Short Communications

Short communication:on the invariance of stationary probabilities of states of a closed star-shaped queueing network with state-dependent transition probabilities

V. A. Ivnitskii

Research Institute of Railway Transport

Abstract: For a closed star-shaped queueing network with arbitrary distributions of service times in queueing systems (QS) in nodes of the network under some constraints on the form of dependence of transition probabilities for customers from the central QS to the rest and a sufficient number of service channels in each QS that queues should not arise, we establish the invariance of stationary probabilities of states with respect to the functional form of distributions of service times for their fixed expectations.

Keywords: central queueing system, outer queueing systems, closed star-shaped queueing network, arbitrary distributions of serving times, independence of stationary probabilities of states of the network.

Received: 11.04.1994

DOI: 10.4213/tvp1719

 English version: Theory of Probability and its Applications, 1998, 42:1, 162–167

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