The Annals of Applied Probability

On the Weak Convergence of Departures from an Infinite Series of $\cdot /M/ 1$ Queues

T. Mountford and B. Prabhakar

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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.

Article information

Source
Ann. Appl. Probab., Volume 5, Number 1 (1995), 121-127.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1177004831

Digital Object Identifier
doi:10.1214/aoap/1177004831

Mathematical Reviews number (MathSciNet)
MR1325044

Zentralblatt MATH identifier
0826.60083

JSTOR
links.jstor.org

Subjects
Primary: 60K25: Queueing theory [See also 68M20, 90B22]
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
Coupling Poisson limit

Citation

Mountford, T.; Prabhakar, B. On the Weak Convergence of Departures from an Infinite Series of $\cdot /M/ 1$ Queues. Ann. Appl. Probab. 5 (1995), no. 1, 121--127. doi:10.1214/aoap/1177004831. https://projecteuclid.org/euclid.aoap/1177004831


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