Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)1899210.22363/2312-9735-2018-26-3-272-284Computer ScienceИнформатика и вычислительная техникаResearch ArticleParametric Study of the System with Active Queue Management ModuleПараметрическое исследование системы с модулем активного управления трафикомVelievaT RВелиеваТатьяна Рефатовна

PhD student of Department of Applied Probability and Informatics of Peoples’ Friendship University of Russia (RUDN University)

аспирант кафедры прикладной информатики и теории вероятностей РУДН

velieva_tr@rudn.universityPeoples’ Friendship University of Russia (RUDN University)Российский университет дружбы народов15122018263VOL 26, NO3 (2018)ТОМ 26, №3 (2018)27228404082018Copyright ©; 2018, Velieva T.R.Copyright ©; 2018, Велиева Т.Р.2018Velieva T.R.Велиева Т.Р.http://creativecommons.org/licenses/by/4.0https://journals.rudn.ru/miph/article/view/18992

Self-oscillating modes in control systems of computer networks quite negatively affect the characteristics of these networks. The problem of finding the areas of self-oscillations is actual and important as the study of parameters of self-oscillations. These studies are extremely labor-intensive because of the substantial non-linear nature of the mathematical model. It is of interest to obtain a so-called parametric portrait describing the zones of occurrence of self-oscillations depending on the value of the parameters: one parameter (two-dimensional graph), two parameters (three-dimensional graph), and so on. Such a parametric portrait allows us to purposefully manage the characteristics of the investigated control system. The investigation of the system under consideration on the basis of ordinary linearization by Taylor expansion is not possible because of the disappearance of the self-oscillatory regime. Therefore, the paper describes a parametric study technique based on the method of harmonic linearization. To verify the theoretical results obtained, simulation is used. In addition, it is proposed to use the computer algebra system for analytical calculations. For this, the criteria for choosing software were formulated. Based on these criteria, a set of software for analytical and numerical calculations was proposed.

Автоколебательные режимы в системах управления в сетях передачи данных крайне негативно влияют на характеристики этих сетей. Актуальной является проблема нахождения зон возникновения автоколебаний, а также исследование параметров автоколебаний. Данные исследования крайне трудоёмки из-за существенной нелинейности математической модели. Представляет интерес получение так называемого параметрического портрета, описывающего зоны возникновения автоколебаний в зависимости от значения параметров: одного (двумерный график), двух (трёхмерый график) и так далее. Подобный параметрический портрет позволяет целенаправленно управлять характеристиками исследуемой системы с управлением. Исследование рассматриваемой системы на основе обычной линеаризации путём разложения в ряд Тейлора не представляется возможным из-за исчезновения собственно автоколебательного режима. Поэтому в работе описывается методика параметрического исследования на основе метода гармонической линеаризации. Для верификации полученных теоретических результатов предлагается использовать имитационное моделирование. Кроме того, в работе предлагается использовать для аналитических расчётов систему компьютерной алгебры. Для этого были сформулированы критерии по выбору программного обеспечения. На основе этих критериев был предложен конкретный набор программного обеспечения для аналитических и численных расчётов.

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