  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.
