Generalization of Formulas for Queue Length Moments under Nonordinary Poissonian Arrivals for Batch Queues in Telecommunication Systems

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Abstract

We propose an approach for generalization of formulas previously obtained by the authors for the first and second queue length moments in a queueing system with a nonordinary Poissonian arrival flow, single server, and constant service time to the case of a variable service time. The service time is assumed to be a random variable with a finite set of values. This model is adequate for a vast class of batch transmission systems, since the batch transmission time in real-world systems can take only finitely many values.

About the authors

B. Ya. Likhttsinder

Povolzhskiy State University of Telecommunications and Informatics

Email: b.lihtcinder@psuti.ru
Samara, Russia

A. Yu. Privalov

Korolyov Samara National Research University; Povolzhskiy State University of Telecommunications and Informatics

Author for correspondence.
Email: privalov1967@gmail.com
Samara, Russia; Samara, Russia

References

  1. Лихтциндер Б.Я., Привалов А.Ю., Моисеев В.И. Неординарные пуассоновские модели трафика мультисервисных сетей // Пробл. передачи информ. 2023. Т. 59. № 1. С. 71–79. https://www.mathnet.ru/ppi2392
  2. Лихтциндер Б.Я. Трафик мультисервисных сетей доступа (интервальный анализ и проектирование). М.: Науч.-тех. изд-во «Горячая линия – Телеком», 2019. 3. Yunhua R. Evaluation and Estimation of Second-Order Self-similar Network Traffic // Comput. Commun. 2004. V. 27. № 9. P. 898–904. https://doi.org/10.1016/j.comcom.2004.02.003
  3. Privalov A.Yu., Tsarev A. Analysis and Simulation of WAN Traffic by Self-similar Traffic Model with OMNET // Proc. 10th Int. Wireless Communications and Mobile Computing Conf. (IWCMC’2014). Nicosia, Cyprus. Aug. 4–8, 2014. P. 629–634. https://doi.org/10.1109/IWCMC.2014.6906429
  4. Mill´an Naveas G., San Juan Urrutia E., Vargas Guzm´an M. A Simple Multifractal Model for Self-similar Traffic Flows in High-Speed Computer Networks // Comp. y Sist. 2019. V. 23. № 4. P. 1517–1521. https://doi.org/10.13053/cys-23-4-2831
  5. Вишневский В.М., Дудин А.Н. Системы массового обслуживания с коррелированными входными потоками и их применение для моделирования телекоммуникационных сетей // Автомат. и телемех. 2017. № 8. С. 3–59. https://www.mathnet.ru/rus/at14562

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