Equilibrium distribution of block-structured Markov chains with repeating rows
- 1 September 1990
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 27 (3) , 557-576
- https://doi.org/10.2307/3214541
Abstract
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.Keywords
This publication has 13 references indexed in Scilit:
- Reduced System Algorithms for Markov ChainsManagement Science, 1988
- A stable recursion for the steady state vector in markov chains of m/g/1 typeCommunications in Statistics. Stochastic Models, 1988
- Reduced systems in Markov chains and their applications in queueing theoryQueueing Systems, 1987
- A note on two matrices occurring in the solution of quasi-birth-and-death processesCommunications in Statistics. Stochastic Models, 1987
- An Algorithm to Compute the Equilibrium Distribution of a One-Dimensional Bounded Random WalkOperations Research, 1986
- The Factorization of Queueing Equations and Their InterpretationJournal of the Operational Research Society, 1985
- Regenerative Analysis and Steady State Distributions for Markov ChainsOperations Research, 1985
- Technical Note—A Markov Chain Partitioning Algorithm for Computing Steady State ProbabilitiesOperations Research, 1985
- Matrix-Geometric Solutions in Stochastic Models. An Algorithmic Approach.Journal of the American Statistical Association, 1982
- Queues Solvable without Rouché's TheoremOperations Research, 1979