The Annals of Probability

One-Dimensional Circuit-Switched Networks

F. P. Kelly

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Abstract

This paper is concerned with the stationary distribution of a one-dimensional circuit-switched network. We show that if arrival rates decay geometrically with distance, then under the stationary distribution the number of circuits busy on successive links of the network at a fixed point in time is a Markov chain. When each link of the network has unit capacity we show that translation invariant arrival rates lead to a stationary distribution which can be described in terms of an alternating renewal process.

Article information

Source
Ann. Probab., Volume 15, Number 3 (1987), 1166-1179.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176992089

Digital Object Identifier
doi:10.1214/aop/1176992089

Mathematical Reviews number (MathSciNet)
MR893922

Zentralblatt MATH identifier
0626.60102

JSTOR
links.jstor.org

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.) [See also 90Bxx] 90B15: Network models, stochastic

Keywords
Circuit-switched network loss probability

Citation

Kelly, F. P. One-Dimensional Circuit-Switched Networks. Ann. Probab. 15 (1987), no. 3, 1166--1179. doi:10.1214/aop/1176992089. https://projecteuclid.org/euclid.aop/1176992089


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