Yoni Nazarathy Applied Mathematics, Faculty of Engineering & Industrial Sciences Swinburne University of Technology Location: Carslaw 173 Time: 2pm Friday, July 29, 2011 Scaling limits of cyclically varying birth-death processes Abstract: Fluid limits of stochastic queueing systems have received considerable attention in recent years. The general idea is to scale space, time and/or system parameters as to obtain a simpler, yet accurate description of the system. A basic example is the single server queue with time speeded up and space scaled down at the same rate. A second well known example is the Markovian infinite server queue with the arrival rate speeded up and space scaled down at the same rate. Such scalings and their network generalizations are often useful for obtaining stability conditions and approximating optimal control policies. In this talk we consider birth-death processes with general transition rates and obtain an asymptotic scaling result, generalizing the Markovian single server and infinite server cases. We apply our results to the steady-state analysis of queueing systems with cyclic or time varying behaviour. Examples are systems governed by deterministic cycles, queues with hysteresis control and queues with Markov-modulated arrival or service rates. The unifying property of such systems, is that if they are properly scaled, the resulting trajectories follow a cyclic or piece-wise deterministic behaviour which is determined by the asymptotic scaling. This yields simple a approximation for the stationary distribution which is shown to be asymptotically exact. Joint work with Matthieu Jonckheere.