Analysis of a discrete-time queue with geometrically distributed gate opening intervals

This paper considers a discrete-time BBP/G1 queue with geometrically distributed gate opening intervals. The system has two queues and a gate. Customers arriving at the system are accommodated in the first queue at the gate. When the gate opens, all the customers who are waiting in the first queue move to the second queue at the server. The gate closes immediately after all the customers in the first queue move to the second queue. The server serves only the customers present in the second queue. For this system, we derive the probability generating functions for the queue length, the amount of work and the waiting time. We also provide some numerical examples in order to show the computational feasibility of the analytical results.