By offloading tasks from the mobile device (MD) to its nearby deployed access points (APs), each of which is connected to one server for task processing, computation offloading can strike a balance between MD's task execution delay and energy consumption in mobile edge computing (MEC) systems. Considering communication and computation dynamics in MEC systems, we aim to design online computation offloading mechanisms in this paper to minimize the time average expected task execution delay under the constraint of average energy consumption. Firstly, with known current channel gains between the MD and APs as well as available computing capability at MEC servers, we leverage the Lyapunov optimization framework to make an optimal one-slot decision on MD's transmit power allocation and MEC server selection. On this basis, we then consider a more realistic scenario, where it is difficult to capture current available computing capability at MEC servers, and combine the multi-armed bandit framework for an online learning based MEC server selection algorithm. Finally, through theoretical analyses and extensive simulations, we demonstrate the near-optimality and feasibility of our proposed algorithms, and present that our proposed algorithms fully explore the interplay between communication and computation with enriched user experience and reduced energy consumption.
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