One-dimensional loss networks and conditioned M/G/∞ queues
- 1 December 1998
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 35 (4) , 963-975
- https://doi.org/10.1239/jap/1032438391
Abstract
We study one-dimensional continuous loss networks with length distribution G and cable capacity C. We prove that the unique stationary distribution ηL of the network for which the restriction on the number of calls to be less than C is imposed only in the segment [−L,L] is the same as the distribution of a stationary M/G/∞ queue conditioned to be less than C in the time interval [−L,L]. For distributions G which are of phase type (= absorbing times of finite state Markov processes) we show that the limit as L → ∞ of ηL exists and is unique. The limiting distribution turns out to be invariant for the infinite loss network. This was conjectured by Kelly (1991).Keywords
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