DOI: https://doi.org/10.32515/2664-262X.2024.9(40).1.165-177
Forecasting the congestion of the streets of large cities, taking into account fluctuations in the density and speed of traffic flows
About the Authors
Viktor Vojtov, Professor, Doctor in Technics (Doctor of Technic Sciences), State Biotechnological University, Kharkiv, Ukraine , e-mail: vavoitovva@gmail.com, ORCID ID: 0000-0001-5383-7566
Natalija Berezhna, Associate Professor, PhD in Technics (Candidate of Technics Sciences), State Biotechnological University, Kharkiv, Ukraine , e-mail: bereg_nat@ukr.net, ORCID ID: 0000-0001-8740-3387
Igor Sysenko, Associate Professor, PhD in Technics (Candidate of Technics Sciences), State Biotechnological University, Kharkiv, Ukraine , e-mail: Igor.sysenko@gmail.com, ORCID ID: 0000-0003-0005-7640
Anton Voitov, Associate Professor, PhD in Technics (Candidate of Technics Sciences), State Biotechnological University, Kharkiv, Ukraine , e-mail: K1kavoitov@gmail.com, ORCID ID: 0000-0002-5626-131X
Leonid Kryvenko, Director of the enterprise 16363, Kharkiv, Ukraine , e-mail: leonid.krivenko@atp16363.org.ua, ORCID ID: 0009-0006-2720-0901
Anna Kozenok, Associate Professor, PhD in Technics (Candidate of Technics Sciences), State Biotechnological University, Kharkiv, Ukraine , e-mail: anna13kozenok@gmail.comt, ORCID ID: 0000-0002-3152-2253
Abstract
The work has developed a methodical approach for forecasting the congestion of the streets of large cities, taking into account the fluctuations in the density of traffic flows and the speed of movement of cars in the traffic flow, which are associated with "peak hours". The methodological approach, unlike the previously known ones, complements the well-known robustness criterion developed by the authors in previous publications, which allows to increase the accuracy of forecasting the occurrence of traffic jams.
Time-varying functions of traffic flow density and vehicle speed in the traffic flow are proposed. In addition to real time, functions contain variable parameters in the form of amplitude of oscillations and period of oscillations. This makes it possible to adapt the forecasting model to the real road network, taking into account the period of network congestion and road infrastructure. The dependences of the change in the range of robustness of the traffic flow when the density and speed of movement of vehicles in the flow change. It has been proven that in the presence of fluctuations of the listed parameters, the appearance of traffic jams occurs at average values of density and speed. A significant influence of the amplitude of fluctuations in the density and speed of movement of vehicles in the stream on the appearance of traffic jams has been proven. It is shown that the magnitude of the amplitude of oscillations during "peak times" significantly reduces the stability range of the traffic flow. The influence of the "peak hour" period on the loss of stability of the traffic flow is given. It has been proven that the period of oscillations is an insignificant factor in forecasting traffic jams. However, accounting for such a factor will allow to adapt the mathematical model to the real conditions of traffic flow behavior and thereby increase the accuracy of forecasting.
It is shown that accounting for the fluctuating component of the traffic flow expands the possibilities of applying the robustness criterion presented by the authors in previous publications and makes it possible to provide a more accurate forecast for various sections of the road network of large cities.
Keywords
traffic flow, forecasting, dynamic model, traffic flow density, traffic speed, traffic flow robustness criterion, oscillation amplitude, oscillation period, traffic flow stability, traffic jam
Full Text:
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References
1. Vojtov, V.A. et al. (2023). Otsinka erhonomichnoi stijkosti transportnoho potoku na dil'nytsiakh dorozhn'oi merezhi. Identyfikatsiia matematychnoi modeli [Assessment of ergonomic sustainability of traffic flow at road network sections. Identification of a mathematical model]. Tsentral'noukrains'kyj naukovyj visnyk. Tekhnichni nauky – Central Ukrainian scientific bulletin. Technical Sciences, 7(38), 236-245 https://doi.org/10.32515/2664-262X.2023.7(38).1.236-245 [in Ukrainian].
