Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Fedorova E. A., Nazarov A. A., Farkhadov M. P. Asymptotic Analysis of the MMРР|M|1 Retrial Queue with Negative Calls under the Heavy Load Condition. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2020, vol. 20, iss. 4, pp. 534-547. DOI: 10.18500/1816-9791-2020-20-4-534-547, EDN: SILKZS

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
30.11.2020
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Language: 
Russian
Heading: 
Computer Sciences
Article type: 
Article
UDC: 
501.1
DOI: 
10.18500/1816-9791-2020-20-4-534-547
EDN: 
SILKZS

Asymptotic Analysis of the MMРР|M|1 Retrial Queue with Negative Calls under the Heavy Load Condition

Autors: 
Fedorova Ekaterina A., Tomsk State University
Nazarov Anatoly A., Tomsk State University
Farkhadov Mais P., V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences
Abstract: 

In the paper, a single-server retrial queueing system with MMPP arrivals and an exponential law of the service time is studied. Unserviced calls go to an orbit and stay there during random time distributed exponentially, they access to the server according to a random multiple access protocol. In the system, a Poisson process of negative calls arrives, which delete servicing positive calls. The method of the asymptotic analysis under the heavy load condition for the system studying is proposed. It is proved that the asymptotic characteristic function of a number of calls on the orbit has the gamma distribution with the obtained parameters. The value of the system capacity is obtained, so, the condition of the system stationary mode is found. The results of a numerical comparison of the asymptotic distribution and the distribution obtained by simulation are presented. Conclusions about the method applicability area are made.

Key words: 
retrial queue
negative calls
MMPP
asymptotic analysis
heavy load
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Received: 
08.11.2019
Accepted: 
30.12.2019
Published: 
30.11.2020
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