We consider a multi-user mobile cloud computing system with a computing access point (CAP) where each mobile user has multiple dependent tasks to be processed using a round-by-round schedule. The CAP can either process the received tasks from mobile users or offload them to the cloud. In each round, we aim to jointly optimize the offloading decisions of all users and the CAP, together with communication and processing resource allocation, to minimize the overall cost of energy, computation, and the maximum delay among all users. Since the centralized optimization problem is non-convex and mobile users may not follow the obtained solution, we further formulate a mobile cloud offloading game. We show the existence of a Nash equilibrium (NE) of this game and propose an algorithm to attain the NE. Simulation results show that our proposed algorithm gives nearly optimal performance in terms of the total system cost under various parameter settings.
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