Asymptotic Diffusion Method for Retrial Queues with State-Dependent Service Rate

Anatoly Nazarov, Ekaterina Fedorova (), Olga Lizyura and Radmir Salimzyanov
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Anatoly Nazarov: Institute of Applied Mathematics and Computer Science, Tomsk State University, 634050 Tomsk, Russia
Ekaterina Fedorova: Institute of Applied Mathematics and Computer Science, Tomsk State University, 634050 Tomsk, Russia
Olga Lizyura: Institute of Applied Mathematics and Computer Science, Tomsk State University, 634050 Tomsk, Russia
Radmir Salimzyanov: Institute of Applied Mathematics and Computer Science, Tomsk State University, 634050 Tomsk, Russia

Mathematics, 2023, vol. 11, issue 14, 1-10

Abstract: In this paper, we consider a retrial queue with a state-dependent service rate as a mathematical model of a node of FANET communications. We suppose that the arrival process is Poisson, the delay duration is exponentially distributed, the orbit is unlimited, and there is multiple random access from the orbit. There is one server, and the service time of every call is distributed exponentially with a variable parameter depending on the number of calls in the orbit. The service rate has an infinite number of values. We propose the asymptotic diffusion method for the model study. The asymptotic diffusion approximation of the probability distribution of the number of calls in the orbit is derived. Some numerical examples are demonstrated.

Keywords: retrial queue; state-dependent service rate; asymptotic diffusion method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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