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Journal Nonlinear World №1 for 2017 г.
Article in number:
Fractal approach to the description of topology and statistical dynamics of large telecommunication networks
Keywords: network topology network system properties mathematical model delay time fractal dimension
Authors:
D.V. Shakhturin - Associate Professor, Department of Radio Electronics and Information-Measuring Techniques, Kazan National Research Technical University named after A.N. Tupolev E-mail: dvshakhturin@kai.ru
Abstract:
The application of fractal geometry methods for determining the system properties of networks distributed in the topological sense is considered. A mathematical model of statistical dynamics of messages passaging through telecommunication systems and networks, based on the modified Fokker-Planck-Kolmogorov (FPK) equations in frame of spatial and temporal variable fractional derivatives is proposed. This model allows exploration of dynamic processes that occur in such systems and networks by means of analysis of their topological structure. Relations for speed and time of message delivery in large telecommunication systems and networks were obtained.
Pages: 13-19
References

 

  1. Marder N.S. Sovremennye telekommunikacii. M.: IRIAS. 2006. 384 s.
  2. Korjachko V.P. Analiz i proektirovanie marshrutov peredachi dannykh v korporativnykh setjakh. M.: Gorjachaja linija-Telekom. 2012. 236 s.
  3. Ortiz J.H. Telecommunications Networks - Current Status and Future Trends. Croatia, Rijeka: InTech. 2012. 458 p.
  4. Hajek B. Communication Network Analysis. Urbana-Champaign: University of Illinois. 2006. 204 p.
  5. Evdokimov JU.K., SHakhturin D.V. Fraktalnyjj kharakter topologii slozhnykh setejj // Metody i sredstva upravlenija tekhnologicheskimi processami: materialy IV Mezhdunar. konf. Saransk: Izd-vo Mordov. un-ta. 2007. S. 244-251.
  6. Evdokimov JU.K., SHakhturin D.V., Potapov A.A. Fraktalnoe modelirovanie zaderzhek soobshhenijj v bolshikh setjakh // Nelinejjnyjj mir. 2008. T. 6. № 8. S. 444-451.
  7. Evdokimov JU.K., SHakhturin D.V. Fraktalnoe modelirovanie zaderzhek soobshhenijj // Problemy tekhniki i tekhnologijj telekommunikacijj: materialy IX Mezhdunar. nauch.-tekhn. konf. (Kazan, 25-27 nojabrja 2008 g.). Kazan: Izd-vo Kazan. gos. tekhn. un-ta. 2008. C. 403-404.
  8. Evdokimov JU.K., Denisov E.S., SHakhturin D.V. Metody fraktalnojj geometrii i drobnykh operatorov v zadachakh analiza i sinteza slozhnykh sistem i ustrojjstv // Fraktaly i drobnye operatory / Pod obshh. red. A.KH. Gilmutdinova. Kazan: Izd-vo «Fehn» Akademii nauk RT. 2010. S. 191-251.
  9. Krylov V.V.,Samokhvalova S.S. Teorija teletrafika i ee prilozhenija. SPb.: BKHV-Peterburg. 2005. 288 s.
  10. KHelebi S., Mak-Ferson D. Principy marshrutizacii v Internet; per. s angl. Izd. 2-e. M.: Izdatelskijj dom «Viljams». 2001. 448 s.
  11. Evdokimov JU.K., SHakhturin D.V. Fraktalnyjj analiz infokommunikacionnykh potokov v bolshikh sistemakh i setjakh // Nelinejjnyjj mir. 2011. T. 9. № 11. S. 726-734.
  12. Evdokimov JU.K., SHakhturin D.V. Drobno-operatornaja model statisticheskojj dinamiki prokhozhdenija soobshhenijj v telekommunikacionnykh sistemakh // Dinamika nelinejjnykh diskretnykh ehlektrotekhnicheskikh i ehlektronnykh sistem: materialy KH Vseros. nauch.-praktich. konf. (CHeboksary, 6-8 ijunja 2013 g.). CHeboksary: Izd-vo CHuvash. un-ta. 2013. C. 69-70.
  13. Uchajjkin V.V. Metod drobnykh proizvodnykh. Uljanovsk: Artishok. 2008. 512 s.
  14. SHakhturin D.V., Evdokimov JU.K. EHksperimentalnoe issledovanie svjazi dinamiki zaderzhek soobshhenijj s fraktalnojj razmernostju topologii kommunikacionnojj seti // Vestnik Kazanskogo gosudarstvennogo tekhnicheskogo universiteta imeni A.N. Tupoleva. 2011. № 1(61). S. 82-88.