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

doi:10.22363/2658-4670-2020-28-1-49-61

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DOI Доступ к ресурсу на сайте издателя			10.22363/2658-4670-2020-28-1-49-61

#метод асимптотического анализа

#гауссовская аппроксимация

Title: Two-way communication retrial queue with unreliable server and multiple types of outgoing calls
Title: RQ-система с ненадёжным прибором и разнотипными вызываемыми заявками
Creator: Nazarov, Anatoly A.
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Paul, Svetlana V.
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Lizyura, Olga D.
Date: 2020
DOI: 10.22363/2658-4670-2020-28-1-49-61
Description: Retrial queue under consideration is the model of call center operator switchingbetween input and outgoing calls. Incoming calls form a Poisson point process. Uponarrival, an incoming call occupies the server for an exponentially distributed servicetime if the server is idle. If the server if busy, an incoming call joins the orbit tomake a delay before the next attempt to take the server. The probability distributionof the length of delay is an exponential distribution. Otherwise, the server makesoutgoing 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 differenttypes of outgoing calls follow distinct exponential distributions. Unsteadiness is thatthe server crashes after an exponentially distributed time and needs recovery. Therates of breakdowns and restorations are different and depend on server state. Ourcontribution is to obtain the probability distribution of the number of calls in theorbit under high rate of making outgoing calls limit condition. Based on the obtainedasymptotics, we have built the approximations of the probability distribution of thenumber of calls in the orbit.