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In this thesis we consider a set of mobile users that employ cloud-based computation offloading. In computation offloading, user energy consumption can be decreased by uploading and executing jobs on a remote server, rather than processing the jobs locally. In order to execute jobs in the cloud however, the user uploads must occur over a base station channel which is shared by all of the uploading users. Since the job completion times are subject to hard deadline constraints, this restricts the feasible set of jobs that can be remotely processed, and may constrain the users ability to reduce energy usage. The system is modelled as a competitive game in which each user is interested in minimizing its own energy consumption. The game is subject to the real-time constraints imposed by the job execution deadlines, user specific channel bit rates, and the competition over the shared communication channel. The thesis shows that for a variety of parameters, a game where each user independently sets its offloading decisions always has a pure Nash equilibrium, and a Gauss-Seidel method for determining this equilibrium is introduced. Results are presented which illustrate that the system always converges to a Nash equilibrium using the GaussSeidel method. Data is also presented which show the number of Nash equilibria that are found, the number of iterations required, and the quality of the solutions.We find that the solutions perform well compared to a lower bound on total energy

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We consider the problem of fair multi-resource allocation for mobile edge computing (MEC) with multiple access points. In MEC, user tasks are uploaded over wireless communication channels to the access points, where they are then processed with multiple types of computing resources. What distinguishes fair multi-resource allocation in the MEC environment from more general cloud computing is that a user may experience different levels of wireless channel quality on different access points, so that the user's channel bandwidth demand is not fixed. Existing resource allocation studies for cloud computing generally consider Pareto Optimality (PO), Envy-Freeness (EF), Sharing Incentive (SI), and Strategy-Proofness (SP) as the most desirable fairness properties. In this work, we show these properties are no longer compatible in MEC, since there exists no resource allocation rule that can satisfy PO+EF+SP or PO+SI+SP. Hence, we propose a resource allocation rule, called Maximum Task Product (MTP), that retains PO, EF, and SI. Extensive simulation driven by Google cluster traces further shows that MTP improves resource utilization while achieving these fairness properties.

We study the problem of fair and efficient mechanism design for allocating multiple resources in multiple servers among a set of users with Leontief utilities. This problem is motivated by a mobile edge computing environment where each mobile user cannot establish a wireless connection simultaneously to multiple edge servers. Each user is a selfish utility maximizing agent that chooses a single server for its job execution. When a server is shared by multiple users, a resource allocation rule decides the utility that each user must receive. Our goal is to design a mechanism that always admits a Nash Equilibrium (NE), i.e., a state where no user has incentive to change its server, that (1) can be reached in polynomial time and (2) provides fair and efficient resource allocation. We propose the Multi-resource Allocation Game Induced by Kalai-Smorodinsky bargaining solution (MAGIKS) and prove that under discrete resource demands it finds an NE in O (poly(n)) moves for any fixed server configuration, where n is the number of users. Furthermore, MAGIKS satisfies envy-freeness, sharing incentive, and Pareto optimality on each server. Regarding fairness among users in different servers, we prove that MAGIKS satisfies 2-approximate envy-freeness and maximin share guarantee. Moreover, we show that 2-approximate envy-freeness is the best that any mechanism that satisfies local Pareto optimality can achieve at its NEs.