The Annals of Probability
- Ann. Probab.
- Volume 15, Number 3 (1987), 1166-1179.
One-Dimensional Circuit-Switched Networks
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.
Ann. Probab., Volume 15, Number 3 (1987), 1166-1179.
First available in Project Euclid: 19 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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