Perturbation Bounds forMt/Mt/NQueue with Catastrophes

DOI10.1080/15326349.2011.614900zbMath1243.60076OpenAlexW1995121809MaRDI QIDQ5389047

Anna Korotysheva, Alexander I. Zejfman

Publication date: 24 April 2012

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

Full work available at URL: https://doi.org/10.1080/15326349.2011.614900

zbMATH Keywords

stabilityboundsweak ergodicitynonstationary Markovian queueing model

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Continuous-time Markov processes on discrete state spaces (60J27) Applications of continuous-time Markov processes on discrete state spaces (60J28)

Related Items (19)

Perturbation analysis for continuous-time Markov chains ⋮ Ergodicity and perturbation bounds for inhomogeneous birth and death processes with additional transitions from and to the origin ⋮ Error Bounds for Augmented Truncations of Discrete-Time Block-Monotone Markov Chains under Subgeometric Drift Conditions ⋮ Estimation of probabilities for multidimensional birth-death processes ⋮ Continuous-time block-monotone Markov chains and their block-augmented truncations ⋮ On the bounds for a two-dimensional birth-death process with catastrophes ⋮ A time-non-homogeneous double-ended queue with failures and repairs and its continuous approximation ⋮ Limiting characteristics for finite birth-death-catastrophe processes ⋮ Truncation Bounds for Approximations of Inhomogeneous Continuous-Time Markov Chains ⋮ On the Study of Forward Kolmogorov System and the Corresponding Problems for Inhomogeneous Continuous-Time Markov Chains ⋮ Perturbation bounds and truncations for a class of Markovian queues ⋮ On perturbation bounds for continuous-time Markov chains ⋮ On limiting characteristics for a non-stationary two-processor heterogeneous system with catastrophes, server failures and repairs ⋮ On a class of Markovian queuing systems described by inhomogeneous birth-and-death processes with additional transitions ⋮ Bounds on the rate of convergence for Markovian queuing models with catastrophes ⋮ \(M^X/M/c\) queue with catastrophes and state-dependent control at idle time ⋮ A catastrophic queueing model with delayed action ⋮ The M/M/c queue with mass exodus and mass arrivals when empty ⋮ On truncations for weakly ergodic inhomogeneous birth and death processes

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• BMAP/SM/1 queue with Markovian input of disasters and non-instantaneous recovery
• The spectral gap and perturbation bounds for reversible continuous-time Markov chains
• Ergodicity coefficient and perturbation bounds for continuous-time Markov chains
• A stable algorithm for stationary distribution calculation for a BMAP/SM/1 queueing system with Markovian arrival input of disasters
• Stability and exponential convergence of continuous-time Markov chains
• A BMAP/SM/1 queueing system with Markovian arrival input of disasters
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