Tandem Retrial Queueing System with Markovian Arrival Process and Common Orbit

In this paper, we investigate a retrial tandem queueing system consisting of two stations in series. Each station is represented by a single server and a buffer of a finite size. Customers arrive at the first station according to a Markovian Arrival Process ($MAP$). The service time at the first and the second server has a Phase type ($PH$) distribution. The novelty of the model under consideration is the presence of a common orbit for blocked customers at both the first and the second stations. Unlike other few studies of retrial tandem systems with a common orbit, our model is more general and we obtain analytical results using matrix-analytic technique. We derive the sufficient conditions for existence and absence of the stationary regime in the system, calculate the stationary distribution of the number of customers in the orbit and at the stations and derive formulas for the most important performance measures.