Transaction Flows in Multi-agent Swarm Systems

  • Eugene LarkinEmail author
  • Alexey Ivutin
  • Alexander Novikov
  • Anna Troshina
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10942)


The article presents a mathematical model of transaction flows between individual intelligent agents in swarm systems. Assuming that transaction flows are Poisson ones, the approach is proposed to the analytical modeling of such systems. Methods for estimating the degree of approximation of real transaction flows to Poisson flows based on Pearson’s criterion, regression, correlation and parametric criteria are proposed. Estimates of the computational complexity of determining the parameters of transaction flows by using the specified criteria are shown. The new criterion based on waiting functions is proposed, which allows obtaining a good degree of approximation of an investigated flow to Poisson flow with minimal costs of computing resources. That allows optimizing the information exchange processes between individual units of swarm intelligent systems.


Transaction flow Poisson flow Exponential distribution Pearson’s criterion Expectation Dispersion Waiting function Statistical estimation Intelligent agents 



The research was carried out within the state assignment of the Ministry of Education and Science of Russian Federation (No 2.3121.2017/PCH).


  1. 1.
    Babishin, V., Taghipour, S.: Optimal maintenance policy for multicomponent systems with periodic and opportunistic inspections and preventive replacements. Appl. Math. Model. 40(23), 10480–10505 (2016)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Berg, B.A.: Markov Chain Monte Carlo Simulations and Their Statistical Analysis: With Web-Based Fortran Code. World Scientific Press, Singapore (2004)CrossRefGoogle Scholar
  3. 3.
    Bian, L., Gebraeel, N.: Stochastic modeling and real-time prognostics for multi-component systems with degradation rate interactions. IIE Trans. 46(5), 470–482 (2014)CrossRefGoogle Scholar
  4. 4.
    Bielecki, T.R., Jakubowski, J., Nieweglowski, M.: Conditional Markov chains: properties, construction and structured dependence. Stochast. Process. Appl. 127(4), 1125–1170 (2017)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Boos, D.D., Stefanski, L.A.: Essential Statistical Inference. Springer, New York (2013)CrossRefGoogle Scholar
  6. 6.
    Ching, W.K., Huang, X., Ng, M.K., Siu, T.K.: Markov Chains: Models, Algorithms and Applications. International Series in Operations Research & Management Science, vol. 189. Springer, New York (2013). Scholar
  7. 7.
    Draper, N.R., Smith, H.: Applied Regression Analysis. John Wiley & Sons, New York (2014)zbMATHGoogle Scholar
  8. 8.
    Grigelionis, B.: On the convergence of sums of random step processes to a poisson process. Theory Probab. Appl. 8(2), 177–182 (1963)CrossRefGoogle Scholar
  9. 9.
    Ivutin, A., Larkin, E.: Simulation of concurrent games. Bull. South Ural State Univ. Ser. Math. Model. Program. Comput. Softw. 8(2), 43–54 (2015)zbMATHGoogle Scholar
  10. 10.
    Larkin, E., Ivutin, A., Kotov, V., Privalov, A.: Interactive generator of commands. In: Tan, Y., Shi, Y., Li, L. (eds.) ICSI 2016, Part II. LNCS, vol. 9713, pp. 601–608. Springer, Cham (2016). Scholar
  11. 11.
    Larkin, E.V., Kotov, V.V., Ivutin, A.N., Privalov, A.N.: Simulation of relay-races. Bull. South Ural State Univ. Ser. Math. Model. Program. Comput. Softw. 9(4), 117–128 (2016)zbMATHGoogle Scholar
  12. 12.
    Limnios, N., Swishchuk, A.: Discrete-time semi-Markov random evolutions and their applications. Adv. Appl. Probab. 45(01), 214–240 (2013)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Lu, H., Pang, G., Mandjes, M.: A functional central limit theorem for Markov additive arrival processes and its applications to queueing systems. Queueing Syst. 84(3–4), 381–406 (2016)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Luedicke, J., Bernacchia, A., et al.: Self-consistent density estimation. Stata J. 14(2), 237–258 (2014)CrossRefGoogle Scholar
  15. 15.
    Markov, A.A.: Extension of the law of large numbers to dependent quantities. Izv. Fiz. Matem. Obsch. Kazan Univ. (2nd Ser.) 15, 135–156 (1906)Google Scholar
  16. 16.
    O’Brien, T.A., Kashinath, K., Cavanaugh, N.R., Collins, W.D., O’Brien, J.P.: A fast and objective multidimensional kernel density estimation method: fastkde. Comput. Stat. Data Anal. 101, 148–160 (2016)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Song, S., Coit, D.W., Feng, Q., Peng, H.: Reliability analysis for multi-component systems subject to multiple dependent competing failure processes. IEEE Trans. Reliab. 63(1), 331–345 (2014)CrossRefGoogle Scholar
  18. 18.
    Stuart, A.: Rank correlation methods. Br. J. Stat. Psychol. 9(1), 68–68 (1956). by M. G. Kendall, 2nd ednCrossRefGoogle Scholar
  19. 19.
    Ventsel, E., Ovcharov, L.: Theory of probability and its engineering applications. Higher School, Moscow (2000)Google Scholar
  20. 20.
    Wang, B., Wertelecki, W.: Density estimation for data with rounding errors. Comput. Stat. Data Anal. 65, 4–12 (2013)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Eugene Larkin
    • 1
    Email author
  • Alexey Ivutin
    • 1
  • Alexander Novikov
    • 1
  • Anna Troshina
    • 1
  1. 1.Tula State UniversityTulaRussia

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