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Generalized semi-Markov schemes and open queueing networks

Published online by Cambridge University Press:  14 July 2016

A. D. Barbour
A. D. Barbour*
Affiliation:
Gonville and Caius College, Cambridge
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Abstract

Generalized semi-Markov schemes were devised to give a versatile general model embracing queueing networks and similar systems of practical importance, and they have proved particularly successful in uniting many disparate results on insensitivity. However, it turns out that, although closed queueing networks are expressible as GSMS, open networks are not, and that the insensitivity results for such networks are not therefore strictly within their scope. In this paper, it is shown that, as one might hope, open networks can be realized as limits of a suitable sequence of closed networks in such a way that the insensitivity properties of the GSMS are transferred to the open network in the limit, and thus that open networks too can, in a sense, be considered to be GSMS. However, it appears from the technical nature of the arguments involved that, despite this close relationship between GSMS and open networks, it may nonetheless be simpler to treat them separately when constructing the proofs of theorems.

Keywords

GENERALIZED SEMI-MARKOV SCHEMEOPEN QUEUEING NETWORKINSENSITIVITYCONTINUITY OF QUEUES
Type
Short Communications
Information
Journal of Applied Probability , Volume 19 , Issue 2 , June 1982 , pp. 469 - 474
Copyright
Copyright © Applied Probability Trust 1982 

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References

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