A CONSTRUCTIVE METHOD FOR FINDING β-INVARIANT MEASURES FOR TRANSITION MATRICES OF M/G/1 TYPE

Quan‐Lin Li · Yiqiang Q. Zhao

27 citations0/0 files storedInternational Conference on Matrix-Analytic Methods in Stochastic Models (MAM)

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Advanced Queuing Theory Analysis Probability and Statistical Research Mathematical Dynamics and Fractals

Abstract

In this paper, we study the transition matrix ofM/G/1 type. The radius of conver-gence is discussed, conditions on the α-classification of the states are obtained, and expressions of the β-invariant measure are constructed. The censoring technique is generalized to deal with nonnegative matrices, which may be neither stochastic nor substochastic. This allows us to prove a factorization result for the discounted transition matrix. This factorization provides a unified algorithmic approach for expressing the β-invariant measure for transition matrices with a block-structure, including the matrix of M/G/1 type.

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References

2014Introduction to Stochastic Processes 1999Introduction to Matrix Analytic Methods in Stochastic Modeling 1990A duality theorem for the matrix paradigms in queueing theory 1990Probabilistic interpretations of some duality results for the matrix paradigms in queueing theory 1993Algorithms for Infinite Markov Chains with Repeating Columns 1998Matrix-geometric invariant measures for G/M/l type Markov chains 2002Analytic Methods in Applied Probability 1998Invariant measures for quasi-birth-and-death processes

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