V.Yu. Stroganov1, V.M. Chernenky2, V.A. Mikheev3

1,2 Bauman Moscow State Technical University (Moscow, Russia)
3 JSC “Concern “Vega”

The article deals with the modeling of non-stationary processes in the simulation models of queuing networks (QMS), which is one of the main problems of the problem of analyzing the convergence of search optimization algorithms included in the QMS simulation models in order to select the optimal controllable parameters. The non-stationary nature of the simulation processes is due to the constant change in the values of the controlled parameters in the process of implementing the search optimization algorithm on the simulation model.

The aim of the study is to build a formal model of a controlled simulation process, which represents a sequence of non-stationary processes with different values of controlled parameters.

To model non-stationary processes, the paper proposes an extended second-order autoregressive model that allows describing a wide class of sample trajectories of the simulation process.

The results obtained make it possible to study the characteristics of controlled simulation processes, when the sample trajectories for various values of the controlled parameters of the model are consistent in terms of the final and initial states of the processes, depending on the behavior of the search optimization algorithm.

Thus, an instrumental environment for modeling and analyzing sample trajectories of random processes has been developed, which allows one to form trajectories of processes with different parameters in one simulation model and combine them into a single controlled simulation process. In this case, the estimates of the functional specified by the simulation model are calculated on the transitional modes of sample trajectories. The obtained general expressions for estimates of the mathematical expectation and increment of the functional depending on the autocorrelation function will allow us to refine the upper and lower convergence estimates in the case of a known autocorrelation function. To estimate the autocorrelation, one can carry out a preliminary simulation without changing the parameters, or one can consistently refine the autocorrelation based on its averaging over various process implementations for various values of the controlled parameter.

Stroganov V.Yu., Chernenkiy V.M., Mikheev V.A. Modeling of nonstationary random processes and search engine optimization processes on simulation models of queuing systems. Dynamics of complex systems. 2022. V. 16. № 1. P. 5−12. DOI: 10.18127/j19997493-202201-01 (In Russian).

1. Anderson T.A. Statisticheskij analiz vremennyh ryadov. M.: Mir. 1976. 756 s. (In Russian).
2. Ganceva E.A., Kaladze V.A., Kaladze G.A. Dinamicheskie modeli nestacionarnyh sluchajnyh processov. Vestnik VGTU. 2006. T. 2. № 5. S. 4–8 (In Russian).
3. Egoshin A.B. Postanovka zadachi prognozirovaniya vremennogo ryada porozhdaemogo dinamicheskoj sistemoj. Joshkar-Ola: Marijskij gos. tekhn. un-t. 2007. S. 136–140 (In Russian).
4. Kuleshov E.L. Babijchuk I.A. Linejnoe prognozirovanie stacionarnyh sluchajnyh processov pri izvestnom i neizvestnom trende. Avtometriya. 2005. T. 41. № 2. S. 23–35 (In Russian).
5. Lapshina S.N., Berg D.B., Bazhenov I.A. i dr. Imitacionnye modeli v ekonomike dlya izucheniya scenariev razvitiya ekonomicheskih sistem. Ekonomika i upravlenie v mashinostroenii. 2016. № 1. S. 53–55 (In Russian).
6. Orlov Yu.N., Osminin K.P. Postroenie vyborochnoj funkcii raspredeleniya dlya prognozirovaniya nestacionarnogo vremennogo ryada.. Matematicheskoe modelirovanie. 2008. № 9. S. 23–33 (In Russian).
7. Palej A.G., Pollak G.A. Imitacionnoe modelirovanie. Razrabotka imitacionnyh modelej sredstvami iWebsim i AnyLogic: Ucheb. posobie. SPb.: Lan'. 2019. 204 s. (In Russian)
8. Stroganov V.Yu, Rogova O.B., Stroganov D.V. Analiz povedeniya algoritmov poiskovoj optimizacii na perekhodnyh rezhimah nestacionarnyh imitacionnyh processov. Dinamika slozhnyh sistem – XXI vek. 2021. № 1. S. 13–21 (In Russian).
9. Fedorov S.L. Analiz funkcionalov, zadannyh na vyborkah iz nestacionarnogo vremennogo ryada. Trudy II Mezhdunar. nauch.-prakt. konferencii «Teoreticheskie i prikladnye aspekty sovremennoj nauki». Belgorod. Avgust 2014. S. 9–16 (In Russian).
10. Cyplakov A.A. Vvedenie v prognozirovanie v klassicheskih modelyah vremennyh ryadov. Kvantil'. 2006. № 1. S. 3–19 (In Russian).
11. Chernen'kij V.M., Stroganov V.Yu. Analiz povedeniya algoritmov poiskovoj optimizacii na modelyah regeneriruyushchih processov slozhnyh dinamicheskih sistem. Dinamika slozhnyh sistem – XXI vek. 2020. № 4. S. 55–64 (In Russian).
12. Chernen'kij V.M., Stroganov D.V., Ocenka effektivnosti zadachi vybora ekstremal'nyh znachenij parametrov imitacionnoj modeli semejstva regeneriruyushchih processov. Dinamika slozhnyh sistem – XXI vek. 2021. № 1. C. 5–12 (In Russian).
13. Chernen'kij V.M., Stroganov D.V., Miheev V.A. Diffuzionnoe priblizhenie povedeniya upravlyaemyh imitacionnyh modelej sistem massovogo obsluzhivaniya. Dinamika slozhnyh sistem – XXI vek. 2021. № 4. C. 21–28 (In Russian).
14. Hassani H., Soofi A., Zhigljavsky A. Predicting Daily Exchange Rate with Singular Spectrum Analysis, Nonlinear Analysis: Real World Applications. 2010. V. 11. № 3. P. 2023–2034.
15. Perslev M., Jensen M.H., Darkner S. et al. U-time: A fully convolutional network for time series segmentation applied to sleep staging. Advances in Neural Information Processing Systems. 2019. P. 4415–4426.