Open Access
February, 1995 On the Weak Convergence of Departures from an Infinite Series of /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 α<1 through a sequence of independent, rate one, exponential server queues is a Poisson process of rate α. This builds on work of Liggett and Shiga and Anantharam.

Citation

Download Citation

T. Mountford. B. Prabhakar. "On the Weak Convergence of Departures from an Infinite Series of /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

Vol.5 • No. 1 • February, 1995
Back to Top