Quasi-birth-and-death processes with restricted transitions and its applications

Juan F. Prez, Benny Van Houdt

Research output: Contribution to journalConference articlepeer-review

9 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)126-141
Number of pages16
JournalPerformance Evaluation
Issue number2
StatePublished - Feb 1 2011
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Software
  • Modeling and Simulation
  • Hardware and Architecture
  • Computer Networks and Communications


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