Bounds for the Coupling Time in Queueing Networks Perfect Simulation

In this paper, the duration of perfect simulations for Markovian finite capacity queuing networks is studied. This corresponds to hitting time (or coupling time) problems in a Markov chain over the Cartesian product of the state space of each queue. We establish an analytical formula for the expected simulation time in the one queue case and we provide simple bounds for acyclic networks of queues with losses. These bounds correspond to sums on the coupling time for each queue and are either almost linear in the queue capacities under light or heavy traffic assumptions or quadratic, when service and arrival rates are similar.

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