Queueing systems with different types of renovation mechanism and thresholds as the mathematical models of active queue management mechanism

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Abstract

This article is devoted to some aspects of using the renovation mechanism (different types of renovation are considered, definitions and brief overview are also given) with one or several thresholds as the mathematical models of active queue management mechanisms. The attention is paid to the queuing systems in which a threshold mechanism with renovation is implemented. This mechanism allows to adjust the number of packets in the system by dropping (resetting) them from the queue depending on the ratio of a certain control parameter with specified thresholds at the moment of the end of service on the device (server) (in contrast to standard RED-like algorithms, when a possible drop of a packet occurs at the time of arrivals of next packets in the system). The models with one, two and three thresholds with different types of renovation are under consideration. It is worth noting that the thresholds determine not only from which place in the buffer the packets are dropped, but also to which the reset of packets occurs. For some of the models certain analytical and numerical results are obtained (the references are given), some of them are only under investigation, so only the mathematical model and current results may be considered. Some results of comparing classic RED algorithm with renovation mechanism are presented.

About the authors

Hilquias Viana Carvalho Cravid

Peoples’ Friendship University of Russia (RUDN University)

Author for correspondence.
Email: hilvianamat1@gmail.com

post-graduate student of Department of Applied Probability and Informatics

6, Miklukho-Maklaya St., Moscow, 117198, Russian Federation

Ivan S. Zaryadov

Peoples’ Friendship University of Russia (RUDN University); Institute of Informatics Problems, FRC CSC RAS

Email: zaryadov-is@rudn.ru

Candidate of Physical and Mathematical Sciences, assistant professor of Department of Applied Probability and Informatics of Peoples’ Friendship University of Russia (RUDN University); Senior Researcher of Institute of Informatics Problems of Federal Research Center “Computer Science and Control” Russian Academy of Sciences

6, Miklukho-Maklaya St., Moscow, 117198, Russian Federation; 44-2, Vavilova St., Moscow 119333, Russian Federation

Tatiana A. Milovanova

Peoples’ Friendship University of Russia (RUDN University)

Email: milovanova-ta@rudn.ru

Candidate of Physical and Mathematical Sciences, lecturer of Department of Applied Probability and Informatics

6, Miklukho-Maklaya St., Moscow, 117198, Russian Federation

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