sibsutisВестник СибГУТИThe Herald of the Siberian State University of Telecommunications and Information Science1998-6920СибГУТИ10.55648/1998-6920-2025-19-3-111-121sibsutis-988Research ArticleСтатьиО границах применимости эмпирических соотношений для очереди с фрактальным дробовым входящим потокомOn Applicability Limits Of Empirical Relationsips For A Queue With Fractal Shot InputСоколовДмитрий ЕвгеньевичSokolovDmitry Evgenievich

Начальник отдела внедрения систем расчетов

dmsok2001@mail.ruТреногинНиколай ГеннадьевичTrenoginNikolai Gennadievich

К.т.н., доцент кафедры телекоммуникационных сетей и вычислительных средств СибГУТИ, директор департамента развития информационных систем и платформ ООО «Ростелеком Информационные Технологии» (ООО «РТК ИТ»)

trenogin@mail.ruООО "Ростелеком Информационные Технологии" (ООО "РТК ИТ")РоссияRostelecom Information Technologies LLC (RTK IT LLC)Russian FederationСибирский Государственный Университет Телекоммуникаций и Информатики (СибГУТИ); ООО "Ростелеком Информационные Технологии" (ООО "РТК ИТ")РоссияSiberian State University of Telecommunications and Informatics (SibSUTI); Rostelecom Information Technologies LLC (RTK IT LLC)Russian Federation202530092025193Вестник СибГУТИ111121Copyright © Соколов Д.Е., Треногин Н.Г., 20252025Соколов Д.Е., Треногин Н.Г.Sokolov D.E., Trenogin N.G.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestnik.sibsutis.ru/jour/article/view/988

 Сформулированы выводы о границах применимости ранее полученных эмпирических соотношений, позволяющих аналитическим путем рассчитать оценку средней длины очереди в системе массового обслуживания с входящим потоком в виде дробового фрактального процесса (FSNDP). Также приведены краткие обзорные сведения о моделировании сетевого трафика в клиент-серверных системах на основе процесса FSNDP, о структуре самого процесса, а также о подходе, применявшемся при получении аналитических соотношений.

Conclusions are formulated about the applicability limits of previously obtained empirical relationships that allow analytical calculation of the average queue length estimate in a queuing system with an incoming flow in the form of a fractal shot process (FSNDP). Brief overviews of network traffic modeling in client-server systems based on the FSNDP process, the structure of the process itself, and the approach used to obtain the analytical relationships are also given.

