  In this paper, we investigate the scheduling design of a mobile-edge
computing (MEC) system, where the random arrival of mobile devices with
computation tasks in both spatial and temporal domains is considered. The
binary computation offloading model is adopted. Every task is indivisible and
can be computed at either the mobile device or the MEC server. We formulate the
optimization of task offloading decision, uplink transmission device selection
and power allocation in all the frames as an infinite-horizon Markov decision
process (MDP). Due to the uncertainty in device number and location,
conventional approximate MDP approaches to addressing the curse of
dimensionality cannot be applied. A novel low-complexity sub-optimal solution
framework is then proposed. We first introduce a baseline scheduling policy,
whose value function can be derived analytically. Then, one-step policy
iteration is adopted to obtain a sub-optimal scheduling policy whose
performance can be bounded analytically. Simulation results show that the gain
of the sub-optimal policy over various benchmarks is significant.
