Mobile edge computing (MEC) can extend the computing capability of mobile users (MUs), by offloading computational tasks from MUs to proximal MEC servers. Specifically, offloaded tasks are firstly transmitted to access points (APs) via wireless channels, and then relayed to MEC servers through backhauls. Due to differentiated wireless channels and input data sizes, offloaded tasks from different MUs arrive at the AP and MEC server in an asynchronous manner. Considering such asynchrony, we design sequential execution model for backhaul transmission and task processing in the MEC server and present its merits in terms of maximum task completion time for different backhaul configurations: 1) With ideal backhaul, the optimal task scheduling order in the MEC server follows the first coming and first scheduling rule; 2) With limited backhaul, an effective two-stage task scheduling order on the backhaul and MEC server is determined by the Johnson's rule. Further, we make suboptimal decisions on wireless resource provisioning and task offloading, with respect to the attained task scheduling order and derived necessary and sufficient conditions under which full local processing and full offloading are optimal. Finally, simulation results demonstrate the superiority of our devised sequential execution model and computation offloading mechanisms.
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