2. Kravtsov, A.H. et al. (2023). Obhruntuvannia kryteriiu stijkosti transportnoho potoku na dil'nytsiakh dorozhn'oi merezhi [Justification of the traffic flow stability criterion at the sections of the road network]. Tsentral'noukrains'kyj naukovyj visnyk. Tekhnichni nauky – Central Ukrainian scientific bulletin. Technical Sciences, 7(38), 222-230 https://doi.org/10.32515/2664-262X.2023.7(38).2.222-230 [in Ukrainian].
3. Horiainov, O.M. et al. (2023). Doslidzhennia matematychnoi modeli stijkosti transportnoho potoku na dil'nytsiakh dorozhn'oi merezhi mista [Study of the mathematical model of the stability of the traffic flow in the sections of the city's road network]. Tsentral'noukrains'kyj naukovyj visnyk. Tekhnichni nauky – Central Ukrainian scientific bulletin. Technical Sciences, 8(39), I, 183-195 https://doi.org/10.32515/2664-262X.2023.8(39).1.183-195 [in Ukrainian].
4. Medina-Salgado, B., Sanchez-DelaCruz, E., Pozos-Parra, P. & Sierra, J. E. (2022). Urban traffic flow prediction techniques: A review. Sustainable Computing: Informatics and Systems, 35, 100739. https://doi.org/10.1016/j.suscom.2022.100739
5. Kechagias, E. P., Gayialis, S. P., Konstantakopoulos, G. D. & Papadopoulos, G. A. (2019). Traffic flow forecasting for city logistics: A literature review and evaluation. International Journal of Decision Support Systems, 4(2), 159-176. https://doi.org/10.1504/IJDSS.2019.104556
6. Verma, A. (2016). Review of studies on mixed traffic flow: perspective of developing economies. Transportation in Developing Economies, 2, 1-16. https://doi.org/10.1007/s40890-016-0010-0
7. Zambrano-Martinez, J. L., T. Calafate, C., Soler, D., Cano, J. C. & Manzoni, P. (2018). Modeling and characterization of traffic flows in urban environments. Sensors, 18(7), 2020. https://doi.org/10.3390/s18072020
8. Horvat, R., Kos, G. & Ševrović, M. (2015). Traffic flow modelling on the road network in the cities. Tehnički vjesnik, 22(2), 475-486. https://doi.org/10.17559/TV-20150127093334
9. Bhanu, M., Priya, S., Dandapat, S. K., Chandra, J. & Mendes-Moreira, J. (2018). Forecasting traffic flow in big cities using modified tucker decomposition. In Advanced Data Mining and Applications: 14th International Conference, ADMA 2018, Nanjing, China, November 16–18, 2018, Proceedings 14 (pp. 119-128). Springer International Publishing. https://doi.org/10.1007/978-3-030-05090-0_10
10. Gora, P. (2012, March). Traffic simulation framework. In 2012 UKSim 14th International Conference on Computer Modelling and Simulation (pp. 345-349). IEEE. https://doi.org/10.1109/UKSim.2012.57
11. Hu, W., Wang, H., Qiu, Z., Yan, L., Nie, C. & Du, B. (2018). An urban traffic simulation model for traffic congestion predicting and avoiding. Neural Computing and Applications, 30, 1769-1781. https://doi.org/10.1007/s00521-016-2785-7
12. Hofer, C., Jäger, G. & Füllsack, M. (2018). Including traffic jam avoidance in an agent-based network model. Computational social networks, 5, 1-12. https://doi.org/10.1186/s40649-018-0053-y
13. Jiang, Y., Kang, R., Li, D., Guo, S. & Havlin, S. (2017). Spatio-temporal propagation of traffic jams in urban traffic networks. arXiv preprint arXiv:1705.08269. https://doi.org/10.48550/arXiv.1705.08269
