Steady state analysis of a bulk queue with multiple vacations, setup times with N-policy and closedown times

In this paper a M X / G ( a , b )/1 queueing system with multiple vacations, setup time with N -policy and closedown times is considered. On completion of a service, if the queue length is ξ , where ξ a , then the server performs closedown work. Following closedown the server leaves for multiple vacations of random length irrespective of queue length. When the server returns from a vacation and if the queue length is still less than ‘ N ’, he leaves for another vacation and so on, until he finds ‘ N ’ ( N > b ) customers in the queue. That is, if the server finds at least ‘ N ’ customers waiting for service, then he requires a setup time ‘ R ’ to start the service. After the setup he serves a batch of ‘ b ’ customers, where b ⩾ a . Various characteristics of the queueing system and a cost model with the numerical solution for a particular case of the model are presented.