A multiclass closed queueing network with unconventional heavy traffic behavior
type: Item
instance of: scholarly article
title: A multiclass closed queueing network with unconventional heavy traffic behavior
zbMATH Open document ID: 0865.60078
author: J. Michael Harrison
author: R. J. Williams
published in: The Annals of Applied Probability
publication date: 1997-07-07T00:00:00Z
full work available at URL: http://purl.umn.edu/2780
review text: This paper discusses a closed network with two-server stations and a fixed customer population of size \(n\). Customers are routed in cyclic fashion through four distinct classes, two of which are served at each station, and each server uses a preemptive resume priority discipline. The service times follow exponential law. When \(n\) approaches infinity, this paper discusses a heavy traffic limit theorem which involves a mixture of Brownian scaling and fluid scaling. The interesting part of the result is the limit process that is not an ordinary reflected Brownian motion (as in conventional heavy traffic theorems). But the limit process is related to Brownian motion process.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 60J70
Mathematics Subject Classification ID: 90B15
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 920835
zbMATH Keywords: multiclass queueing networks
zbMATH Keywords: heavy traffic theory
zbMATH Keywords: Brownian motion
reviewed by: V. Thangaraj
MaRDI profile type: Publication
OpenAlex ID: W2059463621
cites work: Q5560061
cites work: Point processes and queues. Martingale dynamics
cites work: Stochastic discrete flow networks: Diffusion approximations and bottlenecks
cites work: Q3997507
cites work: Stability and Instability of Fluid Models for Reentrant Lines
cites work: Q4866375
cites work: Q3721531
cites work: Q3808989
cites work: Brownian models of multiclass queueing networks: Current status and open problems
cites work: Q4842996
cites work: Brownian models of closed queueing networks with homogeneous customer populations
cites work: Random time changes and convergence in distribution under the Meyer-Zheng conditions
cites work: Weak limit theorems for stochastic integrals and stochastic differential equations
cites work: Q3996259
cites work: Ergodicity of stochastic processes describing the operation of open queueing networks
cites work: Q4040434
cites work: Q3239624
cites work: Some Useful Functions for Functional Limit Theorems
cites work: Q4842997
DOI: 10.1214/AOAP/1034968064
description: scientific article; zbMATH DE number 920835