Journal of Applied Mathematics and Stochastic Analysis
Volume 3 (1990), Issue 2, Pages 141-152
doi:10.1155/S1048953390000120
Markov chains with quasitoeplitz transition matrix: applications
Department of Mathematics, San Francisco State University, San Francisco 94132, CA, USA
Received 1 September 1989; Revised 1 March 1990
Copyright © 1990 A. M. Dukhovny. 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.
Abstract
Application problems are investigated for the Markov chains with quasitoeplitz
transition matrix. Generating functions of transient and steady state probabilities, first
zero hitting probabilities and mean times are found for various particular cases,
corresponding to some known patterns of feedback ( “warm-up,” “switch at threshold”
etc.), Level depending dams and queue-depending queueing systems of both M/G/1 and
MI/G/1 types with arbitrary random sizes of arriving and departing groups are studied.