Distribution of busy period for the bulk-service queueing system \(E_ k/M^{a,b}/1\) (Q1081974)
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scientific article; zbMATH DE number 3971943
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Distribution of busy period for the bulk-service queueing system \(E_ k/M^{a,b}/1\) |
scientific article; zbMATH DE number 3971943 |
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Distribution of busy period for the bulk-service queueing system \(E_ k/M^{a,b}/1\) (English)
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1984
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Using the Erlangian technique the busy-period equations for the single- server bulk-service system \(E_ k/M^{a,b}/1\) are solved to obtain the Laplace transform of the probability density function (pdf) of the busy period. The Laplace transform is expressed in terms of an easily computable real root of the characteristic equation. Expressions for the mean and variance of the busy-period distribution are given. Explicit results for the pdf of the busy period are obtained for the special systems \(M/M^{a,b}/1\) and \(E_ k/M^{a,a}/1\).
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Erlangian technique
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single-server bulk-service system
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Laplace transform
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characteristic equation
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