Control policy of a hysteretic bulk queueing system

This paper is concerned with the optimal control of a batch arrival, 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 idles and waits for the line to grow up to some integer N, (N ≥ r). System characteristics are obtained by means of the embedded Markov chain and semiregenerative techniques, then the expected total cost per unit of time is developed for this model. Finally, a search procedure is presented to determine the optimal thresholds r and N that yield the minimum cost.