Search

The steady state behaviour of a single server non-Markovian queue with multiple vacations and controlled optional re-service is analysed. A batch of customers arrive according to Poisson with rate A, whereas the bulk service is rendered by a single server with a minimum batch size of ‘a and maximum of ‘b’. The service times follow a general distribution. At the completion of an essential service, the leaving batch of customers may request for a re-service with probability n. However, the re-service is rendered only when the number of customers waiting in the queue is less than ‘a’. If no request for re-service is made after the completion of an essential service and numbers of customers in the queue is less than ‘a, then the server will avail a vacation of a random length. When the server returns from vacation and if the queue length is still less than ‘a’ he avails another vacation so on until the server finds ‘a’ customers in the queue. After the completion of an essential service and numbers of... more...

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. more...