Heavy outgoing call asymptotics for retrial queue with two way communication and multiple types of outgoing calls
Journal: Discrete and Continuous Models and Applied Computational Science (Vol.27, No. 1)Publication Date: 2019-11-20
Authors : Anatoly Nazarov; Svetlana Paul; Olga Lizyura;
Page : 5-20
Keywords : retrial queueing system; incoming calls; outgoing calls; asymptotic analysis method; Gaussian approximation;
Abstract
In this paper, we consider a single server queueing model M |M |1|N with two types of calls: incoming calls and outgoing calls, where incoming calls arrive at the server according to a Poisson process. Upon arrival, an incoming call immediately occupies the server if it is idle or joins an orbit if the server is busy. From the orbit, an incoming call retries to occupy the server and behaves the same as a fresh incoming call. The server makes an outgoing calls after an exponentially distributed idle time. It can be interpreted as that outgoing calls arrive at the server according to a Poisson process. There are N types of outgoing calls whose durations follow N distinct exponential distributions. Our contribution is to derive the asymptotics of the number of incoming calls in retrial queue under the conditions of high rates of making outgoing calls and low rates of service time of each type of outgoing calls. Based on the obtained asymptotics, we have built the approximations of the probability distribution of the number of incoming calls in the system.
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