M/G/1/r retrial queueing system with priority service of primary customers and a customers-searching server

In this paper a queueing system with a single customer searching server, retrials, finite buffer, Poisson flow and general distribution of service time is considered. An arriving customer joins a retrial orbit if he finds the buffer fully occupied. Upon completion the service, the server searches for the next customer to be served among the customers in the buffer. The inter-retrial times are exponentially distributed with parameter γ. An orbiting customer can be served only if the buffer is free. A computational algorithm for stationary distribution of the primary queue length and a formula for the mean number of customers in the system are presented.