Matrix-analytic solution of infinite, finite and level-dependent second-order fluid models

DOI10.1007/s11134-017-9544-zzbMath1377.60086OpenAlexW2749148164MaRDI QIDQ1688934

Miklós Telek, Gábor Horváth

Publication date: 12 January 2018

Published in: Queueing Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11134-017-9544-z

zbMATH Keywords

Markov-modulated Brownian motionstationary analysislevel-dependent behaviormatrix-analytic solutionsecond-order Markov fluid queue

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22) Brownian motion (60J65)

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Uses Software

• SMCSolver

Cites Work

• Second-order fluid models with general boundary behaviour
• Performance measures of a multi-layer Markovian fluid model
• Fluid queues with level dependent evolution
• Fluid models in queueing theory and Wiener-Hopf factorization of Markov chains
• Uniqueness for diffusions with piecewise constant coefficients
• Fluid approach to two-sided reflected Markov-modulated Brownian motion
• A quadratically convergent algorithm for first passage time distributions in the Markov-modulated Brownian motion
• Markov-Modulated Brownian Motion with Two Reflecting Barriers
• Exit Problems for Reflected Markov-Modulated Brownian Motion
• The morphing of fluid queues into Markov-modulated Brownian motion
• Lévy processes with adaptable exponent
• Stationary distributions for fluid flow models with or without brownian noise
• An invariant subspace approach in m/g/l and g/m/l type markov chains
• Second-order stochastic fluid models with fluid-dependent flow rates
• Infinite- and finite-buffer Markov fluid queues: a unified analysis
• Second-Order Fluid Flow Models: Reflected Brownian Motion in a Random Environment
• Numerical Methods for Structured Markov Chains
• Erlangized Fluid Queues with Application To Uncontrolled Fire Perimeter