The paper considers a B/G/1 queueing system with vacations, where the server closes the gate when it begins a vacation. In this system, customers arrive according to a Bernoulli process. The service time and the vacation time follow discrete distributions. The distribution of the number of customers at a random point in time is obtained, and, in turn, the distribution of the residence time (queueing time+service time) for a customer. It is observed that solutions for the present discrete time B/G/1 gated vacation model are analogous to those for the continuous time M/G/1 gated vacation model.
