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Solution of finite QBD processes

Part of: Computer system organization Markov processes

Published online by Cambridge University Press:  14 July 2016

Vittoria de Nitto Personè  and
Vincenzo Grassi
Vittoria de Nitto Personè*
Affiliation:
Università di Roma
Vincenzo Grassi*
Affiliation:
Università di Roma
*
∗Postal address: Dipartimento di Ingegneria Elettronica, Universita' Degli Studi di Roma “Tor Vergata”, Via della Ricerca Scientifica, 00133 Roma, Italy.
∗Postal address: Dipartimento di Ingegneria Elettronica, Universita' Degli Studi di Roma “Tor Vergata”, Via della Ricerca Scientifica, 00133 Roma, Italy.
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Abstract

We provide an explicit matrix analytic solution for finite quasi birth and death (QBD) processes, directly expressed in terms of process parameters. We show that this solution has the same asymptotic complexity of previously proposed non-explicit solutions and is more general than some of them. Moreover, it can be easily extended to the case of generalized QBD processes.

Keywords

MARKOV PROCESSFINITE QBD PROCESSMATRIX-ANALYTIC SOLUTION

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 68M20: Performance evaluation; queueing; scheduling
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 4 , December 1996 , pp. 1003 - 1010
Copyright
Copyright © Applied Probability Trust 1996 

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Footnotes

Work partially supported by MURST funds for national project ‘Performance and Reliability V&V for Software Engineering', and for local project ‘Performance Engineering of Software Systems'.

References

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