Relaxed functional iteration techniques for the numerical solution of \(M/G/1\) type Markov chains

DOI10.1007/BF02510257zbMath0914.65145MaRDI QIDQ1272877

Beatrice Meini, Paola Favati

Publication date: 7 March 1999

Published in: BIT (Search for Journal in Brave)

zbMATH Keywords

algorithmconvergencenumerical experimentsmatrix equationminimal nonnegative solution\(M/G/1\) type Markov chainsfunctional iteration method

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Matrix equations and identities (15A24) Iterative numerical methods for linear systems (65F10) Probabilistic methods, stochastic differential equations (65C99)

Related Items (3)

ON LATOUCHE–RAMASWAMI'S LOGARITHMIC REDUCTION ALGORITHM FOR QUASI-BIRTH-AND-DEATH PROCESSES ⋮ Highly accurate doubling algorithm for quadratic matrix equation from quasi-birth-and-death process ⋮ Highly Accurate Latouche-Ramaswami Logarithmic Reduction Algorithm for Quasi-Birth-and-Death Process

Uses Software

• na12

Cites Work

• Solving certain queueing problems modelled by Toeplitz matrices
• Improved cyclic reduction for solving queueing problems
• New convergence results on functional iteration techniques for the numerical solution of M/G/1 type Markov chains
• Nonlinear Matrix Equations in Applied Probability—Solution Techniques and Open Problems
• A stable recursion for the steady state vector in markov chains of m/g/1 type
• On functional iteration methods for solving nonlinear matrix equations arising in queueing problems
• A logarithmic reduction algorithm for quasi-birth-death processes
• Solutions of the basic matrix equation for M/G/l AND G/M/1 type markov chains
• Newton's iteration for non-linear equations in Markov chains
• An invariant subspace approach in m/g/l and g/m/l type markov chains
• On the Solution of a Nonlinear Matrix Equation Arising in Queueing Problems
• Iteration Methods for Finding all Zeros of a Polynomial Simultaneously
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