Journal of Applied Mathematics and Stochastic Analysis
Volume 12 (1999), Issue 4, Pages 393-415

Multi-dimensional quasitoeplitz Markov chains

Alexander N. Dudin and Valentina I. Klimenok

Belarus State University, Department of Applied Mathematics and Informatics , 4, F. Skorina Ave, Minsk 50, Belarus

Received 1 November 1997; Revised 1 July 1998

Copyright © 1999 Alexander N. Dudin and Valentina I. Klimenok. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.