  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and the optimality loss on system utility under outdated NSI is analyzed.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.
