisting of a modified Knapsack problem. A polynomial-time approximation algorithm is proposed using dynamic programming to solve it efficiently, by violating its constraints by at most a given factor. A generalization of the model selection problem is then given and the thesis proposes an approximation algorithm using dependent rounding to solve it efficiently with guaranteed constraint violations. A variety of simulation results are presented that demonstrate the excellent performance of the proposed solutions.