Multi‐dimensional quasitoeplitz Markov chains

Alexander N. Dudin · Valentina Klimenok

29 citations0/0 files storedInternational Journal of Stochastic Analysis

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Advanced Queuing Theory Analysis Probability and Statistical Research Stochastic processes and statistical mechanics

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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References

1991Structured Stochastic Matrices of M/G/1 Type and Their Applications.1963Stochastic Service Systems.1980The N/G/1 queue and its detailed analysis 1994Some steady-state distributions for theMAP /SM /1 queue 1980The N/G/1 queue and its detailed analysis 1995Linear independence of root equations forM/G/1 type Markov chains 1990Queues with Slowly Varying Arrival and Service Processes

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