Delay analysis of the approximate maximum weight scheduling in wireless networks

We provide bounds for the expectations of the stationary delay and the sum of the stationary queue sizes under the approximate maximum weight scheduling (MWS) policy and under the longest-queue-first (LQF) policy in one-hop wireless networks. For MWS, our results improves the previously provided bounds; for LQF, the results are new. In the derivation of the new bounds, a connection with certain graph theory quantities has been established. We also derive bounds for the sum of the second moments of the stationary queue sizes, which are also bounds for the sum of the queue-size variances. The method is general and it can be used to derive bounds for the sum of even higher moments of the stationary queue sizes. However, for the approximate MWS policy, the bounds for the second or higher moments are only valid when the average arrival rate vector is confined to a subset of the capacity region that depends on the order of the moment.