Computational aspects of bulk-service queueing system with variable capacity and finite waiting space: M/GY/1/N+B

In this paper, a comparative analysis of the computational aspects of a bulk-service queueing system with variable capacity and finite waiting space is carried out using the Jacobi method of iteration and the rootfinding method. Steady-state probabilities and moments of the number of customers in system at post-departure epochs have been obtained. In the special case when service is performed in batches of fixed size B, a set of relations among post-departure, random and pre-arrival epochs probabilities has also been obtained. For this special case, the authors present various performance measures such as moments of number in system at random epoch, probability of blocking, probability that server is busy, etcetera. A variety of numerical results have been obtained for several service-time distributions: Erlang, deterministic and hyperexponential. It was finally observed that the Jacobi method is less cumbersome than the rootfinding method.