On the quasireversibility of a multiclass Brownian service station
type: Item
instance of: scholarly article
title: On the quasireversibility of a multiclass Brownian service station
zbMATH Open document ID: 0709.60081
author: J. Michael Harrison
author: R. J. Williams
published in: The Annals of Probability
publication date: 1990-01-01T00:00:00Z
review text: This paper studies a Brownian model of a multiclass service station. Such Brownian models arise as heavy traffic limits of conventional queueing models in which several different types or classes of customers are processed through a common service facility. Assuming that the Brownian service station is initialized with its stationary distribution, four different model characteristics are shown to be equivalent, and the station is said to be quasireversible if these equivalent conditions pertain. Three of the four conditions characterize the vector departure process from the Brownian service station, and the definition of quasireversibility parallels that proposed for conventional queueing models. The last of the four conditions is expressed directly in terms of primitive model parameters, so one may determine from basic data whether or not a Brownian station model is quasireversible. Rather than characterizing the complete vector of departure processes from a Brownian service station, the paper proves a more general theorem expressed in terms of arbitrary linear combinations of the departure processes; this yields a generalized notion of quasireversibility. In a future paper on multiclass Brownian network models, it promises to be shown that there is an intimate relationship between product form stationary distributions and the generalized notion of quasireversibility developed here. (From the authors' abstract.)
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 60J70
zbMATH DE Number: 4166238
zbMATH Keywords: Brownian model of a multiclass service station
zbMATH Keywords: stationary distribution
zbMATH Keywords: quasireversibility
zbMATH Keywords: Brownian network models
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176990745
OpenAlex ID: W2054705374
DOI: 10.1214/AOP/1176990745
description: scientific article; zbMATH DE number 4166238