The finite-buffer M/G/1 queue with general bulk-service rule and single vacation

This paper studies a single server finite-buffer bulk-service queue in which the inter-arrival and service times are exponentially and arbitrarily distributed, respectively. The service is performed in batches of maximum size ‘b’ and minimum size ‘a’. Server takes a single vacation when he finds less than ‘a’ customers after the service completion. The distributions of the number of customers in the queue at arbitrary, service completion and vacation termination epochs have been obtained. Finally, some key performance measures such as average queue length, probability of blocking etc. are discussed.