One-dimensional circuit-switched networks
type: Item
instance of: scholarly article
title: One-dimensional circuit-switched networks
zbMATH Open document ID: 0626.60102
author: Frank Kelly
published in: The Annals of Probability
publication date: 1987-01-01T00:00:00Z
review text: In a one-dimensional (linear) circuit-switched network arriving calls request for an interconnection between two nodes of the network. If such a ``route'' which consists of a sequence of successive circuits is not available the call is lost. (The constraint on the availability originates from the finite capacity condition for the links between two neighboured nodes.) Calls for different routes arrive in independent Poisson processes. The stochastic process describing the number of occupied routes for each type of route has a well-known ``product form'' steady-state distribution. A much more complicated problem is to describe the process which records the joint number of occupied circuits on the links of the network. The author proves that under some restrictions on the arrival intensities the steady state of that process is an inhomogeneous Markov chain which additionally can be identified to be a quasistationary distribution of a suitable homogeneous Markov chain. Under the additional restriction that each link comprises one circuit the steady-state distribution can be reduced in an analogous way to distributions obtained from alternating renewal processes.
reviewed by: Hans Daduna
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60K30
Mathematics Subject Classification ID: 90B15
zbMATH DE Number: 4018081
zbMATH Keywords: circuit-switched network
zbMATH Keywords: steady-state distribution
zbMATH Keywords: quasistationary distribution
zbMATH Keywords: alternating renewal processes
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176992089
OpenAlex ID: W2016454220
DOI: 10.1214/AOP/1176992089
description: scientific article; zbMATH DE number 4018081