A Two Phase Service M/G/1 Vacation Queue With General Retrial Times and Non-persistent Customers

This paper is motivated by an open problem posed by Senthil Kumar and Arumuganathan in their paper published in June 2009 [10]. We study the steady state behavior of an M/G/1 retrial queue with non-persistent customers, two phases of heterogeneous service and different vacation policies. We consider the case where the customer after obtaining the first essential service may or may not opt for a second optional service. In [10], the authors have taken the interretrial times to be exponentially distributed. In this paper, we consider a general retrial time distribution with a constant retrial policy. We have obtained the steady state probability generating function of the system size and the orbit size. Also, we obtain expressions for the performance measures of the system. We discuss some particular cases.