Achieving Optimal Throughput and Near-Optimal Asymptotic Delay Performance in Multi-Channel Wireless Networks with Low Complexity: A Practical Greedy Scheduling Policy

In this paper, we focus on the scheduling problem in multi-channel wireless networks, e.g., the downlink of a single cell in fourth generation (4G) OFDM-based cellular networks. Our goal is to design practical scheduling policies that can achieve provably good performance in terms of both throughput and delay, at a low complexity. While a class of \(O(n^{2.5} \log n)\)-complexity hybrid scheduling policies are recently developed to guarantee both rate-function delay optimality (in the many-channel many-user asymptotic regime) and throughput optimality (in the general non-asymptotic setting), their practical complexity is typically high. To address this issue, we develop a simple greedy policy called Delay-based Server-Side-Greedy (D-SSG) with a \lower complexity \(2n^2+2n\), and rigorously prove that D-SSG not only achieves throughput optimality, but also guarantees near-optimal asymptotic delay performance. Specifically, we show that the rate-function attained by D-SSG for any delay-violation threshold \(b\), is no smaller than the maximum achievable rate-function by any scheduling policy for threshold \(b-1\). Thus, we are able to achieve a reduction in complexity (from \(O(n^{2.5} \log n)\) of the hybrid policies to \(2n^2 + 2n\)) with a minimal drop in the delay performance. More importantly, in practice, D-SSG generally has a substantially lower complexity than the hybrid policies that typically have a large constant factor hidden in the \(O(\cdot)\) notation. Finally, we conduct numerical simulations to validate our theoretical results in various scenarios. The simulation results show that D-SSG not only guarantees a near-optimal rate-function, but also empirically is virtually indistinguishable from delay-optimal policies.