Analysis of $$MAP, PH_{2}^{OA}/PH_{1}^{I}, PH_{2}^{O}/1$$ retrial queue with vacation, feedback, two-way communication and impatient customers

This article concentrates on the steady-state analysis of a constant retrial queueing system with impatient customers, vacation, feedback, and two types of arrivals, namely the incoming calls which are made by the customers and the outgoing calls which are made by the server during the idle period. The incoming calls arrive at the system by following the Markovian Arrival Process(MAP) and service times of incoming/outgoing calls follow phase-type (PH) distribution, and the rest of the random variables are exponentially distributed. We have framed our model for analyzing some of the basic situations/problems in telecommunication systems. With the support of matrix analytic method, the invariant analysis of our system has been carried out. We have also discussed the busy period and have performed the cost analysis for our model. At last, we have validated our model through numerical and graphical exemplifications.