Multi-Objective Optimization of Fog Computing Assisted Wireless Powered Networks: Joint Energy and Time Minimization

This paper studies the optimal design of the fog computing assisted wireless powered network, where an access point (AP) transmits information and charges an energy-limited sensor device with Radio Frequency (RF) energy transfer. The sensor device then uses the harvested energy to decode information and execute computing. Two candidate computing modes, i.e., local computing and fog computing modes, are considered. Two multi-objective optimization problems are formulated to minimize the required energy and time for the two modes, where the time assignments and the transmit power are jointly optimized. For the local computing mode, we obtain the closed-form expression of the optimal time assignment for energy harvesting by solving a convex optimization problem, and then analyze the effects of scaling factor between the minimal required energy and time on the optimal time assignment. For the fog computing mode, we derive closed-form and semi-closed-form expressions of the optimal transmit power and time assignment for offloading by adopting the Lagrangian dual method, the Karush–Kuhn–Tucker (KKT) conditions and Lambert W Function. Simulation results show that, when the sensor device has poor computing capacity or when it is far away from the AP, the fog computing mode is the better choice; otherwise, the local computing is preferred to achieve a better performance.