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We construct a generic, simple, and efficient scheduling policy forstochastic processing networks, and provide a general framework to establishits stability. Our policy is randomized and prioritized: with high probabilityit prioritizes jobs which have been least routed through the network. We showthat the network is globally stable under this policy if there exists anappropriate quadratic local Lyapunov function that provides a negative driftwith respect to nominal loads at servers. Applying this generic framework, weobtain stability results for our policy in many important examples ofstochastic processing networks: open multiclass queueing networks, parallelserver networks, networks of input-queued switches, and a variety of wirelessnetwork models with interference constraints. Our main novelty is theconstruction of an appropriate global Lyapunov function from quadratic localLyapunov functions, which we believe to be of broader interest.

From Local to Global Stability in Stochastic Processing Networks through Quadratic Lyapunov Functions