Delay Analysis of Max-Weight Queue Algorithm for Time-varying Wireless Adhoc Networks - Control Theoretical Approach

TL;DR

This paper analyzes the delay performance of the Max-Weight Queue algorithm in time-varying wireless ad hoc networks using control theory, providing delay bounds and proposing an improved iterative algorithm for better convergence.

Contribution

It introduces a stochastic stability analysis for MWQ in dynamic environments and proposes a compensation-based iterative algorithm to enhance convergence.

Findings

Derived a closed-form delay bound based on channel fading rate.

Proposed a modified MWQ algorithm with improved convergence properties.

Established conditions under which the algorithm converges despite time-varying CSI and QSI.

Abstract

Max weighted queue (MWQ) control policy is a widely used cross-layer control policy that achieves queue stability and a reasonable delay performance. In most of the existing literature, it is assumed that optimal MWQ policy can be obtained instantaneously at every time slot. However, this assumption may be unrealistic in time varying wireless systems, especially when there is no closed-form MWQ solution and iterative algorithms have to be applied to obtain the optimal solution. This paper investigates the convergence behavior and the queue delay performance of the conventional MWQ iterations in which the channel state information (CSI) and queue state information (QSI) are changing in a similar timescale as the algorithm iterations. Our results are established by studying the stochastic stability of an equivalent virtual stochastic dynamic system (VSDS), and an extended Foster-Lyapunov criteria is applied for the stability analysis. We derive a closed form delay bound of the wireless network in terms of the CSI fading rate and the sensitivity of MWQ policy over CSI and QSI. Based on the equivalent VSDS, we propose a novel MWQ iterative algorithm with compensation to improve the tracking performance. We demonstrate that under some mild conditions, the proposed modified MWQ algorithm converges to the optimal MWQ control despite the time-varying CSI and QSI.