## The Annals of Applied Probability

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

#### 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

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
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