14. Nagy, A. M. & Simon, V. (2021). Traffic congestion propagation identification method in smart cities. Infocommunications Journal, 13(1), 45-57. https://doi.org/10.36244/ICJ.2021.1.6
15. Nagy, A. M. & Simon, V. (2021). Improving traffic prediction using congestion propagation patterns in smart cities. Advanced Engineering Informatics, 50, 101343. https://doi.org/10.1016/j.aei.2021.101343
16. Nagy, A. M. & Simon, V. (2021). A novel congestion propagation modeling algorithm for smart cities. Pervasive and Mobile Computing, 73, 101387. https://doi.org/10.1016/j.pmcj.2021.101387
17. Liu, X. C., Zhang, G., Lao, Y. & Wang, Y. (2012). Modeling traffic flow dynamics on managed lane facility: approach based on cell transmission model. Transportation research record, 2278(1), 163-170. https://doi.org/10.3141/2278-18
18. Xu, N., Shang, P. & Kamae, S. (2010). Modeling traffic flow correlation using DFA and DCCA. Nonlinear Dynamics, 61, 207-216. https://doi.org/10.1007/s11071-009-9642-5
19. Fulari, S., Thankappan, A., Vanajakshi, L. & Subramanian, S. (2019). Traffic flow estimation at error prone locations using dynamic traffic flow modeling. Transportation letters, 11(1), 43-53. https://doi.org/10.1080/19427867.2016.1271761
20. Yang, H., Yu, W., Zhang, G. & Du, L. (2024). Network-Wide Traffic Flow Dynamics Prediction Leveraging Macroscopic Traffic Flow Model and Deep Neural Networks. IEEE Transactions on Intelligent Transportation Systems.https://doi.org/10.1109/TITS.2023.3329489
21. Kalair, K. & Connaughton, C. (2021). Anomaly detection and classification in traffic flow data from fluctuations in the flow–density relationship. Transportation Research Part C: Emerging Technologies, 127, 103178. https://doi.org/10.1016/j.trc.2021.103178
22. Moosavi, V. & Hovestadt, L. (2013, August). Modeling urban traffic dynamics in coexistence with urban data streams. In Proceedings of the 2nd ACM SIGKDD International Workshop on Urban Computing (pp. 1-7). https://doi.org/10.1145/2505821.2505822
23. Zhou, Z., Zhang, X., Guo, Q. & Sun, H. (2021). Analyzing power and dynamic traffic flows in coupled power and transportation networks. Renewable and Sustainable Energy Reviews, 135, 110083. https://doi.org/10.1016/j.rser.2020.110083
24. Celikoglu, H. B. (2014). Dynamic classification of traffic flow patterns simulated by a switching multimode discrete cell transmission model. IEEE Transactions on Intelligent Transportation Systems, 15(6), 2539-2550. https://doi.org/10.1109/TITS.2014.2317850
Citations
1. Оцінка ергономічної стійкості транспортного потоку на дільницях дорожньої мережі. Ідентифікація математичної моделі / Войтов В.А. та ін. Центральноукраїнський науковий вісник. Технічні науки. 2023. Вип. 7(38), ч.І. С. 236-245 https://doi.org/10.32515/2664-262X.2023.7(38).1.236-245
2. Обгрунтування критерію стійкості транспортного потоку на дільницях дорожньої мережі / Кравцов А.Г. та ін. Центральноукраїнський науковий вісник. Технічні науки. 2023. Вип. 7(38), ч.ІІ. С. 222-230 https://doi.org/10.32515/2664-262X.2023.7(38).2.222-230
3. Дослідження математичної моделі стійкості транспортного потоку на дільницях дорожньої мережі міста / Горяїнов О.М. та ін. Центральноукраїнський науковий вісник. Технічні науки. 2023. Вип. 8(39), ч.І. С. 183-195 https://doi.org/10.32515/2664-262X.2023.8(39).1.183-195
