Journal of Applied Mathematics and Stochastic Analysis
Volume 16 (2003), Issue 4, Pages 327-347

Multi-threshold control of the BMAP/SM/1/K queue with group services

Alexander N. Dudin1 and Srinivas R. Chakravarthy2

1Belarussian State University, Department of Applied Mathematics and Computer Science, Minsk , Belarus
2Kettering University, Department of Industrial and Manufacturing Engineering and Business, Flint, MI, USA

Received 1 March 2002; Revised 1 March 2003

Copyright © 2003 Alexander N. Dudin and Srinivas R. Chakravarthy. 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 a finite capacity queue in which arrivals occur according to a batch Markovian arrival process (BMAP). The customers are served in groups of varying sizes. The services are governed by a controlled semi-Markovian process according to a multithreshold strategy. We perform the steady-state analysis of this model by computing (a) the queue length distributions at departure and arbitrary epochs, (b) the Laplace-Stieltjes transform of the sojourn time distribution of an admitted customer, and (c) some selected system performance measures. An optimization problem of interest is presented and some numerical examples are illustrated.