Digital simulators of the random processes

  • Oleg Chernoyarov 
  • Alexey Glushkov,
  • Larisa Korableva,
  • Vladimir Litvinenko,
  • Alexander Makarov
  • National Research Tomsk State University, Lenin Avenue 36, Tomsk, 634050, Russia University
  • a,e National Research University “Moscow Power Engineering Institute”, Krasnokazarmennaya st. 14, Moscow, 111250, Russia
  • Maikop State Technological University, Pervomayskaya st. 191, Maikop, 385000, Russia 
  • Voronezh Institute of the Ministry of Internal Affairs of the Russian Federation, Patriots Avenue 53, Voronezh, 394065, Russia
  • c  Moscow State University, Leninskiye Gory 1, Moscow, 119991, Russia
  • Voronezh State Technical University, Moscow Avenue 14, Voronezh, 394026, Russia
Cite as
Chernoyarov O., Glushkov A., Korableva L., Litvinenko V., Makarov A. (2021). Digital simulators of the random processes. Proceedings of the 33rd European Modeling & Simulation Symposium (EMSS 2021), pp. 45-51. DOI:


The proposed universal digital simulators of random processes based on their Markov models are considered as capable of generating sequences of samples of unlimited duration. It is shown that a simple Markov chain allows generating the random numbers with a specified two-dimensional probability distribution of the neighboring values while a doubly connected Markov model makes it possible to get the three-dimensional random numbers. The parameters of the model are determined from either a known probability density or experimental samples of the simulated random process. It is demonstrated that the simulation algorithms do not require complex mathematical transformations and that they can be implemented using a simple element base. To change the properties of the generated random processes one needs to reload the memory device with a pre-formed data array. The block diagrams of the simulators are studied and the probabilistic and correlation characteristics of the generated random processes are determined. It is established that with these simulators a high accuracy of convergence of the probability distributions of the selected model and the histograms of the generated sample sequences is ensured. In the common studies, one can hardly find the results that can surpass by their efficiency the ones that the proposed simulation algorithms demonstrate accounting for their non-problematic hardware implementation (the minimum computational costs) and the simplicity of reconfiguring the Markov model based simulators for generating new random processes. The introduced simulators can be used in the design, development and testing of the multi-purpose electronic equipment, with different meters and the devices for simulating radio paths.


  1. Bardis, N.G., Markovskyi, A.P., Doukas, N., & Karadimas N.V. (2009). True random number generation based on environmental noise measurements for military applications. Proceedings of the 8th WSEAS international conference on Signal processing, robotics and automation (ISPRA), pp. 68-73, February 21-23, Cambridge (England). Retrieved from
  2. Chernoyarov, O., Glushkov, A., Linvinenko, V., Litvinenko, Y., & Melnikov, K. (2020). The digital random signal simulator. Advances in Intelligent Systems and Computing, 1295, 79-93. Retrieved from
  3. Chernoyarov, O.V., Litvinenko, V.P., Matveev, B.V., Dachian, S., & Melnikov, K.A. (2020). The high-speed random number generator with the specified two-dimensional probability distribution. Proceedings of the 32nd European Modeling and Simulation Symposium (EMSS), pp. 16-21, September 16-18, Athens (Greece). Retrieved from
  4. Devroye, L. (1986). Non-uniform random variate generation. Berlin, Germany: Springer-Verlag.
  5. Dobkin, B. & Hamburger, J. (2014). Analog circuit design, vol. 3. Oxford, UK: Newnes.
  6. Dynkin, E.B. (2006). Theory of Markov processes. Mineola, NY: Dover Publications.
  7. Glushkov, A.N., Kalinin, M.Y., Litvinenko, V.P., & Litvinenko, Y.V. (2020). Digital simulator of a random process using Markov model. Journal of Physics: Conference Series, 1479 (1), 1-9. Retrieved from
  8. Glushkov, A.N., Menshikh, V.V., Khohlov, N.S., Bokova, O.I., & Kalinin, M.Y. (2017). Gaussian signals simulation using biconnected Markov chain. Proceedings of the 2nd International Ural Conference on Measurements (URALCON), pp. 245-250, October 16-19, Chelyabinsk (Russia). Retrieved from
  9. Law, A.M. & Kelton, W.D. (2000). Simulation modeling and analysis. New York, NY: McGraw-Hill.
  10. Lee, B.G. & Kim, B.-H. (2002). Scrambling techniques for CDMA communications. The international series in engineering and computer science, vol. 624. Boston, MA: Springer. Retrieved from
  11. Pchelintsev, E.A. & Pergamenshchikov, S.M. (2019). Model selection method for efficient signals processing from discrete data. Proceedings of the 31st European Modeling and Simulation Symposium (EMSS), pp. 90-95, September 18-20, Lisbon (Portugal). Retrieved from
  12. Radchenko, D., Tokarev, A., Makarov, A., Gulmanov, A., & Melnikov, K. (2020). Evaluation of information protection against leakage through the compromising electromagnetic emanations during data exchange via USB interface. Proceedings of the 32nd European Modeling and Simulation Symposium (EMSS), pp. 16-21, September 16-18, Athens (Greece). Retrieved from
  13. Robinson, E. (1985). Probability theory and applications. Amsterdam, NLD: Springer.