In this paper, we investigate the allocation of resource in D2D-aided Fog computing system with multiple mobile user equipments (MUEs). We consider each MUE has a request for task from a task library and needs to make a decision on task performing with a selection of three processing modes which include local mode, fog offloading mode, and cloud offloading mode. Two scenarios are considered in this paper, which mean task caching and its optimization in off-peak time, task offloading, and its optimization in immediate time. In particular, task caching refers to cache the completed task application and its related data. In the first scenario, to maximize the average utility of MUEs, a task caching optimization problem is formulated with stochastic theory and is solved by a GA-based task caching algorithm. In the second scenario, to maximize the total utility of system, the task offloading and resource optimization problem is formulated as a mixed integer nonlinear programming problem (MINLP) with a joint consideration of the MUE allocation policy, task offloading policy, and computational resource allocation policy. Due to the nonconvex of the problem, we transform it into multi-MUEs association problem (MMAP) and mixed Fog/Cloud task offloading optimization problem (MFCOOP). The former problem is solved by a Gini coefficient-based MUEs allocation algorithm which can select the most proper MUEs who contribute more to the total utility. The task offloading optimization problem is proved as a potential game and solved by a distributed algorithm with Lagrange multiplier. At last, the simulations show the effectiveness of the proposed scheme with the comparison of other baseline schemes.
