Quasi-birth-and-death processes with an explicit rate matrix

J.S.H. Leeuwaarden, van, E.M.M. Winands

Research output: Contribution to journalArticleAcademicpeer-review

21 Citations (Scopus)
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Abstract

We determine the equilibrium distribution for a class of quasi-birth-and-death (QBD) processes using the matrix-geometric method, which requires the determination of the rate matrix R. In contrast to most QBD processes, the class under consideration allows for an explicit description of R, by exploiting its probabilistic interpretation. We show that the problem of finding each element of R reduces to counting lattice paths in the transition diagram. For resolving this counting problem, we present an extended version of the classical Ballot theorem. We also present various examples of queueing models that fit into the class.
Original languageEnglish
Pages (from-to)77-98
JournalStochastic Models
Volume22
Issue number1
DOIs
Publication statusPublished - 2006

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