Control policy of a hysteretic queueing system

This paper is concerned with the optimal control of a bulk service queueing system under N-policy. If the number of customers in the system at a service completion is larger than some integer r, then the server starts processing a group of r customers. If, on the other hand, it is smaller than r, then the server goes through an idle period and waits for the line to grow up to some integer N (N ≥ r). We present some system characteristics by means of the embedded Markov chains and semi-regenerative techniques. We also construct the expected total cost for this model and develop a procedure to determine the optimal thresholds r and N that yield the minimum cost.

Authors and Affiliations

1. Department of Statistics and Operations Research, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia (e-mail: lotftadj@ksu.edu.sa), , , , , , SA

   Lotfi Tadj

2. Department of Statistics, National Taichung Institute of Technology, No. 129, Sec. 3, Sanmin Rd., Taichung 404, Taiwan, R. O. C. (email: jauchuan@mail.ntit.edu.tw), , , , , , TW

   Jau-Chuan Ke

Manuscript received: June 2002/Final version received: October 2002

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