Poisson's equation for queues driven by a Markovian marked point process

DOI10.1007/BF01158696zbMath0809.60093OpenAlexW2024989604MaRDI QIDQ1339064

Mogens Bladt, Soren Asmussen

Publication date: 28 March 1995

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

Full work available at URL: https://doi.org/10.1007/bf01158696

zbMATH Keywords

queueinfinitesimal generatorvirtual waiting timephase-type distributions

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (14)

General Solution of the Poisson Equation for Quasi-Birth-and-Death Processes ⋮ The estimation of phase-type related functionals using Markov chain Monte Carlo methods ⋮ An algorithm for asymptotic mean and variance for Markov renewal process of \(M/G/1\) type with finite level ⋮ Matrix Structures in Queuing Models ⋮ Poisson equation and discrete one-sided Hilbert transform for \((C, \alpha)\)-bounded operators ⋮ Poisson's equation for discrete-time single-birth processes ⋮ The variance constant for continuous-time level dependent quasi-birth-and-death processes ⋮ Augmented truncation approximations to the solution of Poisson's equation for Markov chains ⋮ Deviation matrix and asymptotic variance for \(\mathrm{GI}/\mathrm{M}/1\)-type Markov chains ⋮ Asymptotic mean and variance of departures in an \(M/G/1/K + 1\) queue ⋮ Hoeffding's inequality for Markov processes via solution of Poisson's equation ⋮ Additive Functionals for Discrete-Time Markov Chains with Applications to Birth-Death Processes ⋮ The variance constant for the actual waiting time of the PH/PH/1 queue ⋮ Central limit theorems for ergodic continuous-time Markov chains with applications to single birth processes

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