Asymptotic Diffusion Analysis of Multi-Server Retrial Queue with Hyper-Exponential Service

Alexander Moiseev, Anatoly Nazarov and Svetlana Paul
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Alexander Moiseev: Institute of Applied Mathematics and Computer Science, Tomsk State University, Tomsk 634050, Russia
Anatoly Nazarov: Institute of Applied Mathematics and Computer Science, Tomsk State University, Tomsk 634050, Russia
Svetlana Paul: Institute of Applied Mathematics and Computer Science, Tomsk State University, Tomsk 634050, Russia

Mathematics, 2020, vol. 8, issue 4, 1-16

Abstract: A multi-server retrial queue with a hyper-exponential service time is considered in this paper. The study is performed by the method of asymptotic diffusion analysis under the condition of long delay in orbit. On the basis of the constructed diffusion process, we obtain approximations of stationary probability distributions of the number of customers in orbit and the number of busy servers. Using simulations and numerical analysis, we estimate the accuracy and applicability area of the obtained approximations.

Keywords: multi-server retrial queue; hyper-exponential service time; asymptotic analysis; diffusion process (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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