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February, 1995 On the Weak Convergence of Departures from an Infinite Series of $\cdot /M/ 1$ Queues
T. Mountford, B. Prabhakar
Ann. Appl. Probab. 5(1): 121-127 (February, 1995). DOI: 10.1214/aoap/1177004831

Abstract

In this note we observe that the recent argument of Ekhaus and Gray combined with the approach of Liggett and Shiga shows that the limit from passing a stationary ergodic arrival process of rate $\alpha < 1$ through a sequence of independent, rate one, exponential server queues is a Poisson process of rate $\alpha$. This builds on work of Liggett and Shiga and Anantharam.

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T. Mountford. B. Prabhakar. "On the Weak Convergence of Departures from an Infinite Series of $\cdot /M/ 1$ Queues." Ann. Appl. Probab. 5 (1) 121 - 127, February, 1995. https://doi.org/10.1214/aoap/1177004831

Information

Published: February, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0826.60083
MathSciNet: MR1325044
Digital Object Identifier: 10.1214/aoap/1177004831

Subjects:
Primary: 60K25
Secondary: 60K35

Keywords: coupling , Poisson limit

Rights: Copyright © 1995 Institute of Mathematical Statistics

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Vol.5 • No. 1 • February, 1995
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