Single and Bulk Service Queueing Model with Second Optional Service Multiple Vacation Closedown and Balking

Abstract

A batch arrival queueing model wherein a single server provides two types of service (single and bulk) is analyzed in this article along with the parameters such as multiple vacation of the single server, balking behavior of customers, closedown the system whenever it becomes empty and second optional service facility to the demanding customers. The probability generating function of queue size is obtained at an arbitrary time instant under stationary case by supplementary variable method. Some interesting performance measures are also derived.