MaxWeight Scheduling in a Generalized Swith: State Space Collapse and Equivalent Workload Minimization under Complete Resource Pooling

We consider a generalized switch model, which includes as special cases the model of multiuser data scheduling over a wireless medium, the input-queued cross-bar switch model, and a discrete time version of a parallel server queueing system. Input flows, n = 1,...,N, are served in discrete time by a switch. Switch state follows a finite discrete time Markov chain. In each state m, the switch chooses as scheduling decision k from a finite set K (m,) which has the associated service rate vector (mu sup m sub 1 (k),...,mu sup m sub N (k)).