Maxweight Scheduling in a Generalized Switch: State Space Collapse and Workload Minimization in Heavy Traffic by Alexander L. Stolyar

We consider a generalized switch model, which includes as special cases the model of multiuser data scheduling over a wireless medium, the inputqueued 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. The switch state follows a finite state, discrete time Markov chain. In each state m, the switch chooses a scheduling decision k from a finite set K(m), which has the associated service rate vector (μ1 (k), . . . ,μ m N(k)). We consider a heavy traffic regime, and assume a Resource Pooling (RP) condition. Associated with this condition is a notion of workload X= ∑n ζnQn, where ζ = (ζ1, . . . , ζN ) is some fixed nonzero vector with nonnegative components, and Q1, . . . ,QN are the queue lengths. We study the MaxWeight discipline which always chooses a decision k maximizing ∑ n γn[Qn]μn (k), that is, k ∈ arg max i ∑