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In this work, we consider a multi-user mobile edge computing system withmultiple computing access points (CAPs). Each mobile user has multipledependent tasks that must be processed in a round-by-round schedule. In everyround, a user may process their individual task locally, or choose to offloadtheir task to one of the $M$ CAPs or the remote cloud server, in order topossibly reduce their processing cost. We aim to jointly optimize theoffloading decisions of the users and the resource allocation decisions foreach CAP over a global objective function, defined as a weighted sum of totalenergy consumption and the round time. We first present a centralized heuristicsolution, termed MCAP, where the original problem is relaxed to a semi-definiteprogram (SDP) to probabilistically generate the offloading decision. Then,recognizing that the users often exhibit selfish behavior to reduce theirindividual cost, we propose a game-theoretical approach, termed MCAP-NE, whichallows us to compute a Nash Equilibrium (NE) through a finite improvementmethod starting from the previous SDP solution. This approach leads to asolution from which the users have no incentive to deviate, with substantiallyreduced NE computation time. In simulation, we compare the system cost of theNE solution with those of MCAP, MCAP-NE, a random mapping, and the optimalsolution, showing that our NE solution attains near optimal performance under awide set of parameter settings, as well as demonstrating the advantages ofusing MCAP to produce the initial point for MCAP-NE.

Task Offloading and Resource Allocation with Multiple CAPs and Selfish Users