On the M/G/1 Bernoulli feedback queue with multi-class customers

We consider an M/G/1 queue with Bernoulli feedback policy and multi-class c ustomers. We assume that different classes of customers have different arri val rates, service time distributions and feedback parameters. We obtain th e joint probability generating function of system size of each class and al so obtain the Laplace-Stieltjes transform of the total response time of a c ustomer in each class, Using these results we obtain the moments of system size of each class and total response time of a customer in each class.