Stability of multi-class queueing systems with state-dependent service rates

We examine the stability of multi-class queueing systems with the special feature that the service rates of the various classes depend on the number of users present of each of the classes. As a result, the various classes interact in a complex dynamic fashion. Such models arise in several contexts, especially in wireless networks, as resource sharing algorithms become increasingly elaborate, giving rise to scaling efficiencies and complicated interdependencies among traffic classes. Under certain monotonicity assumptions we provide an exact characterization of stability region. We also discuss how some of the results extend to weaker notions of monotonicity. The results are illustrated for simple examples of wireless networks with two or three interfering base stations.

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