A Retrial Queueing System with Renewal Input and Phase Type Service Time Distribution

Abstract

In this paper, a single-server retrial queue with renewal input, phase type service time distribution and a constant retrial rate is analyzed. A constant retrial rate is typical for some real world systems where the intensity of individual retrials is inversely proportional to the number of customers in the orbit or only one customer from the orbit is allowed to make the retrials. A distinguishing feature of the system under consideration is an arbitrary distribution of inter-arrival times and phase type service time distribution while the vast majority of previous research is devoted to retrial systems with a stationary Poisson input or Markovian extensions and exponentially distributed service times. We derive the stationary distributions of the system states and the Laplace-Stieltjes transform of the sojourn time distribution.