Throughput Optimal Scheduling Policies in Networks of Interacting Queues

This report considers a fairly general model of constrained queuing networks that allows us to represent both MMBP (Markov Modulated Bernoulli Processes) arrivals and time-varying service constraints. We derive a set of sufficient conditions for throughput optimality of scheduling policies that encompass and generalize all the previously obtained results in the field. This leads to the definition of new classes of (non diagonal) throughput optimal scheduling policies. We prove the stability of queues by extending the traditional Lyapunov drift criteria methodology.