4. Medina-Salgado B., Sanchez-DelaCruz E., Pozos-Parra P., Sierra J. E. Urban traffic flow prediction techniques: A review. Sustainable Computing: Informatics and Systems. 2022. №35. Р. 100739. https://doi.org/10.1016/j.suscom.2022.100739
5. Kechagias E. P., Gayialis S. P., Konstantakopoulos G. D., Papadopoulos G. A. Traffic flow forecasting for city logistics: A literature review and evaluation. International Journal of Decision Support Systems. 2019. №4(2). Р. 159-176. https://doi.org/10.1504/IJDSS.2019.104556
6. Verma A. Review of studies on mixed traffic flow: perspective of developing economies. Transportation in Developing Economies. 2016. № 2. Р. 1-16. https://doi.org/10.1007/s40890-016-0010-0
7. Zambrano-Martinez J. L., T. Calafate C., Soler D., Cano J. C., Manzoni P. Modeling and characterization of traffic flows in urban environments. Sensors. 2018. 18(7). Р. 2020. https://doi.org/10.3390/s18072020
8. Horvat R., Kos G., Ševrović M. Traffic flow modelling on the road network in the cities. Tehnički vjesnik. 2015. №22(2). Р. 475-486. https://doi.org/10.17559/TV-20150127093334
9. Bhanu M., Priya S., Dandapat S. K., Chandra J., Mendes-Moreira J. Forecasting traffic flow in big cities using modified tucker decomposition. In Advanced Data Mining and Applications: 14th International Conference, ADMA 2018, Nanjing, China, November 16–18, 2018, Proceedings. 2018. 14. (pp. 119-128). Springer International Publishing. https://doi.org/10.1007/978-3-030-05090-0_10
10. Gora P. Traffic simulation framework. In 2012 UKSim 14th International Conference on Computer Modelling and Simulation. 2012, March. pp. 345-349. IEEE. https://doi.org/10.1109/UKSim.2012.57
11. Hu W., Wang H., Qiu Z., Yan L., Nie C., Du B. An urban traffic simulation model for traffic congestion predicting and avoiding. Neural Computing and Applications. 2018. №30. Р.1769-1781. https://doi.org/10.1007/s00521-016-2785-7
12. Hofer C., Jäger G., Füllsack M. Including traffic jam avoidance in an agent-based network model. Computational social networks. 2018. №5. Р.1-12. https://doi.org/10.1186/s40649-018-0053-y
13. Jiang Y., Kang R., Li D., Guo S., Havlin S. Spatio-temporal propagation of traffic jams in urban traffic networks. arXiv preprint arXiv:1705.08269. 2017. https://doi.org/10.48550/arXiv.1705.08269
14. Nagy A. M., Simon V. Traffic congestion propagation identification method in smart cities. Infocommunications Journal. 2021. №13(1). Р. 45-57. https://doi.org/10.36244/ICJ.2021.1.6
15. Nagy A. M., Simon V. Improving traffic prediction using congestion propagation patterns in smart cities. Advanced Engineering Informatics. 2021. № 50. Р. 101343. https://doi.org/10.1016/j.aei.2021.101343
16. Nagy A. M., Simon V. A novel congestion propagation modeling algorithm for smart cities. Pervasive and Mobile Computing. 2021. №73. Р. 101387. https://doi.org/10.1016/j.pmcj.2021.101387
17. Liu X. C., Zhang G., Lao Y., Wang, Y. Modeling traffic flow dynamics on managed lane facility: approach based on cell transmission model. Transportation research record. 2012. № 2278(1). Р. 163-170. https://doi.org/10.3141/2278-18
18. Xu N., Shang P., Kamae S. Modeling traffic flow correlation using DFA and DCCA. Nonlinear Dynamics. 2010. №61. Р. 207-216. https://doi.org/10.1007/s11071-009-9642-5
