A bulk quorum queueing system with a random setup time under N-policy and with Bernoulli vacation schedule

Abstract

This paper is concerned with the optimal management of a batch arrival, bulk service queueing system with random set-up time under Bernoulli vacation schedule and 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 other integer N, (N ≥ r). Using the embedded Markov chain and semi-regenerative techniques, we obtain all the system characteristics required to build a linear cost structure. Then, we implement a simple search procedure to determine the optimal thresholds levels r and N. An illustrative example is presented.