On the asymptotic behaviour of the stationary distribution of markov chains of M/G/1-type

Egbert Falkenberg

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Advanced Queuing Theory Analysis Probability and Statistical Research Probability and Risk Models

Abstract

The asymptotic behaviour of the stationary distribution of Markov chains of the M/G/1-type is investigated. Necessary and sufficient conditions for an asymptotic geometric behaviour are given. In the case of Markov chains arising in single server models with a general Markovian arrival process (MAP) and general service times these conditions turn out to be simple and the coefficients of an asymptotically geometric expansion can be calculated easily. Some numerical results concerning the stationary distribution of embedded Markov chains in Ph/G/1 models are presented

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References

1984Matrix-Geometric Solutions to Stochastic Models 1991Structured Stochastic Matrices of M/G/1 Type and Their Applications.1990A single-server queue with server vacations and a class of non-renewal arrival processes 1988A stable recursion for the steady state vector in markov chains of m/g/1 type 1959Imbedded Markov Chain Analysis of a Waiting-Line Process in Continuous Time 1985Opsearch 1985Tables for multi-server queues 1981Asymptotic exponentiality of the tail of the waiting-time distribution in a Ph/Ph/C queue

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