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Task admission is critical to delay-sensitive applications in mobile edge computing, but technically challenging due to its combinatorial mixed nature and consequently limited scalability. We propose an asymptotically optimal task admission approach which is able to guarantee task delays and achieve (1 −)-approximation of the computationally prohibitive maximum energy saving at a time-complexity linearly scaling with devices. is linear to the quantization interval of energy. The key idea is to transform the mixed integer programming of task admission to an integer programming (IP) problem with the optimal substructure by pre-admitting resource-restrained devices. Another important aspect is a new quantized dynamic programming algorithm which we develop to exploit the optimal substructure and solve the IP. The quantization interval of energy is optimized to achieve an [O(), O(1/)]-tradeoff between the optimality loss and time-complexity of the algorithm. Simulations show that our approach is able to dramatically enhance the scalability of task admission at a marginal cost of extra energy, as compared to the optimal branch and bound method, and can be efficiently implemented for online programming.

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A spurt of progress in wireless power transfer (WPT) and mobile edge computing (MEC) provides a promising approach for Industrial Internet of Things (IIoT) to enhance the quality and productivity of manufacturing. Scheduling in such a scenario is challenging due to congested wireless channels, time-dependent energy constraints, complicated device heterogeneity, and prohibitive signaling overheads. In this paper, we first propose an online algorithm, called energy-aware resource scheduling (ERS), to maximize the system utility comprising throughput and fairness, with consideration on both system sustainability and stability. Based on Lyapunov optimization and convex optimization techniques, the proposed algorithm achieves asymptotic optimality for heterogeneous IIoT systems without prior knowledge of network state information (NSI). Subsequently, we extend the ERS algorithm to a more realistic scenario where the overhead and delay of NSI feedbacks are nonnegligible. The optimal scheduling decisions of the scenario are provided, and the optimality loss on system utility under outdated NSI is analyzed. Simulations verify our theoretical claims and demonstrate the gains of our proposed ERS algorithm over alternative benchmark schemes.

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