The Factorization of Queueing Equations and Their Interpretation

Grassman, W. K.

doi:10.1057/jors.1985.183

Cited by 25 publications

(1 citation statement)

References 11 publications

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“…We show in this paper that analyses based on censoring are equivalent to block-elimination, except that censoring can also be applied if the state space is infinite. The resulting approach is similar to the approaches used earlier by Sheskin (1985), Grassmann et al (1985), Grassmann (1985), Bhat (1987), (1988) for finite state-spaces.…”

Section: Introductionmentioning

confidence: 53%

Equilibrium distribution of block-structured Markov chains with repeating rows

Grassmann,

Heyman

1990

Journal of Applied Probability

114

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In this paper we consider two-dimensional Markov chains with the property that, except for some boundary conditions, when the transition matrix is written in block form, the rows are identical except for a shift to the right. We provide a general theory for finding the equilibrium distribution for this class of chains. We illustrate theory by showing how our results unify the analysis of the M/G/1 and GI/M/1 paradigms introduced by M. F. Neuts.

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Section: Introductionmentioning

confidence: 53%

Equilibrium distribution of block-structured Markov chains with repeating rows

Grassmann,

Heyman

1990

Journal of Applied Probability

114

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Numerical computation of mean passage times and absorption probabilities in Markov and Semi-Markov models

Kohlas

1986

Zeitschrift für Operations Research

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This paper discusses an efficient method to compute mean passage times and absorption probabilities in Markov and Semi-Markov models. It uses the state reduction approach introduced by Winfried Grassmann for the computation of the stationary distribution of a Markov model. The method is numerically stable and has a simple probabilistic interpretation. It is especially stressed, that the natural frame for the state reduction method is rather Semi-Markov theory than Markov theory.Zusammenfassung: Es wird ein wirkungsvolles Rechenverfahren zur Bestimmung von mittleren Zeiten bis zur Absorption und yon Absorptions-Wahrscheinlichkeiten in Markoff-und Semi-MarkoffModellen dargestellt. Die Methode beruht aufdem Zustands-Reduktions-Ansatz, der yon Grassmann ftir die Berechnung station~er Verteilungen yon Markoff-Ketten eingeftihrt wurde. Das Verfahren ist numerisch stabil und hat eine einfaehe wahrscheinlichkeitstheoretisehe Interpretation. Es wird hervorgehoben, daft der natiirliche Rahmen der Methode eher die Semi-Markoff-Theorie als die Markoff-Theorie ist.

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An analytic solution of the waiting time distribution for the discrete-time GI/G/1 queue

Murata

Miyahara

1991

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The Factorization of Queueing Equations and Their Interpretation

Cited by 25 publications

References 11 publications

Equilibrium distribution of block-structured Markov chains with repeating rows

Equilibrium distribution of block-structured Markov chains with repeating rows

Numerical computation of mean passage times and absorption probabilities in Markov and Semi-Markov models

An analytic solution of the waiting time distribution for the discrete-time GI/G/1 queue

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