фрактальный трафикфрактальный дробовой процесстеория очередейтеория телетрафикаFSNDPСМОfractal trafficfractal shot processqueuing theoryteletraffic theoryFSNDPqueuing systemReferencesShelukhin O. I., Teniakshev A. M., Osin A. V. Fraktal'nye protsessy v telekommunikatsiiakh : monografiia [Fractal processes in telecommunications : monograph]. Moscow, Radiotekhnika, 2003. 480 p.Shelukhin O. I., Teniakshev A. M., Osin A. V. Fraktal'nye protsessy v telekommunikatsiiakh : monografiia [Fractal processes in telecommunications : monograph]. Moscow, Radiotekhnika, 2003. 480 p.Tsybakov B. S. Model' teletrafika na osnove samopodobnogo sluchainogo protsessa [Teletraffic model based on a self-similar stochastic process]. Radiotekhnika, 1999, no. 5, pp. 24–31.Shelukhin O. I., Teniakshev A. M., Osin A. V. Fraktal'nye protsessy v telekommunikatsiiakh : monografiia [Fractal processes in telecommunications : monograph]. Moscow, Radiotekhnika, 2003. 480 p.Neiman V. I. Novoe napravlenie v teorii teletrafika [A Novel Approach in Teletraffic Theory]. Elektrosviaz', 1998, no 7, pp. 27–30.Tsybakov B. S. Model' teletrafika na osnove samopodobnogo sluchainogo protsessa [Teletraffic model based on a self-similar stochastic process]. Radiotekhnika, 1999, no. 5, pp. 24–31.Neiman V. I. Samopodobnye protsessy i ikh primenenie v teorii teletrafika [Self-similar processes and theirs application in teletraffic theory] // Trudy Mezhdunarodnoi Akademii sviazi, 1999, no 1, pp. 11–15.Neiman V. I. Novoe napravlenie v teorii teletrafika [A Novel Approach in Teletraffic Theory]. Elektrosviaz', 1998, no 7, pp. 27–30.Leland W. E., Taqqu M. S., Willinger W., Wilson D. V. On the self-similar nature of Ethernet traffic (extended version). IEEE/ACM Transactions on Networking, 1994, vol. 2, no 1, pp. 1–15.Neiman V. I. Samopodobnye protsessy i ikh primenenie v teorii teletrafika [Self-similar processes and theirs application in teletraffic theory] // Trudy Mezhdunarodnoi Akademii sviazi, 1999, no 1, pp. 11–15.Norros I. The Management of Large Flows of Connectionless Traffic on the Basis of Self-Similar Modeling. ICC ’95. IEEE International Conference on Communications. Seattle, 1995, pp. 451-455.Leland W. E., Taqqu M. S., Willinger W., Wilson D. V. On the self-similar nature of Ethernet traffic (extended version). IEEE/ACM Transactions on Networking, 1994, vol. 2, no 1, pp. 1–15.Shelukhin O. I., Rybakov S. Yu., Vanyushina A. V. Modifikatsiya algoritma obnaruzheniya setevykh atak metodom fiksatsii skachkov fraktalnoy razmernosti v rezhime online. [Modification Of The Network Attack Detection Algorithm By Recording Fractal Dimension Jumps In Online Mode] . Proceedings of Telecom. Universities. 2022. No. 3. PP. 117-126.Norros I. The Management of Large Flows of Connectionless Traffic on the Basis of Self-Similar Modeling. ICC ’95. IEEE International Conference on Communications. Seattle, 1995, pp. 451-455.Zhang, Y., Wang, Y., Cao, H., Hu, Y., Lin, Z., An, K., Li, D. Self-similar traffic prediction for LEO satellite networks based on LSTM. IET Commun. 2025. No 19. PP. 1-9.Shelukhin O. I., Rybakov S. Yu., Vanyushina A. V. Modifikatsiya algoritma obnaruzheniya setevykh atak metodom fiksatsii skachkov fraktalnoy razmernosti v rezhime online. [Modification Of The Network Attack Detection Algorithm By Recording Fractal Dimension Jumps In Online Mode] . Proceedings of Telecom. Universities. 2022. No. 3. PP. 117-126.Shelukhin O., Rybakov S. Statisticheskiye kharakteristiki fraktalnoy razmernosti trafika IoT na primere nabora dannykh Kitsune [IoT Traffic Fractal Dimension Statistical Characteristics on the Kitsune Dataset Example]. Proceedings of Telecommunication Universities, 2023, no 9(5), pp. 112-119.Zhang, Y., Wang, Y., Cao, H., Hu, Y., Lin, Z., An, K., Li, D. Self-similar traffic prediction for LEO satellite networks based on LSTM. IET Commun. 2025. No 19. PP. 1-9.Popoola J., Popoola O., Olaniran O. An Exact Method for a Class of Self-Similar M/Ga/1/KShelukhin O., Rybakov S. Statisticheskiye kharakteristiki fraktalnoy razmernosti trafika IoT na primere nabora dannykh Kitsune [IoT Traffic Fractal Dimension Statistical Characteristics on the Kitsune Dataset Example]. Proceedings of Telecommunication Universities, 2023, no 9(5), pp. 112-119.Queueing System of Internet Stream. FUOYE Journal of Engineering and Technology. 2022 - vol. 7, issue 1., pp. 11-16.Popoola J., Popoola O., Olaniran O. An Exact Method for a Class of Self-Similar M/Ga/1/KRyzhikov Yu. I., Ulanov A. V. Chislenniy Metod rascheta mnogokanalnykh sistem massovogo obsluzhivaniya s potokom Pareto [Numerical Method For Calculating Multichannel Queuing Systems With Pareto Flow]. Sistemy upravleniya, svyazi i bezopasnosti. 2021. No 2. PP. 1-11.Queueing System of Internet Stream. FUOYE Journal of Engineering and Technology. 2022 - vol. 7, issue 1., pp. 11-16.Norros I. On the use of fractional Brownian motion in the theory of connectionless networks. IEEE Journal on Selected Areas in Communications, 1995, vol. 13, no 6, pp. 953–962.Ryzhikov Yu. I., Ulanov A. V. Chislenniy Metod rascheta mnogokanalnykh sistem massovogo obsluzhivaniya s potokom Pareto [Numerical Method For Calculating Multichannel Queuing Systems With Pareto Flow]. Sistemy upravleniya, svyazi i bezopasnosti. 