Mx/G(a,b)/1 WITH VACATION INTERRUPTED, OPTIONAL RESERVICE AND BALKING

AbstractIn this paper, a single server bulk service queuing system with interrupted vacation, request for Re-service and Balking is considered. At a service completion, if the server finds at least „a‟ customers waiting for service say ξ, he serves a batch of min (ξ ,b ) customers, whereb ≥ a. At the completion of an essential service, the leaving batch of customers may request for a re-service with probability π. 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 then „a‟ the server will avail a vacation of a random length. If the queue size reaches „a‟ during the vacation, the server terminates the vacation abruptly and resumes for primary service. On completion of the vacation the server remains in the system (dormant period) until the queue length reaches „a‟. Customers arrive in batches to the system and are served on a first come-first served basis. Also assuming that the batch arrival units may decide not to join the system (balks) by estimating the duration of waiting time for a service to get completed or by witnessing the long length of the queue. Analytical treatment of this model is obtained by the supplementary variable technique.