Computing the conditional stationary distribution in Markov chains of level-dependent M/G/1-type

DOI10.1080/15326349.2018.1451753zbMath1391.60223OpenAlexW2797291416MaRDI QIDQ4643640

Masatoshi Kimura, Tetsuya Takine

Publication date: 28 May 2018

Published in: Stochastic Models (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/15326349.2018.1451753

zbMATH Keywords

error boundcomputational algorithmlevel dependenceconditional stationary distributionMarkov chains of \(\mathrm{M}/\mathrm{G}/1\)-type

Mathematics Subject Classification ID

Computational methods in Markov chains (60J22) Queueing theory (aspects of probability theory) (60K25)

Related Items (5)

On level-dependent QBD processes with explosive state space ⋮ A new matrix-infinite-product-form solution for upper block-Hessenberg Markov chains and its quasi-algorithmic constructibility ⋮ A sequential update algorithm for computing the stationary distribution vector in upper block-Hessenberg Markov chains ⋮ Characterization of the conditional stationary distribution in Markov chains via systems of linear inequalities ⋮ Subexponential asymptotics of asymptotically block-Toeplitz and upper block-Hessenberg Markov chains

Cites Work

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• Analysis and computation of the stationary distribution in a special class of Markov chains of level-dependent \(\mathrm{M}/\mathrm{G}/1\)-type and its application to \(\mathrm{BMAP}/\mathrm{M}/\infty\) and \(\mathrm{BMAP}/\mathrm{M}/c+\mathrm{M}\) queues
• Multi-dimensional asymptotically quasi-Toeplitz Markov chains and their application in queueing theory
• Introduction to Matrix Analytic Methods in Stochastic Modeling
• Calculating the equilibrium distribution in level dependent quasi-birth-and-death processes
• AnRG-Factorization Approach for a BMAP/M/1 Generalized Processor-Sharing Queue

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