19. Fulari S., Thankappan A., Vanajakshi L., Subramanian S. Traffic flow estimation at error prone locations using dynamic traffic flow modeling. Transportation letters. 2019. №11(1). Р. 43-53. https://doi.org/10.1080/19427867.2016.1271761
20. Yang H., Yu W., Zhang G., Du L. Network-Wide Traffic Flow Dynamics Prediction Leveraging Macroscopic Traffic Flow Model and Deep Neural Networks. IEEE Transactions on Intelligent Transportation Systems. 2024. https://doi.org/10.1109/TITS.2023.3329489
21. Kalair K., Connaughton C. Anomaly detection and classification in traffic flow data from fluctuations in the flow–density relationship. Transportation Research Part C: Emerging Technologies. 2021. №127. Р. 103178. https://doi.org/10.1016/j.trc.2021.103178
22. Moosavi V., Hovestadt L. Modeling urban traffic dynamics in coexistence with urban data streams. In Proceedings of the 2nd ACM SIGKDD International Workshop on Urban Computing. 2013, August. pp. 1-7. https://doi.org/10.1145/2505821.2505822
23. Zhou Z., Zhang X., Guo Q., Sun H. Analyzing power and dynamic traffic flows in coupled power and transportation networks. Renewable and Sustainable Energy Reviews. 2021. №135. Р. 110083. https://doi.org/10.1016/j.rser.2020.110083
24. Celikoglu H. B. Dynamic classification of traffic flow patterns simulated by a switching multimode discrete cell transmission model. IEEE Transactions on Intelligent Transportation Systems. 2014. №15(6). Р. 2539-2550. https://doi.org/10.1109/TITS.2014.2317850
Copyright (c) 2024 Viktor Vojtov, Natalija Berezhna, Igor Sysenko, Anton Voitov, Leonid Kryvenko, Anna Kozenok
Forecasting the congestion of the streets of large cities, taking into account fluctuations in the density and speed of traffic flows
About the Authors
Viktor Vojtov, Professor, Doctor in Technics (Doctor of Technic Sciences), State Biotechnological University, Kharkiv, Ukraine , e-mail: vavoitovva@gmail.com, ORCID ID: 0000-0001-5383-7566
Natalija Berezhna, Associate Professor, PhD in Technics (Candidate of Technics Sciences), State Biotechnological University, Kharkiv, Ukraine , e-mail: bereg_nat@ukr.net, ORCID ID: 0000-0001-8740-3387
Igor Sysenko, Associate Professor, PhD in Technics (Candidate of Technics Sciences), State Biotechnological University, Kharkiv, Ukraine , e-mail: Igor.sysenko@gmail.com, ORCID ID: 0000-0003-0005-7640
Anton Voitov, Associate Professor, PhD in Technics (Candidate of Technics Sciences), State Biotechnological University, Kharkiv, Ukraine , e-mail: K1kavoitov@gmail.com, ORCID ID: 0000-0002-5626-131X
Leonid Kryvenko, Director of the enterprise 16363, Kharkiv, Ukraine , e-mail: leonid.krivenko@atp16363.org.ua, ORCID ID: 0009-0006-2720-0901
Anna Kozenok, Associate Professor, PhD in Technics (Candidate of Technics Sciences), State Biotechnological University, Kharkiv, Ukraine , e-mail: anna13kozenok@gmail.comt, ORCID ID: 0000-0002-3152-2253
Abstract
Keywords
Full Text:
PDFReferences
1. Vojtov, V.A. et al. (2023). Otsinka erhonomichnoi stijkosti transportnoho potoku na dil'nytsiakh dorozhn'oi merezhi. Identyfikatsiia matematychnoi modeli [Assessment of ergonomic sustainability of traffic flow at road network sections. Identification of a mathematical model]. Tsentral'noukrains'kyj naukovyj visnyk. Tekhnichni nauky – Central Ukrainian scientific bulletin. Technical Sciences, 7(38), 236-245 https://doi.org/10.32515/2664-262X.2023.7(38).1.236-245 [in Ukrainian].
