Journal of Applied Mathematics and Stochastic Analysis
Volume 12 (1999), Issue 4, Pages 393-415
Multi-dimensional quasitoeplitz Markov chains
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.