Application of Queueing System Elements in Mathematical Modeling of Production Processes


Аuthors

Liin E. A.*, Borisova E. V.**

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: elijn@bk.ru
**e-mail: borisovaev@mai.ru

Abstract

 The article explores the application of queueing system (QS) elements in mathematical modeling of production processes. Simulation modeling is used to analyze the load of production equipment, identify bottlenecks, and optimize material flows. Within the research, a model is presented, the behavior of which is described by a developed state diagram, and the introduction of superelements for its description is also considered. The developed model will simplify the process of hardware modernization of production while minimizing downtime. Additionally, the introduction of QS parameters into the system is described, along with an analysis of efficiency using the example of printed circuit board production. The results obtained can be used for the digitalization and optimization of production systems.

The transition to the Industry 4.0 concept is accompanied by the digitalization and automation of production processes. To improve the efficiency of such processes, simulation modeling is widely used, allowing the prediction of equipment load, identification of bottlenecks, and development of optimization strategies. However, traditional modeling methods do not always account for the variability of system parameters. The article proposes the use of QS as a tool for analyzing and optimizing production processes.

The study uses simulation modeling methods to investigate the behavior of the production system under different load parameters. The operation of production positions is described by a finite state machine with defined states and transitions. The approach based on superelements is also considered, which allows treating positions individually by isolating them from the general node, increasing the flexibility of the model. The analysis takes into account the time parameters of processing and the transfer of semi-finished products between positions.

Modeling of printed circuit board production processes showed that the use of QS elements allows for a more accurate analysis of equipment load and identification of bottlenecks. The introduced superelements provide the ability to adapt models to changing conditions. The analysis showed that the use of QS allows for analyzing downtime, throughput, and optimizing resource allocation based on the results. Optimization options include increasing equipment capacity and parallel aggregation of production positions.

The application of simulation modeling methods with the use of QS elements improves the accuracy of analysis and the efficiency of managing production processes. The introduction of superelements facilitates the creation of universal models applicable in different conditions. The results obtained can be used for the digitalization of industrial enterprises and the development of adaptive production systems. Further research may focus on expanding the model by incorporating additional factors that influence the production environment. 

Keywords:

simulation modeling, production efficiency assessment, queueing system, state diagram, digital transformation

References

  1. R. Belinski, A.M.M. Peixe, G.F. Frederico., J.A. Garza-Reyes. Organizational learning and Industry 4.0: findings from a systematic literature review and research agenda. Benchmarking: An International Journal. 2020. Vol. 27, No. 8. P. 2435–2457. DOI: 10.1108/BIJ-04-2020-0158

  2. K. Fettig, T. Gacic, A. Köskal, A. Kühn, F. Stuber. Impact of Industry 4.0 on Organizational Structures. 2018 IEEE International Conference on Engineering, Technology and Innovation (ICE/ITMC), Stuttgart, Germany. 2018. P. 1–8. DOI: 10.1109/ICE.2018.8436284

  3. G. Hoellthaler, S. Braunreuther, G. Reinhart. Requirements for a methodology for the assessment and selection of technologies of digitalization for lean production systems. Procedia CIRP. 2019. Vol. 79, P. 198–203. DOI: 10.1109/ICE.2018.8436284

  4. Mechikova M.N., Klimachev T.D. Practice and prospects of implementing Industry 4.0 technologies in Russian industrial enterprises under adverse external economic conditions. Vestnik Sibirskogo instituta biznesa i informatsionnykh tekhnologii. 2023. No. 12 (2). P. 100–106. (In Russ.). URL: https://doi.org/10.24412/2225-8264-2023-2-100-106

  5. Deniskin Yu.I., Dubrovin A.V., Podkolzin V.G. Innovative production life cycle processes quality management on basis of computer aided quality management system. Trudy MAI. 2017. No. 95. (In Russ.). URL: https://trudymai.ru/eng/published.php?ID=84603

  6. Zaitseva N.I., Pogarskaya T.A. Development of software complex for analysis and optimization of the aircraft assembly process. Trudy MAI. 2022. No. 124. (In Russ.). URL: https://trudymai.ru/eng/published.php?ID=167106. DOI: 10.34759/trd-2022-124-23

  7. Makeev P.A., Chermoshentsev S.F. Testing the method of automated placement of elements on a rigid-flexible printed board using practical examples. Trudy MAI. 2024. No. 134. (In Russ.). URL: https://trudymai.ru/eng/published.php?ID=178481

  8. A. Negahban, J.S. Smith. Simulation for manufacturing system design and operation: Literature review and analysis. Journal of Manufacturing Systems. 2013. No. 33. P. 241–261. DOI: 10.1016/j.jmsy.2013.12.007

  9. Vantsov S.V., Khomutskaya O.V., Liin E.A. New automation opportunities for technological processes in instrument engineering. Vestnik MGTU «Stankin». 2023. No. 3 (66). P. 129–136. (In Russ.)

