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.