Joint Scheduling and Routing for Ad-hoc Networks Under Channel State Uncertainty

We determine a joint link activation and routing policy that maximizes the stable throughput region of time-varying wireless ad-hoc networks with multiple commodities. In practice, the state of the channel process from the time it is observed till the time a transmission actually takes place can be significantly different. With this in mind, we introduce a stationary policy that takes scheduling and routing decisions based on a possibly inaccurate estimate of the true channel state. We show optimality of this policy within a broad class of link activation processes under certain mild conditions. In particular, processes in this class may be induced almost by any policy, possibly non-stationary, even anticipative and aware of the entire sample paths of the arrival, estimated and true channel processes, provided that it has no knowledge on the current true channel state, besides that available through its estimate.