Low-Complexity Scheduling Policies for Achieving Throughput and Asymptotic Delay Optimality in Multichannel 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.

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

“…In each time-slot, a channel can be allocated only to one user, but a user can be allocated with multiple channels simultaneously. As in [5], [9]- [13], and [15], for ease of presentation, we assume that the number of users is equal to the number of channels. (If the number of users scales linearly with the number of channels, the rate-function delay analysis follows similarly.…”

“…The throughput analysis is carried out under Assumption 1 only, which is mild and has also been used in [15] and [19].…”

“…In contrast, we show that D-SSG achieves a rate-function that is not only positive but also near-optimal, for more general arrival processes. Thus, we are able to achieve a reduction in complexity (from of the hybrid policies [15] to ) with a minimal drop in the delay performance. More importantly, the practical complexity of D-SSG is substantially lower than that of the hybrid policies since we can precisely bound the constant factor in its complexity.…”

“…In [12] and [13], the authors developed a scheduling policy called Delay Weighted Matching (DWM), which maximizes the sum of the delay of the scheduled packets in each time-slot. It has been shown in [12], [13], and [15] that DWM is not only throughput-optimal, but also rate-function delay-optimal (i.e., maximizing the delay rate-function, rather than the queue-length rate-function as considered in [5], [9]- [11]). Moreover, the authors of [13] used the derived rate-function of DWM to develop a simple threshold policy for admission control when the number of users scales linearly with the number of channels in the system.…”

“…However, DWM incurs a high complexity , which renders it impractical for modern OFDM systems with many channels and users (e.g., on the order of hundreds). In [15], the authors proposed a class of hybrid scheduling policies with a much lower complexity , while still guaranteeing both throughput optimality and rate-function delay optimality (with an additional minor technical assumption). However, the practical complexity of the hybrid policies is still high as the constant factor hidden in the notation is typically large due to the required two-stage scheduling operations and the operation of computing a maximum-weight matching in the first stage.…”