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

Benny Van Houdt B · Johan S. H. van Leeuwaarden

26 citations0/0 files storedINFORMS journal on computing

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Advanced Queuing Theory Analysis Probability and Statistical Research Matrix Theory and Algorithms

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.

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1999Introduction to Matrix Analytic Methods in Stochastic Modeling 1991Structured Stochastic Matrices of M/G/1 Type and Their Applications.1998Combining make to order and make to stock 2006Structured Markov chains solver 1994Matrix product-form solutions for Markov chains with a tree structure 2006Analysis of a simple Markovian re-entrant line with infinite supply of work under the LBFS policy 1995A generalization of the matrix M/G/l paradigm for Markov chains with a tree structure 1999The quasi-birth-death type markov chain with a tree structure

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