Task Offloading and Resource Allocation with Multiple CAPs and Selfish Users

In this work, we consider a multi-user mobile edge computing system with multiple computing access points (CAPs). Each mobile user has multiple dependent tasks that must be processed in a round-by-round schedule. In every round, a user may process their individual task locally, or choose to offload their task to one of the $M$ CAPs or the remote cloud server, in order to possibly reduce their processing cost. We aim to jointly optimize the offloading decisions of the users and the resource allocation decisions for each CAP over a global objective function, defined as a weighted sum of total energy consumption and the round time. We first present a centralized heuristic solution, termed MCAP, where the original problem is relaxed to a semi-definite program (SDP) to probabilistically generate the offloading decision. Then, recognizing that the users often exhibit selfish behavior to reduce their individual cost, we propose a game-theoretical approach, termed MCAP-NE, which allows us to compute a Nash Equilibrium (NE) through a finite improvement method starting from the previous SDP solution. This approach leads to a solution from which the users have no incentive to deviate, with substantially reduced NE computation time. In simulation, we compare the system cost of the NE solution with those of MCAP, MCAP-NE, a random mapping, and the optimal solution, showing that our NE solution attains near optimal performance under a wide set of parameter settings, as well as demonstrating the advantages of using MCAP to produce the initial point for MCAP-NE.