2. Kravtsov, A.H. et al. (2023). Obhruntuvannia kryteriiu stijkosti transportnoho potoku na dil'nytsiakh dorozhn'oi merezhi [Justification of the traffic flow stability criterion at the sections of the road network]. Tsentral'noukrains'kyj naukovyj visnyk. Tekhnichni nauky – Central Ukrainian scientific bulletin. Technical Sciences, 7(38), 222-230 https://doi.org/10.32515/2664-262X.2023.7(38).2.222-230 [in Ukrainian].
3. Horiainov, O.M. et al. (2023). Doslidzhennia matematychnoi modeli stijkosti transportnoho potoku na dil'nytsiakh dorozhn'oi merezhi mista [Study of the mathematical model of the stability of the traffic flow in the sections of the city's road network]. Tsentral'noukrains'kyj naukovyj visnyk. Tekhnichni nauky – Central Ukrainian scientific bulletin. Technical Sciences, 8(39), I, 183-195 https://doi.org/10.32515/2664-262X.2023.8(39).1.183-195 [in Ukrainian].
4. Medina-Salgado, B., Sanchez-DelaCruz, E., Pozos-Parra, P. & Sierra, J. E. (2022). Urban traffic flow prediction techniques: A review. Sustainable Computing: Informatics and Systems, 35, 100739. https://doi.org/10.1016/j.suscom.2022.100739
5. Kechagias, E. P., Gayialis, S. P., Konstantakopoulos, G. D. & Papadopoulos, G. A. (2019). Traffic flow forecasting for city logistics: A literature review and evaluation. International Journal of Decision Support Systems, 4(2), 159-176. https://doi.org/10.1504/IJDSS.2019.104556
6. Verma, A. (2016). Review of studies on mixed traffic flow: perspective of developing economies. Transportation in Developing Economies, 2, 1-16. https://doi.org/10.1007/s40890-016-0010-0
7. Zambrano-Martinez, J. L., T. Calafate, C., Soler, D., Cano, J. C. & Manzoni, P. (2018). Modeling and characterization of traffic flows in urban environments. Sensors, 18(7), 2020. https://doi.org/10.3390/s18072020
8. Horvat, R., Kos, G. & Ševrović, M. (2015). Traffic flow modelling on the road network in the cities. Tehnički vjesnik, 22(2), 475-486. https://doi.org/10.17559/TV-20150127093334
9. Bhanu, M., Priya, S., Dandapat, S. K., Chandra, J. & Mendes-Moreira, J. (2018). Forecasting traffic flow in big cities using modified tucker decomposition. In Advanced Data Mining and Applications: 14th International Conference, ADMA 2018, Nanjing, China, November 16–18, 2018, Proceedings 14 (pp. 119-128). Springer International Publishing. https://doi.org/10.1007/978-3-030-05090-0_10
10. Gora, P. (2012, March). Traffic simulation framework. In 2012 UKSim 14th International Conference on Computer Modelling and Simulation (pp. 345-349). IEEE. https://doi.org/10.1109/UKSim.2012.57
11. Hu, W., Wang, H., Qiu, Z., Yan, L., Nie, C. & Du, B. (2018). An urban traffic simulation model for traffic congestion predicting and avoiding. Neural Computing and Applications, 30, 1769-1781. https://doi.org/10.1007/s00521-016-2785-7
12. Hofer, C., Jäger, G. & Füllsack, M. (2018). Including traffic jam avoidance in an agent-based network model. Computational social networks, 5, 1-12. https://doi.org/10.1186/s40649-018-0053-y
13. Jiang, Y., Kang, R., Li, D., Guo, S. & Havlin, S. (2017). Spatio-temporal propagation of traffic jams in urban traffic networks. arXiv preprint arXiv:1705.08269. https://doi.org/10.48550/arXiv.1705.08269
14. Nagy, A. M. & Simon, V. (2021). Traffic congestion propagation identification method in smart cities. Infocommunications Journal, 13(1), 45-57. https://doi.org/10.36244/ICJ.2021.1.6
