In this paper, we investigate a mobile edge computing (MEC) system with its computation task subjected to sequential task dependency, which is critical for video stream processing and intelligent MEC applications. To minimize energy consumption per mobile device while limiting task processing delay, task offloading strategy, communication resource, and computation resource are optimized jointly under both slow and fast fading channels. In slow fading channels, an optimization problem is formulated, which is mixed-integer and non-convex. To solve this challenging problem, we decompose it as a one-dimensional search of task offloading decision problem and a non-convex optimization problem with task offloading decision given. Through mathematical manipulations, the non-convex problem is transformed to be a convex one, which is shown to be solvable only with the simple Golden search method. In fast fading channels, optimal online policy depending on instant channel state is derived. In addition, it is proved that the derived policy will converge to be offline when channel coherence time is low, which can help to save extra computation complexity. Numerical results verify the correctness of our analysis and the effectiveness of our proposed strategies over existing methods.
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