Annals of Probability 15 (1987) 1166-1179.
Available from JSTOR.
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.
AMS 1980 subject classifications. Primary 60K35; secondary 60K30, 90B15.
Keywords and phrases. Circuit-switched network, loss probability.