ON A BATCH SERVICE QUEUE WITH SINGLE VACATION

Abstract

We consider a batch service queueing system with a single-vacation policy. The server leaves for a vacation as soon as the system empties. If more than B customers are present when the server returns from a vacation, the first B customers are taken into service. If fewer than B customers are present, all waiting customers go into service. If the server finds no customers, the server waits idle for the first customer to arrive. We assume that late arrivals are not allowed to join the ongoing service. We derive the queue size distribution at random points, the system size at departure points, queue waiting time distribution, and other performance measures.