  10. C. Sassanelli, P. Rosa, S. Terzi. Supporting disassembly processes through simulation tools: A systematic literature review with a focus on printed circuit boards. Journal of Manufacturing Systems. 2021. No. 3360. P. 429–448. DOI: 10.1016/j.jmsy.2021.07.009

  11. Zheleznyakov A.O., Sidorchuk V.P., Podrezov S.N. Simulation model of the system of maintenance and repair of electronic equipment. Trudy MAI. 2022. No. 123. (In Russ.). URL: https://trudymai.ru/eng/published.php?ID=165538. DOI: 10.34759/trd-2022-123-26

  12. Kurennykh A.E. Software development for the integration of decision support models.Trudy MAI. 2022. No. 123. (In Russ.). URL: https://trudymai.ru/ eng/published.php?ID=165567. DOI: 10.34759/trd-2022-123-19

  13. Liin E.A., Khomutskaya O.V., Vantsov S.V. Application of algorithmization methods in the process of simulation modeling of technological processes. Elektronika: nauka, tekhnologiya, biznes. 2023. No. 1. P. 122–127. (In Russ.). DOI: 10.22184/1992-4178.2023.222.1.122.127

  14. Liin E.A., Korobkov M.A., Khomutskaya O.V., Vantsov S.V. Formalization of the work of a production site for the development of a simulation model for shift-daily task execution. Nauchno-tekhnicheskii vestnik Povolzh'ya. 2023. No. 5. P. 212–215. (In Russ.)

  15. Gerasimchuk V.V., Efanov V.V., Kuznetsov D.A., Telepnev P.P. Methodological aspects of modeling stochastic vibrodynamic effects. Trudy MAI. 2024. No. 139. (In Russ.). URL: https://trudymai.ru/eng/published.php?ID=183467

  16. Khatuntseva O.N. On the «determinization» of stochastic processes with increasing degrees of freedom in the system. Trudy MAI. 2023. No. 128. (In Russ.). URL: https://trudymai.ru/ eng/published.php?ID=171388. DOI: 10.34759/trd-2023-128-07

  17. Dorozhko I.V., Musienko A.S. A model for monitoring the technical condition of complex using artificial intelligence. Trudy MAI. 2024. No. 137. (In Russ.). URL: https://trudymai.ru/eng/published.php?ID=181885

  18. Dorozhko I.V., Musienko A.S., Sundiev D.S. Simulation model linking reliability indicators with indicators of test and functional control of technical systems. Trudy MAI. 2023. No. 130. (In Russ.). URL: https://trudymai.ru/eng/published.php?ID=174618. DOI: 10.34759/trd-2023-130-19

  19. Pavlov D.A., Popov A.M., Tkachenko V.V. A model for correcting the initial marking of a classical Petri net based on solving a discrete programming problem. Trudy MAI. 2023. No. 131. (In Russ.). URL: https://trudymai.ru/eng/published.php?ID=175928. DOI: 10.34759/trd-2023-131-22

  20. Kulikov N., Khomutskaya O., Vantsov S. Digital method for automated assessment of printed circuit board deformation. Elektronika: nauka, tekhnologiya, biznes. 2018. No. 2 (173). P. 186–191. (In Russ.). DOI: 10.22184/1992-4178.2018.173.2.186.191

  21. Isaev V. Relationship of parameters affecting the reliability of printed circuit boards. Elektronika: nauka, tekhnologiya, biznes. 2020. No. 5 (196). P. 128–137. (In Russ.). DOI: 10.22184/1992-4178.2020.196.5.128.134

  22. Vasil'ev F.V. Fizicheskaya nadezhnost' elektroniki (Physical reliability of electronics). Moscow: MAI Publ., 2022. 160 p.

  23. Kuznetsov A.S., Kruchinin A.A., Ushkar M.N. Methodology for increasing the reliability and efficiency of on-board radio equipmentstructure at the early stages of design. Trudy MAI. 2024. No. 137. (In Russ.). URL: https://trudymai.ru/eng/published.php?ID=181879

Download

mai.ru — informational site MAI

Copyright © 2000-2025 by MAI

 Вход