Journal of Applied Mathematics and Stochastic Analysis 
Volume 12 (1999), Issue 4, Pages 393-415
doi:10.1155/S1048953399000337

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

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.