Abstract
In ultra-dense networks, the increasing popularity of computation intensive applications imposes challenges to the resource-constrained smart mobile devices (SMDs), which may be solved by offloading these computation tasks to the nearby mobile edge computing centers. However, when massive SMDs offload computation tasks in a dynamic wireless environment simultaneously, the joint optimization of their offloading decisions becomes prohibitively complex. In this paper, we firstly model the joint optimization problem as a multi-user non-cooperative dynamic stochastic game, then propose a mean field game based algorithm to solve it with a drastically reduced complexity. We derive the two partial differential equations ruling the optimal strategies of the mean field game, namely the Hamilton-Jacobi-Bellman and Fokker-Planck-Kolmogorov equations, which are solved in an iterative manner in our proposed algorithm. Numerical results demonstrate that the proposed mean field game-based offloading algorithm requires a lower cumulated cost than the conventional strategies under the latency constraints of computation tasks, with perfect prediction of future channel states. It also appears that the performance of the mean field game-based offloading strategy depends on the accuracy of the future channel knowledge provided to the system, as the uncertainty may compromise its cumulated cost performance.