Analysis of a discrete-time queue with gated priority

Abstract

This paper considers a discrete-time queue with gated priority. Low priority customers arrive at the first queue at the gate in batches according to a batch Bernoulli process (BBP). When the gate opens, all low priority customers at the first queue move to the second queue at a single server. On the other hand, high priority customers directly join the second queue upon arrival. The arrival process of high priority customers is assumed to be a BBP. The server serves only customers in the second queue. For this queue, we derive the probability generating functions for the amount of work in the system, the waiting times and the queue lengths of high and low priority customers under the assumption of bounded gate opening intervals. We also provide some numerical examples.