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Stability and heavy traffic results for the general bulk queue

Published online by Cambridge University Press:  01 July 2016

John Dagsvik
John Dagsvik*
Affiliation:
Central Bureau of Statistics, Oslo
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Abstract

In this paper we prove that the limiting distribution of the general bulk queue exists and is independent of the initial conditions if and only if the traffic intensity is less than one. We further generalize the following heavy traffic results of the GI/G/1 model to the general bulk queue model. When ρ > 1 or ρ = 1 the waiting time is distributed approximately as a Gaussian variable and the absolute value of a Gaussian variable, respectively. The exponential approximation is derived from the Wiener–Hopf matrix equations established in a previous paper while the unstable case ρ ≧ 1 is treated by means of functional central limit theorems for mixing processes.

Keywords

BULK QUEUESCHAIN-DEPENDENT VARIABLESMATRIX WIENER–HOPF EQUATIONSSEMI-MARKOV KERNELSHEAVY TRAFFIC APPROXIMATIONSWEAK CONVERGENCEFUNCTIONAL CENTRAL LIMIT THEOREMSMIXING PROCESSES
Type
Research Article
Information
Advances in Applied Probability , Volume 10 , Issue 1 , March 1978 , pp. 213 - 231
Copyright
Copyright © Applied Probability Trust 1978 

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