A Single Server Bernoulli Vacation Queue with two Type of Services and with Restricted Admissibility

A single server queue with Bernoulli vacation has been considered. In addition the admission to queue is based on a Bernoulli process and the server gives two type of services. For this model the probability generating function for the number of customers in the queue at different servers state are obtained using supplementary variable technique. Some performance measures are calculated. Some particular cases are obtained and numerical examples are also presented.