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.

💡 Research Summary

The paper addresses the downlink scheduling problem in multi‑channel wireless networks, exemplified by a single‑cell 4G OFDM system. The authors aim to devise a practical scheduler that simultaneously guarantees throughput optimality (i.e., stability for any arrival vector inside the network’s capacity region) and strong delay performance measured by the large‑deviation rate‑function, while keeping computational complexity low.

Existing “hybrid” policies achieve both goals but require $O(n^{2.5}\log n)$ operations per time slot, where $n$ denotes the number of users (and, equivalently, the number of sub‑carriers). The high order and large hidden constants make them unattractive for real‑time implementation.

To overcome this, the authors propose Delay‑based Server‑Side‑Greedy (D‑SSG). In each slot every server (sub‑carrier) independently scans the set of queues it can serve and selects the queue whose head‑of‑line (HOL) packet has the largest waiting time. Ties are broken by a fixed rule (e.g., smallest index). Because each of the $n$ servers examines at most $n$ queues, the total number of elementary operations is $2n^{2}+2n$, i.e., $O(n^{2})$, a substantial reduction in complexity.

Throughput optimality is proved via a Lyapunov drift argument. The quadratic Lyapunov function $L(\mathbf{Q})=\sum_i Q_i^{2}$ is shown to have a negative expected drift under D‑SSG for any arrival rate vector strictly inside the capacity region. Consequently the system is stable, and D‑SSG attains the same throughput region as the optimal Max‑Weight scheduler.

Near‑optimal delay performance is established through a large‑deviation analysis. The authors first define a fictitious “Greedy‑FBS” (Fluid‑Based Scheduler) that is known to achieve the optimal rate‑function for a delay threshold $b-1$. They then demonstrate a sample‑path dominance property: for any realization of arrivals and channel states, D‑SSG serves at least as many packets as Greedy‑FBS in every slot. This dominance yields the inequality
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