Mathematical Problems in Engineering 
Volume 5 (2000), Issue 5, Pages 397-419
doi:10.1155/S1024123X99001167

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

Alexander N. Dudin1 and Shoichi Nishimura2

 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

Abstract

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.