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1998•International Journal of Stochastic AnalysisOpen access

Multi‐dimensional quasitoeplitz Markov chains

Alexander N. Dudin, Valentina Klimenok

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Abstract

This paper deals with multi‐dimensional quasitoeplitz Markov chains. We establish a sufficient equilibrium condition and derive a functional matrix equation for the corresponding vector‐generating function, whose solution is given algorithmically. The results are demonstrated in the form of examples and applications in queues with BMAP‐input, which operate in synchronous random environment.

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What this paper is about

This paper deals with multi‐dimensional quasitoeplitz Markov chains. We establish a sufficient equilibrium condition and derive a functional matrix equation for the corresponding vector‐generating function, whose solution is given algorithmically. The results are demonstrated in the form of examples and applications in queues with BMAP‐input, which operate in synchronous random environment.

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Available abstract

This paper deals with multi‐dimensional quasitoeplitz Markov chains. We establish a sufficient equilibrium condition and derive a functional matrix equation for the corresponding vector‐generating function, whose solution is given algorithmically. The results are demonstrated in the form of examples and applications in queues with BMAP‐input, which operate in synchronous random environment.

Key concepts: Mathematics, Markov chain, Examples of Markov chains, Balance equation, Markov chain mixing time, Pure mathematics, Markov model, Statistics

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