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

Bo Ji, Gagan Raj Gupta+2 more|arXiv (Cornell University)|Jan 16, 2013

Advanced Wireless Network Optimization15 references3 citations

TL;DR

This paper proposes a hybrid scheduling policy combining Oldest Packets First (OPF) and Maximum Weight in the Fluid limit (MWF) strategies to achieve both throughput and asymptotic delay optimality in multi-channel wireless networks. The method uses novel sufficient conditions for delay and throughput optimality, enabling a complexity of $O(n^{2.5} an n)$, significantly lower than prior optimal policies like DWM, which has $O(n^5)$ complexity.

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.

Motivation & Objective

• Address the challenge of designing scheduling policies that simultaneously achieve optimal throughput and asymptotic delay performance in multi-channel wireless networks.
• Overcome the high complexity of existing delay- and throughput-optimal policies, such as Delay Weighted Matching (DWM), which has $O(n^5)$ complexity.
• Develop a unifying framework using new sufficient conditions to verify both rate-function delay optimality and throughput optimality in asymptotic regimes.
• Design hybrid scheduling policies that combine OPF and MWF principles to maintain optimality while reducing computational cost.
• Validate theoretical findings through numerical experiments demonstrating the superiority of the proposed policy over existing alternatives.

Proposed method

• Introduce new, easy-to-verify sufficient conditions for rate-function delay optimality and throughput optimality in multi-channel systems.
• Apply the sufficient conditions to prove that a class of OPF policies achieves rate-function delay optimality and a class of MWF policies achieves throughput optimality.
• Design a hybrid OPF-MWF scheduling policy by combining stage-wise operations: first apply OPF to prioritize oldest packets, then apply MWF to balance queue weights.
• Use the sufficient conditions to show that the hybrid policy satisfies both delay and throughput optimality criteria.
• Prove that the Delay Weighted Matching (DWM) policy is rate-function delay-optimal under the new conditions, explaining its optimality with a formal framework.
• Analyze the complexity of the hybrid policy as $O(n^{2.5} an n)$, derived from combining DWM-$n$ ($O(n^{2.5} an n)$) and MWS ($O(n^2)$) components.

Experimental results

Research questions

• RQ1 Can a low-complexity scheduling policy achieve both throughput optimality and asymptotic delay optimality in multi-channel wireless networks?
• RQ2 What sufficient conditions can be used to verify rate-function delay optimality and throughput optimality in the many-channel many-user asymptotic regime?
• RQ3 How can hybrid scheduling policies combining OPF and MWF principles maintain optimality while reducing computational complexity?
• RQ4 Is the previously proposed DWM policy rate-function delay-optimal, and can this be formally established using new theoretical conditions?
• RQ5 Can the complexity of delay- and throughput-optimal scheduling be reduced below $O(n^5)$, and if so, by what design principles?

Key findings

• The proposed hybrid OPF-MWF policy achieves both rate-function delay optimality and throughput optimality under the new sufficient conditions.
• The complexity of the hybrid policy is $O(n^{2.5} an n)$, which is significantly lower than the $O(n^5)$ complexity of the previously known DWM policy.
• The paper formally proves that DWM is rate-function delay-optimal by showing it satisfies the newly proposed sufficient condition.
• Numerical experiments validate the theoretical results, confirming the improved performance and lower complexity of the hybrid policy.
• The sufficient conditions introduced are general and easy to verify, enabling systematic design and analysis of low-complexity optimal scheduling policies.
• The hybrid policy maintains optimality by ensuring that in each time slot, the scheduling decisions satisfy both the OPF and MWF sufficient conditions simultaneously.