Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)2369610.22363/2658-4670-2020-28-1-49-61Research ArticleTwo-way communication retrial queue with unreliable server and multiple types of outgoing callsNazarovAnatoly A.<p>Doctor of Technical Sciences, head of Department of Probability Theory and Mathematical Statistics</p>nazarov.tsu@gmail.comPaulSvetlana V.<p>Candidate of Physical and Mathematical Sciences, Assistant Professor of Department of Probability Theory and Mathematical Statistics</p>paulsv82@mail.ruLizyuraOlga D.<p>Master’s Degree Student of Institute of Applied Mathematics and Computer Science</p>oliztsu@mail.ruNational Research Tomsk State University15122020281496109052020Copyright © 2020, Nazarov A.A., Paul S.V., Lizyura O.D.2020<p>Retrial queue under consideration is the model of call center operator switching between input and outgoing calls. Incoming calls form a Poisson point process. Upon arrival, an incoming call occupies the server for an exponentially distributed service time if the server is idle. If the server if busy, an incoming call joins the orbit to make a delay before the next attempt to take the server. The probability distribution of the length of delay is an exponential distribution. Otherwise, the server makes outgoing calls in its idle time. There are multiple types of outgoing calls in the system. Outgoing call rates are different for each type of outgoing call. Durations of different types of outgoing calls follow distinct exponential distributions. Unsteadiness is that the server crashes after an exponentially distributed time and needs recovery. The rates of breakdowns and restorations are different and depend on server state. Our contribution is to obtain the probability distribution of the number of calls in the orbit under high rate of making outgoing calls limit condition. Based on the obtained asymptotics, we have built the approximations of the probability distribution of the number of calls in the orbit.</p>retrial queuePoisson processunreliable servertwoway communicationoutgoing callsincoming callsasymptotic analysisGaussian approximationRQ-системапростейший потокненадёжный приборвызываемые заявкиметод асимптотического анализагауссовская аппроксимация[G. Koole and A. Mandelbaum, “Queueing models of call centers: An introduction,” Annals of Operations Research, vol. 113, no. 1-4, pp. 41- 59, 2002. DOI: 10.1023/A:1020949626017.][S. Bhulai and G. Koole, “A queueing model for call blending in call centers,” IEEE Transactions on Automatic Control, vol. 48, no. 8, pp. 1434- 1438, 2003. DOI: 10.1109/TAC.2003.815038.][S. Aguir, F. Karaesmen, O. Z. Akşin, and F. Chauvet, “The impact of retrials on call center performance,” OR Spectrum, vol. 26, no. 3, pp. 353-376, 2004.][J. R. Artalejo and A. Gómez-Corral, Retrial Queueing Systems: A Computational Approach. 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