Triangular M/G/1-Type and Tree-Like Quasi-Birth-Death Markov Chains

Authors:
Benny Van Houdt;Johan S. H. van Leeuwaarden
Affiliations:
University of Antwerp -- IBBT, B2020 Antwerp, Belgium;Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
Venue:
INFORMS Journal on Computing
Year:
2011

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Abstract

In applying matrix-analytic methods to M/G/1-type and tree-like quasi-birth-death (QBD) Markov chains, it is crucial to determine the solution to a (set of) nonlinear matrix equation(s). This is usually done via iterative methods. We consider the highly structured subclass of triangular M/G/1-type and tree-like QBD Markov chains that allows for an efficient direct solution of the matrix equation.