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Mathematical Problems in Engineering
Volume 5, Issue 5, Pages 397-419

Optimal hysteretic control for a BMAP/SM/1/N queue with two operation modes

1Laboratory of Applied Probabilistic Analysis, Faculty of Applied Mathematics and Computer Sciences, Belarus State University, 4, F. Skorina Ave., Minsk-50 220050, Belarus
2Department of Applied Mathematics, Faculty of Science, Science University of Tokyo, Kagurazaka, Tokyo 162, Japan

Received 11 September 1998

Copyright © 2000 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.


We consider BMAP/SM/1 type queueing system with finite buffer of size N. The system has two operation modes, which are characterized by the matrix generating function of BMAP-input, the kernel of the semi-Markovian service process, and utilization cost. An algorithm for determining the optimal hysteresis strategy is presented.