 9379 P.A.Ferrari , L.R.G.Fontes
 The net output process of a system with infinitely many queues
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Apr 7, 93

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Abstract. We study a system of infinitely many queues with Poisson arrivals and
exponential service times. Let the net output process be the difference
between the departure process and the arrival process. We impose certain
ergodicicity conditions on the underlying Markov chain governing the customer
path. These conditions imply the existence of an invariant measure under which
the average net output process is positive and proportional to the time.
Starting the system with that measure we
prove that the net output process is a Poisson
process plus a perturbation of order 1. This generalizes a classical theorem
(Burke (1956), Kelly (1979)) asserting that the departure process is a Poisson
process.
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