Delay Analysis of Max-Weight Queue Algorithm for Time-Varying Wireless Ad hoc Networks—Control Theoretical Approach

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.