Abstract
Consider a closed queueing network of single-server stations, as introduced by Jackson, Gordon-Newell and Whittle, but with service times that are arbitrarily distributed with finite means. We verify that such a network has a unique stationary distribution if one of its service times is unbounded. The proof is carried out by modeling the network as a piecewise-deterministic Markov process which is shown to be regenerative. If, furthermore, the unbounded service-time distribution is non-lattice, then the stationary distribution is also the unique equilibrium. When the service-times enjoy finite second moments, and the number of customers in the network grows indefinitely, this equilibrium (properly normalized) converges to the equilibrium of a reflected Brownian motion on a simplex
Published Version
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