One-dimensional loss networks and conditioned M/G/∞ queues
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).
Permanent link to this document: http://projecteuclid.org/euclid.jap/1032438391
Digital Object Identifier: doi:10.1239/jap/1032438391
Mathematical Reviews number (MathSciNet): MR1671246
Zentralblatt MATH identifier: 0934.60014