Multi-dimensional asymptotically quasi-Toeplitz Markov chains and their application in queueing theory

Authors:
Valentina Klimenok;Alexander Dudin
Affiliations:
Department of Applied Mathematics and Computer Science, Belarusian State University, Minsk, Belarus 220030;Department of Applied Mathematics and Computer Science, Belarusian State University, Minsk, Belarus 220030
Venue:
Queueing Systems: Theory and Applications
Year:
2006

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Abstract

Multi-dimensional asymptotically quasi-Toeplitz Markov chains with discrete and continuous time are introduced. Ergodicity and non-ergodicity conditions are proven. Numerically stable algorithm to calculate the stationary distribution is presented. An application of such chains in retrial queueing models with Batch Markovian Arrival Process is briefly illustrated.