Numerical solution of a system of equations arising in telecommunication system modeling

  • 1 Meshcheryakov Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna, Russia
  • 2 Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria


An overall telecommunication system including users and a queuing system with FIFO discipline of services of the requests at the switching stage is considered. A detailed conceptual model has been developed including BPP (Bernoulli-Poisson-Pascal) input flow; repeated calls; limited number of homogeneous terminals; losses due to abandoned and interrupted dialing, blocked and interrupted switching, not available intent terminal, blocked and abandoned ringing and abandoned communication. Previously, on the basis of this conceptual model, a system of algebraic equations has been derived characterizing the overall state of the telecommunication system. In the present paper, a method for solving the system of equations with respect to certain dynamic parameters is proposed.



  1. A. S. Poryazov, E. Saranova, Models of telecommunication networks with virtual channel switching and applications (Prof.Marin Drinov Academic Publishing House, Sofia, 2012, in Bulgarian)
  2. V. Andonov, S. Poryazov, A. Otsetova, E. Saranova, LN of the Inst. for Comp. Sc., Soc. Inf. and Telecom. Eng., 283 (2019), 243– 262.
  3. V. Andonov, S. Poryazov, E. Saranova, Proc. of the Ninth International Conference on Advanced Communications and Computation – INFOCOMP 2019 (Nice, France, 28 July – 2 August, 2019), 29–34.
  4. V. Andonov, S. Poryazov, E. Saranova, Inf. Mod. And Analyses, 8 (2019), 212–230.
  5. ITU-T E.600, ITU-T Recommendation E.600: Terms and Definitions of Traffic Engineering (Melbourne, 1988; revised at Helsinki, 1993).
  6. V. B. Iversen, Teletraffic Engineering Handbook (ITU-D SG 2/16 & ITC. Draft, December, 2003).
  7. Gh. Adam, et al., Selected Papers of the 8th International Conference “Distributed Computing and Grid-technologies in Science and Education” (GRID 2018), Dubna, Russia, September 10–14, 2018 (, 2267(2018), 638–644).

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