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A Queueing Network Model for a Communication System with Channel Allocation

Published online by Cambridge University Press:  27 July 2009

A. Brandt  and
H. Sulanke
A. Brandt
Affiliation:
Fachbereich Mathematik, Humboldt-Universität, zu Berlin PSF 1297, Germany
H. Sulanke
Affiliation:
Fachbereich Mathematik, Humboldt-Universität, zu Berlin PSF 1297, Germany
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Abstract

A communication system of n stations is studied. Poisson arrival streams of messages enter the stations and require transmission to a destination station. Each station is equipped with k channels and has a waiting room for messages. For transmission of a message, one channel is needed both at the arrival and at the destination station. The transmission time is exponentially distributed. Messages are lost (possibly after a waiting time) if, at the destination station, all channels are busy. The queueing network model is of the nonproduct type. Sufficient conditions for the existence of an equilibrium distribution are given. For determining the losses at the n stations, a heuristical approximation that requires us to solve a system of nonlinear equations is developed. For this, an efficient iterative numerical algorithm is given. Simulation studies show that the approximation is accurate enough for larger n.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 5 , Issue 2 , April 1991 , pp. 171 - 183
Copyright
Copyright © Cambridge University Press 1991

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