A Retrial Queueing System with a Finite Buffer, several Input Flows and a Customer Searching Server

We consider a single-server retrial queueing system with K Poisson flows of customers, which arrive to a buffer of finite capacity. If a customer upon arrival finds the buffer full, he joins an orbit of limited capacity in order to return to the queue again after an exponentially distributed time interval. An arriving customer is lost if he finds the buffer and orbit fully occupied. The service time of an i-type customer has an arbitrary distribution function Bi(x). Every service completion is followed by a search phase with exponentially distributed duration to seek for the next customer for service. Customers are taken by the server from the queue according to the FCFS discipline. It is proved that the analysis of this queueing system is reduced to the analysis of a similar queueing system but with only one Poisson flow.