• SINGLE SERVER BULK QUEUE WITH FEEDBACK, TWO CHOICES OF SERVICE AND COMPULSORY VACATION

Abstract

The concept of this paper deals with the customers arriving in bulk or group, in a single server queueing system, in Poisson distribution which provides two types of general services in bulk of fixed size  in first come first served basis. After first stage service, the server must provide the second stage service. However after the completion of second stage service, if the batch of customer is dissatisfied with his service, he can immediately join the tail of the queue as a feedback customer with probability  to repeat the service until it is successful. Otherwise the batch of customer may depart the system with probability. After completion of the service, the server takes compulsory vacation under general distribution. If the required bulk of customers is not available on the return of the server, the server again goes for vacation or remains in the system till bulk is reached. Taking this concept into account, we derive the time dependent probability generating functions and from it the corresponding steady state results are obtained. The average queue size, the system size and numerical results are discussed.