15. Nagy, A. M. & Simon, V. (2021). Improving traffic prediction using congestion propagation patterns in smart cities. Advanced Engineering Informatics, 50, 101343. https://doi.org/10.1016/j.aei.2021.101343
16. Nagy, A. M. & Simon, V. (2021). A novel congestion propagation modeling algorithm for smart cities. Pervasive and Mobile Computing, 73, 101387. https://doi.org/10.1016/j.pmcj.2021.101387
17. Liu, X. C., Zhang, G., Lao, Y. & Wang, Y. (2012). Modeling traffic flow dynamics on managed lane facility: approach based on cell transmission model. Transportation research record, 2278(1), 163-170. https://doi.org/10.3141/2278-18
18. Xu, N., Shang, P. & Kamae, S. (2010). Modeling traffic flow correlation using DFA and DCCA. Nonlinear Dynamics, 61, 207-216. https://doi.org/10.1007/s11071-009-9642-5
19. Fulari, S., Thankappan, A., Vanajakshi, L. & Subramanian, S. (2019). Traffic flow estimation at error prone locations using dynamic traffic flow modeling. Transportation letters, 11(1), 43-53. https://doi.org/10.1080/19427867.2016.1271761
20. Yang, H., Yu, W., Zhang, G. & Du, L. (2024). Network-Wide Traffic Flow Dynamics Prediction Leveraging Macroscopic Traffic Flow Model and Deep Neural Networks. IEEE Transactions on Intelligent Transportation Systems.https://doi.org/10.1109/TITS.2023.3329489
21. Kalair, K. & Connaughton, C. (2021). Anomaly detection and classification in traffic flow data from fluctuations in the flow–density relationship. Transportation Research Part C: Emerging Technologies, 127, 103178. https://doi.org/10.1016/j.trc.2021.103178
22. Moosavi, V. & Hovestadt, L. (2013, August). Modeling urban traffic dynamics in coexistence with urban data streams. In Proceedings of the 2nd ACM SIGKDD International Workshop on Urban Computing (pp. 1-7). https://doi.org/10.1145/2505821.2505822
23. Zhou, Z., Zhang, X., Guo, Q. & Sun, H. (2021). Analyzing power and dynamic traffic flows in coupled power and transportation networks. Renewable and Sustainable Energy Reviews, 135, 110083. https://doi.org/10.1016/j.rser.2020.110083
24. Celikoglu, H. B. (2014). Dynamic classification of traffic flow patterns simulated by a switching multimode discrete cell transmission model. IEEE Transactions on Intelligent Transportation Systems, 15(6), 2539-2550. https://doi.org/10.1109/TITS.2014.2317850
Citations
1. Оцінка ергономічної стійкості транспортного потоку на дільницях дорожньої мережі. Ідентифікація математичної моделі / Войтов В.А. та ін. Центральноукраїнський науковий вісник. Технічні науки. 2023. Вип. 7(38), ч.І. С. 236-245 https://doi.org/10.32515/2664-262X.2023.7(38).1.236-245
2. Обгрунтування критерію стійкості транспортного потоку на дільницях дорожньої мережі / Кравцов А.Г. та ін. Центральноукраїнський науковий вісник. Технічні науки. 2023. Вип. 7(38), ч.ІІ. С. 222-230 https://doi.org/10.32515/2664-262X.2023.7(38).2.222-230
3. Дослідження математичної моделі стійкості транспортного потоку на дільницях дорожньої мережі міста / Горяїнов О.М. та ін. Центральноукраїнський науковий вісник. Технічні науки. 2023. Вип. 8(39), ч.І. С. 183-195 https://doi.org/10.32515/2664-262X.2023.8(39).1.183-195
4. Medina-Salgado B., Sanchez-DelaCruz E., Pozos-Parra P., Sierra J. E. Urban traffic flow prediction techniques: A review. Sustainable Computing: Informatics and Systems. 2022. №35. Р. 100739. https://doi.org/10.1016/j.suscom.2022.100739
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