2021. No 2. PP. 1-11.Chen J., Bhatia H. S., Addie R. G., Zukerman M. Statistical characteristics of queue with fractional Brownian motion input. Electronics Letters, 2015, vol. 51, no 9, pp. 699–701.Norros I. On the use of fractional Brownian motion in the theory of connectionless networks. IEEE Journal on Selected Areas in Communications, 1995, vol. 13, no 6, pp. 953–962.Petrov M. N., Ponomarev D. Iu. Samopodobie v sistemakh massovogo obsluzhivaniia s ogranichennym buferom [Self-similarity in Queuing Systems With Limited Buffer]. Elektrosviaz', 2002, no 2, pp. 35–39.Chen J., Bhatia H. S., Addie R. G., Zukerman M. Statistical characteristics of queue with fractional Brownian motion input. Electronics Letters, 2015, vol. 51, no 9, pp. 699–701.Trenogin N. G., Petrov M. N., Sokolov D. E. Empirical Relationship for Queue Length Estimation in a System With Fractal Shot Input // Siberian Journal of Science and Technology, 2017, Vol. 18, no 2, pp. 294–299.Petrov M. N., Ponomarev D. Iu. Samopodobie v sistemakh massovogo obsluzhivaniia s ogranichennym buferom [Self-similarity in Queuing Systems With Limited Buffer]. Elektrosviaz', 2002, no 2, pp. 35–39.Ryu B., Lowen S. Modeling, analysis and simulation of self-similar traffic using the fractal-shot-noise-driven Poisson process. Proc. IASTED Modeling and Simulation. Pittsburgh, PA, 1995, pp. 1-4.Trenogin N. G., Petrov M. N., Sokolov D. E. Empirical Relationship for Queue Length Estimation in a System With Fractal Shot Input // Siberian Journal of Science and Technology, 2017, Vol. 18, no 2, pp. 294–299.Ryu B. K. Fractal Network Traffic: From Understanding to Implications : Ph.D. thesis. Columbia University, 1996, 143 p.Ryu B., Lowen S. Modeling, analysis and simulation of self-similar traffic using the fractal-shot-noise-driven Poisson process. Proc. IASTED Modeling and Simulation. Pittsburgh, PA, 1995, pp. 1-4.Trenogin N. G., Sokolov D. E. Modelirovanie setevogo trafika v informatsionnykh sistemakh na osnove fraktal'nogo tochechnogo protsessa [Modeling Of Network Traffic In Information Systems Basing On Fractal Point Process]. Vestnik universitetskogo kompleksa : sb. nauch. tr. pod obshch. red. prof. N. V. Vasilenko, Krasnoiarsk, VSF RGUITP, NII SUVPT, 2004, – vol. 2(16), pp. 12–21.Ryu B. K. Fractal Network Traffic: From Understanding to Implications : Ph.D. thesis. Columbia University, 1996, 143 p.Trenogin N. G., Sokolov D. E. Fraktal'nye svoistva setevogo trafika v klient-servernoi informatsionnoi sisteme [Fractal Properties Of Network Traffic In Client-Server Information System]. Vestnik NII SUVPT : sb. nauch. tr. Krasnoiarsk, 2003, vol. 14, pp. 163–172.Trenogin N. G., Sokolov D. E. Modelirovanie setevogo trafika v informatsionnykh sistemakh na osnove fraktal'nogo tochechnogo protsessa [Modeling Of Network Traffic In Information Systems Basing On Fractal Point Process]. Vestnik universitetskogo kompleksa : sb. nauch. tr. pod obshch. red. prof. N. V. Vasilenko, Krasnoiarsk, VSF RGUITP, NII SUVPT, 2004, – vol. 2(16), pp. 12–21.Trenogin N. G., Petrov M. N., Sokolov D. E. Svoistva fraktal'nogo trafika pri prokhozhdenii sistemy massovogo obsluzhivaniia s ochered'iu. [Properties Of Fractal Traffic Passing A Queuing System]. Vestnik SibGAU, 2017, vol. 18, no 1, pp. 105–110.Trenogin N. G., Sokolov D. E. Fraktal'nye svoistva setevogo trafika v klient-servernoi informatsionnoi sisteme [Fractal Properties Of Network Traffic In Client-Server Information System]. Vestnik NII SUVPT : sb. nauch. tr. Krasnoiarsk, 2003, vol. 14, pp. 163–172.Petrov M. N., Trenogin N. G., Velovatyi E. A. Sistema podderzhki operatsionnoi i biznes-deiatel'nosti predpriiatiia sviazi s ispol'zovaniem tenzornoi metodologii analiza sistem [Operation And Buisness Support System Of Telecommunication Operator Using Tensor System Analysis Methodology]. Elektrosviaz', 2013, no 1, pp. 17–20.Trenogin N. G., Petrov M. N., Sokolov D. E. Svoistva fraktal'nogo trafika pri prokhozhdenii sistemy massovogo obsluzhivaniia s ochered'iu. [Properties Of Fractal Traffic Passing A Queuing System]. Vestnik SibGAU, 2017, vol. 18, no 1, pp. 105–110.Petrov M. N., Trenogin N. G., Velovatyi E. A. Sistema podderzhki operatsionnoi i biznes-deiatel'nosti predpriiatiia sviazi s ispol'zovaniem tenzornoi metodologii analiza sistem [Operation And Buisness Support System Of Telecommunication Operator Using Tensor System Analysis Methodology]. Elektrosviaz', 2013, no 1, pp. 17–20.Petrov M. N., Trenogin N. G., Velovatyi E. A. Sistema podderzhki operatsionnoi i biznes-deiatel'nosti predpriiatiia sviazi s ispol'zovaniem tenzornoi metodologii analiza sistem [Operation And Buisness Support System Of Telecommunication Operator Using Tensor System Analysis Methodology]. Elektrosviaz', 2013, no 1, pp. 17–20.

The authors declare that there are no conflicts of interest present.