Title
Quasi-birth-and-death processes with restricted transitions and its applications Quasi-birth-and-death processes with restricted transitions and its applications
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Amsterdam ,
Subject
Mathematics
Source (journal)
Performance evaluation. - Amsterdam
Volume/pages
68(2011) :2 , p. 126-141
ISSN
0166-5316
ISI
000287422400004
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
In this paper, we identify a class of quasi-birth-and-death (QBD) processes where the transitions to higher (respectively lower) levels are restricted to occur only from (respectively to) a subset of the phase space. These restrictions induce a specific structure in the R or G matrix of the QBD process, which can be exploited to reduce the time required to compute these matrices. We show how this reduction can be achieved by first defining and solving a censored process, and then solving a Sylvester matrix equation. To illustrate the applicability and computational gains obtained with this approach, we consider several examples where the referred structures either arise naturally or can be induced by adequately modeling the system at hand. The examples include the general MAP/PH/1 queue, a priority queue with two customer classes, an overflow queueing system and a wireless relay node.
Full text (open access)
https://repository.uantwerpen.be/docman/irua/45519a/5096.pdf
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