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February, 1993 Uniqueness of Stationary Ergodic Fixed Point for $A \cdot / M/ K Node$
V. Anantharam
Ann. Appl. Probab. 3(1): 154-172 (February, 1993). DOI: 10.1214/aoap/1177005512

Abstract

We view a $\bullet/M/K$ node having $K$ exponential servers of service rate $\mu$ as a map on the space of stationary ergodic arrival processes of rate $\lambda, \lambda < K\mu$. It is well known that the Poisson process of rate $\lambda$ is a fixed point of this map. We prove there is no other fixed point.

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V. Anantharam. "Uniqueness of Stationary Ergodic Fixed Point for $A \cdot / M/ K Node$." Ann. Appl. Probab. 3 (1) 154 - 172, February, 1993. https://doi.org/10.1214/aoap/1177005512

Information

Published: February, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0786.60112
MathSciNet: MR1202520
Digital Object Identifier: 10.1214/aoap/1177005512

Subjects:
Primary: 60K25
Secondary: 60G55 , 60K20

Keywords: Poisson processes , quasireversibility , Queueing networks , stationary ergodic fixed points

Rights: Copyright © 1993 Institute of Mathematical Statistics

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Vol.3 • No. 1 • February, 1993
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