Quasi-birth-and-death processes, lattice path counting, and hypergeometric functions

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

Research output: Contribution to journalArticleAcademicpeer-review

15 Citations (Scopus)


In this paper we consider a class of quasi-birth-and-death processes for which explicit solutions can be obtained for the rate matrix R and the associated matrix G. The probabilistic interpretations of these matrices allow us to describe their elements in terms of paths on the two-dimensional lattice. Then determining explicit expressions for the matrices becomes equivalent to solving a lattice path counting problem, the solution of which is derived using path decomposition, Bernoulli excursions, and hypergeometric functions. A few applications are provided, including classical models for which we obtain some new results.
Original languageEnglish
Pages (from-to)507-520
JournalJournal of Applied Probability
Issue number2
Publication statusPublished - 2009


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