Exploiting restricted transitions in Quasi-Birth-and-Death processes

Juan F. Pérez; Benny Van Houdt

doi:10.1109/QEST.2009.18

Exploiting restricted transitions in Quasi-Birth-and-Death processes

Juan F. Pérez, Benny Van Houdt

Research output: Contribution to conference › Conference proceedings › peer-review

2 Scopus citations

Abstract

In this paper we consider Quasi-Birth-and-Death (QBD) processes where the upward (resp. downward) transitions are restricted to occur only from (resp. to) a subset of the phase space. This property is exploited to reduce the computation time to find the matrix R or G of the process. The reduction is done through the definition of a censored process which can be of the M/G/1- or GI/M/1-type. The approach is illustrated through examples that show the applicability and benefits of making use of the additional structure. The examples also show how these special structures arise naturally in the analysis of queuing systems. Even more substantial gains can be realized when we further restrict the class of QBD processes under consideration.

Original language	English (US)
Pages	123-132
Number of pages	10
DOIs	https://doi.org/10.1109/QEST.2009.18
State	Published - Oct 23 2009
Externally published	Yes
Event	QEST - 6th International Conference on the Quantitative Evaluation of Systems - Budapest, Hungary Duration: Sep 13 2009 → Sep 16 2009

Conference

Conference	QEST - 6th International Conference on the Quantitative Evaluation of Systems
Country/Territory	Hungary
City	Budapest
Period	9/13/09 → 9/16/09

All Science Journal Classification (ASJC) codes

Computer Networks and Communications
Control and Systems Engineering
Electrical and Electronic Engineering

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10.1109/QEST.2009.18

Cite this

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abstract = "In this paper we consider Quasi-Birth-and-Death (QBD) processes where the upward (resp. downward) transitions are restricted to occur only from (resp. to) a subset of the phase space. This property is exploited to reduce the computation time to find the matrix R or G of the process. The reduction is done through the definition of a censored process which can be of the M/G/1- or GI/M/1-type. The approach is illustrated through examples that show the applicability and benefits of making use of the additional structure. The examples also show how these special structures arise naturally in the analysis of queuing systems. Even more substantial gains can be realized when we further restrict the class of QBD processes under consideration.",

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Exploiting restricted transitions in Quasi-Birth-and-Death processes

Abstract

Conference

All Science Journal Classification (ASJC) codes

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