Tandem Queue with Three Multiserver Units and Bulk Service with Accessible and Non Accessble Batch in Unit Iii with Vacation

This paper analyses two different queuing model (Model I and Model II) both consisting of three units connected in series separated by a buffer of finite capacity with finite number of parallel servers in each unit. Queuing model differs only on the provision of availing vacation to the servers in unit III. In Model I server can avail exponential vacation, whereas in Model II the server takes only single vacation. Customers of unit I and Unit II are served singly but in unit III, they are served in groups according to bulk service rule. This rule admits each batch to be served only if the batch size is not less than ‘a’ and not more than ‘b’, customers arriving late can also enter service station without affecting the service time if the size of the batch being served is less than ‘d’ (a d” d d” b). The occurrence time and service time have negative exponential distributions. The steady state probability vector of the number of customers in the queue is obtained by using a modified geometric method. The stability condition is also obtained. AMS (2000) Subject Classification Number: 60k25 and 65k30.