Low-Complexity Scheduling Policies for Achieving Throughput and Asymptotic Delay Optimality in Multi-Channel Wireless Networks

Abstract: In this paper, we study the scheduling problem for downlink transmission in a multi-channel (e.g., OFDM-based) wireless network. We focus on a single cell, with the aim of developing a unifying framework for designing low-complexity scheduling policies that can provide optimal performance in terms of both throughput and delay. We develop new easy-to-verify sufficient conditions for rate-function delay optimality (in the many-channel many-user asymptotic regime) and throughput optimality (in general non-asymptotic setting), respectively. The sufficient conditions allow us to prove rate-function delay optimality for a class of Oldest Packets First (OPF) policies and throughput optimality for a large class of Maximum Weight in the Fluid limit (MWF) policies, respectively. By exploiting the special features of our carefully chosen sufficient conditions and intelligently combining policies from the classes of OPF and MWF policies, we design hybrid policies that are both rate-function delay-optimal and throughput-optimal with a complexity of $O(n^{2.5} \log n)$, where $n$ is the number of channels or users. Our sufficient condition is also used to show that a previously proposed policy called Delay Weighted Matching (DWM) is rate-function delay-optimal. However, DWM incurs a high complexity of $O(n^5)$. Thus, our approach yields significantly lower complexity than the only previously designed delay and throughput optimal scheduling policy. We also conduct numerical experiments to validate our theoretical results.