On the Stability of a Queueing System with Uncountably Branching Fluid Limits

Authors:
A. P. Kovalevskii;V. A. Topchii;S. G. Foss
Affiliations:
Novosibirsk State Technical University, Novosibirsk, Russia;Omsk Branch, S.L. Sobolev Institute of Mathematics, Russia;S.L. Sobolev Institute of Mathematics, Novosibirsk Heriot-Watt University, Edinburgh, UK
Venue:
Problems of Information Transmission
Year:
2005

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Abstract

It is known that in many queueing systems uid limits are deterministic functions. Models and conditions which lead to random uid limits have not received much attention. This paper is devoted to a study of a queueing network whose uid limits admit a random and uncountable branching at certain points. Stability conditions for this model are investigated by the use of recent results from the theory of branching processes.