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Journal of Applied Mathematics and Simulation
Volume 2, Issue 1, Pages 71-82
http://dx.doi.org/10.1155/S1048953389000055

Markov chains with quasitoeplitz transition matrix

Received 1 January 1989; Revised 1 March 1989

Copyright © 1989 Hindawi Publishing Corporation. 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

This paper investigates a class of Markov chains which are frequently encountered in various applications (e.g. queueing systems, dams and inventories) with feedback. Generating functions of transient and steady state probabilities are found by solving a special Riemann boundary value problem on the unit circle. A criterion of ergodicity is established.