On the weak convergence of departures from an infinite series of \(\cdot{}/M /1\) queues
type: Item
instance of: scholarly article
title: On the weak convergence of departures from an infinite series of \(\cdot{}/M /1\) queues
zbMATH Open document ID: 0826.60083
author: Thomas Mountford
author: Balaji Prabhakar
published in: The Annals of Applied Probability
publication date: 1995-08-10T00:00:00Z
review text: Given a stationary point process \(A\) indexed by two-sided time, the authors construct a stationary output process obtained from passing \(A\) through an independent single-server queue whose service times are independent and identically distributed exponentials of rate \(l\). They prove an old conjecture, viz., if \(A\) is a stationary, ergodic point process of rate \(\alpha < 1\), then \(A^n\) converges in distribution to a Poisson process of rate \(\alpha\).
reviewed by: P. R. Parthasarathy
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 780983
zbMATH Keywords: coupling
zbMATH Keywords: Poisson limit
zbMATH Keywords: stationary point process
zbMATH Keywords: ergodic point process
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aoap/1177004831
OpenAlex ID: W2036117388
DOI: 10.1214/AOAP/1177004831
description: scientific article; zbMATH DE number 780983