A successive censoring algorithm for a system of connected LDQBD-processes

Niek Baer, Ahmad Al Hanbali*, Richard J. Boucherie, Jan Kees van Ommeren

*Corresponding author for this work

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Abstract

We consider a Markov Chain in which the state space is partitioned into sets where both transitions within sets and between sets have a special structure. Transitions within each set constitute a finite level dependent quasi-birth-and-death-process (LDQBD), and transitions between sets are restricted to six types of transitions. These latter types are needed to preserve the sets structure in the reduction step of our algorithm. Specifically, we present a successive censoring algorithm, based on matrix analytic methods, to obtain the stationary distribution of this system of connected LDQBD-processes.

Original languageEnglish
Pages (from-to)389–410
Number of pages22
JournalAnnals of operations research
Volume310
Early online date1 Jan 2021
DOIs
Publication statusPublished - Mar 2022

Keywords

  • Connected level dependent QBD-processes
  • Exact aggregation/disaggregation
  • Matrix analytic methods
  • Steady state analysis
  • Successive censoring algorithm

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