Two-way communication retrial queue with unreliable server and multiple types of outgoing calls

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Abstract

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.

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About the authors

Anatoly A. Nazarov

National Research Tomsk State University

Email: nazarov.tsu@gmail.com
Doctor of Technical Sciences, head of Department of Probability Theory and Mathematical Statistics 36, Lenina St., Tomsk, 634050, Russian Federation

Svetlana V. Paul

National Research Tomsk State University

Email: paulsv82@mail.ru
Candidate of Physical and Mathematical Sciences, Assistant Professor of Department of Probability Theory and Mathematical Statistics 36, Lenina St., Tomsk, 634050, Russian Federation

Olga D. Lizyura

National Research Tomsk State University

Email: oliztsu@mail.ru
Master’s Degree Student of Institute of Applied Mathematics and Computer Science 36, Lenina St., Tomsk, 634050, Russian Federation

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Copyright (c) 2020 Nazarov A.A., Paul S.V., Lizyura O.D.

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