Optimal Computation Offloading with a Shared MEC Center: A Mean Field Game Approach

In this paper, we consider the scenario of a multi-cell 5G ultra-dense network where a shared mobile edge computing (MEC) center is built. Each smart mobile device is required to offload its computation-heavy tasks to the MEC center, within a predefined time, at a minimal cost. We firstly model the problem as a N-users non-cooperative dynamic stochastic game (DSG). Bypassing the complexity of analyzing a Nash equilibrium, we turn a N-body problem into an equivalent mean field game, which is a 2-body problem only. Then, the related Hamilton-Jacobi-Bellman (HJB) and Fokker-Planck-Kolmogorov (FPK) equations are deduced, and the optimal offloading strategy is obtained by solving these two partial differential equations (PDEs) interactively. Numerical results reveal that the optimal offloading strategy can reduce the average system cost by at least 36:5% compared to the maximum rate offloading strategy under the given latency constraint.