Annals of Probability 15 (1987) 1166-1179.

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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.

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Frank Kelly's papers