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Convergence of Departures in Tandem Networks of ./GI/infinity Queues

Prabhakar, Balaji; Mountford, Tom; Bambos, Nicholas


Keyword(s): distributional convergence; couplings; Poisson limits

Abstract: We consider an infinite series of independent and identical ./GI/infinity queues fed by an arbitrary stationary and ergodic arrival process. Using couplings for random walks, we show that the limiting distribution of the departure process from the nth queue converges in distribution either to a Poisson process or to a stationary v Poisson process (defined below) depending on the joint distribution of the original arrival process and the service process.

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