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.