Asymptotic stationarity of queues in series and the heavy traffic approximation
type: Item
instance of: scholarly article
title: Asymptotic stationarity of queues in series and the heavy traffic approximation
zbMATH Open document ID: 0726.60092
author: Frank Kelly
author: Władysław Szczotka
published in: The Annals of Probability
publication date: 1990-01-01T00:00:00Z
review text: For a sequence of single server queues with infinite waiting rooms under FCFS the joint departure processes, waiting time processes, and sojourn time processes are considered with respect to asymptotic behaviour in the sense of weak and strong convergence and convergence in variation of the random sequences, as well as that of Cesàro type limits. It is proved that if the input sequences (interarrival and service times) for the system are asymptotically stationary in one sense of the above definitions, then the process of the functionals mentioned above is asymptotically stationary in the same sense. Certain refinements of this are derived and heavy traffic results are obtained providing diffusion approximations.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 60K20
Mathematics Subject Classification ID: 60F17
zbMATH DE Number: 4199219
zbMATH Keywords: tandem queues
zbMATH Keywords: heavy traffic limits
zbMATH Keywords: asymptotic stationarity
zbMATH Keywords: single server queues
zbMATH Keywords: weak and strong convergence
zbMATH Keywords: convergence in variation
zbMATH Keywords: Cesàro type limits
zbMATH Keywords: diffusion approximations
reviewed by: Hans Daduna
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176990744
OpenAlex ID: W2050056804
DOI: 10.1214/AOP/1176990744
description: scientific article; zbMATH DE number 4199219