Energy-efficient scheduling with individual packet delay constraints over a fading channel

This article focuses on energy-efficient packet transmission with individual packet delay constraints over a fading channel. The problem of optimal offline scheduling (vis-à-vis total transmission energy), assuming information of all packet arrivals and channel states before scheduling, is formulated as a convex optimization problem with linear constraints. The optimality conditions are analyzed. From the analysis, a recursive algorithm is developed to search for the optimal offline scheduling. The optimal offline scheduler tries to equalize the energy-rate derivative function as much as possible subject to causality and delay constraints, in contrast to the equalization of transmission rates for optimal scheduling in static channels. It is shown that the optimal offline schedulers for fading and static channels have a similar symmetry property. Combining the symmetry property with potential idling periods, upper and lower bounds on the average packet delay are derived. The properties of the optimal offline schedule and the impact of packet sizes, individual delay constraints, and channel variations are demonstrated via simulations. A heuristic online scheduling algorithm, assuming causal traffic and channel information, is proposed and shown via simulations to achieve energy and delay performances comparable to those of the optimal offline scheduler in a wide range of scenarios.