Note—A Single Server Queue with Constant Service Time and Restricted Accessibility

Abstract

A queuing system has restricted accessibility if not every customer is admitted to the system. In this paper a single server queuing system is studied, where the arriving customers are rejected if their waiting plus service times would exceed a fixed amount K. The arrivals follow a Poisson process. In this case an equation for the stationary waiting time distribution is given. The explicit solution of this equation is obtained, when the service time is assumed to be constant. For this model the queue length distribution is also easily derived. It is observed that the queue with finite waiting room is a special case of this model.queues: balking and reneging