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Analysis of MAP, PH2OA /PH1I , PH2O /1 retrial queue with vacation, feedback, two-way communication and impatient customers G. Ayyappan1 · R. Gowthami1

© Springer-Verlag GmbH Germany, part of Springer Nature 2020

Abstract 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. Keywords PH distribution · MAP · Vacation · Feedback · Impatient customers · Two way communication

1 Introduction The contribution of Artalejo and Gómez-Corral (2008) in the field of retrial queueing models is noteworthy. They have made a comparison between the classical and retrial queues and have also discussed the advanced retrial queues. They have also discussed the busy period and the sojourn time for some well-known Markovian and non-Markovian models. Further, they have analyzed the retrial queues by employing the matrix analytic method. A bibliography on retrial queues has been provided by Artalejo (1999), Artalejo (2010) which serves as an index for referring various books and articles on retrial queues. He has also published an updated bibliography on retrial queues in the year 2010, and it mainly focussed on highlighting the progress of retrial queues in the decade

Communicated by Kannan.

B

R. Gowthami [email protected] G. Ayyappan [email protected]

1

2000−2009. He has structured the bibliography in such a way that it provides a detailed account of various books, chapters, bibliographic works, survey papers, published articles and forthcoming articles on retrial queueing models. The first monograph on retrial queues has been published by Falin and Templeton (1997), and it provides a detailed account of basic methods and results on retrial queues. They have discussed both single and multiserver retrial queues and have derived various analytical results. Phung-Duc (2017) has provided a survey on the theory and applications of retrial queues. He has given an overview of retrial models that arise from real-world situations and has also suggested some open problems and promising research directions. The concept of Versatile Markovian Point Process(VMPP) has been introduced by Neuts (1979) which forms the basis for the evolution of the Markovian Arrival Proces

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