New convergence results on functional iteration techniques for the numerical solution of M/G/1 type Markov chains

DOI10.1007/s002110050303zbMath0889.65145OpenAlexW2006924038MaRDI QIDQ1374752

Publication date: 10 December 1997

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s002110050303

zbMATH Keywords

convergence matrix equation minimal nonnegative solution functional iteration methods M/G/1 type Markov chains

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Queueing theory (aspects of probability theory) (60K25) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Matrix equations and identities (15A24) Stochastic matrices (15B51) Probabilistic methods, stochastic differential equations (65C99)

Related Items (13)

Nonlinear matrix equations and structured linear algebra ⋮ Solving nonlinear matrix equations arising in tree-like stochastic processes. ⋮ Efficient computation of the extreme solutions of $X+A^*X^{-1}A=Q$ and $X-A^*X^{-1}A=Q$ ⋮ ON LATOUCHE–RAMASWAMI'S LOGARITHMIC REDUCTION ALGORITHM FOR QUASI-BIRTH-AND-DEATH PROCESSES ⋮ Note on functional iteration technique for $M/G/1$ type Markov chains ⋮ Exploiting the Toeplitz structure in certain queueing problems ⋮ Solving Quadratic Matrix Equations Arising in Random Walks in the Quarter Plane ⋮ A note on the fixed-point iteration for the matrix equations $X \pm A^* X^{-1}A=I$ ⋮ Solving matrix polynomial equations arising in queueing problems ⋮ Risk processes analyzed as fluid queues ⋮ Relaxed functional iteration techniques for the numerical solution of $M/G/1$ type Markov chains ⋮ Solving certain queueing problems by means of regular splittings ⋮ On the numerical solution of a nonlinear matrix equation in Markov chains

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