High-Resolution Cross-Layer Scheduling for Low-Latency Communications: When Infinitesimal Method Meets Stochastic Order

Latency-aware scheduling has attracted considerable recent attention due to its potential wide-ranging applications in smart grids, automatic driving, telesurgery, and factory automation. Existing scheduling policies mainly exploit low-resolution adaptive modulation and coding (AMC), in which the number of legitimate transmission rate is quite limited or even binary owing to the stringently constrained hardware complexity. Recently, rate adaption with a huge number of selectable rates is made practical by cutting-edge AMC, e.g., deep neural network (DNN) empowered transceivers. However, the performance limit of high-resolution scheduling remains open. In this paper, its optimal delay-power tradeoff is presented by adopting infinitesimal analysis and stochastic order. Particularly, we conceive two quantized version of a high-resolution scheduling that reveal its upper and lower performance bounds. The two bounds are shown to converge to the performance limit of infinite-resolution scheduling with controllable variables as the resolution or the number of optional rates increases, thereby allowing us to leverage the squeeze theorem to attain its delay-power tradeoff. We show that the gap between two quantized cross-layer optimization under delay and power constraints respectively vanishes as the quantization error diminishes, thereby attaining the optimal scheduling through a fitting approach. Simulation results demonstrate the substantial gain of high-resolution scheduling.