DOI: https://doi.org/10.32515/2664-262X.2023.7(38).1.236-245

Assessment of the Ergonomic Stability of the Traffic Flow on Sections of the Road Network. Identification of the Mathematical Model

Viktor Vojtov, Andrey Кravtsov, Mykola Karnaukh, Oleksiy Goryayinov, Anna Kozenok, Inna Babych

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

Andrey Кravtsov, Associate Professor, PhD in Technics (Candidate of Technics Sciences), State Biotechnological University, Kharkiv, Ukraine, Україна, e-mail: kravcov_84@ukr.net, ORCID ID: 0000-0003-3103-6594

Mykola Karnaukh, Associate Professor, PhD in Technics (Candidate of Technics Sciences), State Biotechnological University, Kharkiv, Ukraine, e-mail: nikolay.karnauh@gmail.com, ORCID ID: 0000-0002-9220-7986

Oleksiy Goryayinov, Associate Professor, PhD in Technics (Candidate of Technics Sciences), State Biotechnological University, Kharkiv, Ukraine, e-mail: goryainov@ukr.net, ORCID ID: 0000-0002-5967-2835

Anna Kozenok, Associate Professor, PhD in Technics (Candidate of Technics Sciences), State Biotechnological University, Kharkiv, Ukraine, e-mail: anna13kozenok@gmail.comm, ORCID ID: 0000-0002-3152-2253

Inna Babych, Senior Lecturer, State Biotechnological University, Kharkiv, Ukraine, e-mail: ines.babochka@gmail.com, ORCID ID: 0009-0006-2158-0261

Abstract

The paper discusses the structure of the mathematical model featuring assessment of the ergonomic stability of the traffic flow in various sections of the road network under the influence of external disturbances, which is the result of structural identification. The mathematical model differs from the known ones in that it takes into account the dynamics of the process development. In addition to the gradients of speed and density of traffic flows, the research takes into account the dynamic properties of vehicles and the multi-lane road network, as well as the time of delays at pedestrian crossings and traffic lights. The dynamic properties of the traffic flow are described with a third-order differential equation. The mathematical model is parametrically identified; expressions for determining the gains and time constants included in the differential equation are obtained. The input parameters impacting and affecting the stability of the traffic flow are substantiated – these are the gradients of the density and speed of the flow. The parameters characterizing the response of the traffic flow to disturbances are substantiated – these are time constants, the physical meaning of which is the inertia of all links included in the model. The study presents expressions for determining the gains and time constants included in the differential equation. The gain coefficient K1 characterizes the degree of influence of the density of the traffic flow on the reaction time of the driver. The gain coefficient K2 characterizes the influence of the degree of dynamism of the traffic flow on the time of delays during movement and loss of stability. The gain coefficient K3 characterizes the degree of influence of a change in the traffic situation on the delay time when moving in the stream and loss of stability. The value of the time constant T1 characterizes the inertia of the driver depending on the density and intensity of the traffic flow. The value of the time constant T2 characterizes the inertia of the car and is expressed in the ability to maneuver. The value of the time constant T3 characterizes the inertia of changing the traffic situation.

Keywords

transport flow, modeling, dynamic model, structural identification, parametric identification, density gradient, speed gradient, gain coefficient, time constant

Full Text:

PDF

References

1. Ishii, M. & Hibiki, T. (2006). Two-Fluid Model. In: Thermo-Fluid Dynamics of Two-Phase Flow. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-29187-1_9 [in English].

2. Martin Luther Mfenjou, Ado Adamou Abba Ari, Wahabou Abdou, François Spies Kolyang. (2018). Methodology and trends for an intelligent transport system in developing countries. Sustainable Computing: Informatics and Systems, 19, 96-111. https://doi.org/10.1016/j.suscom.2018.08.002 [in English].

3. Ingridvan SCHAGEN, Theo JANSSEN. (2000). MANAGING ROAD TRANSPORT RISKS: Sustainable Safety in the Netherlands. IATSS Research, 24(2), 18-27. https://doi.org/10.1016/S0386-1112(14)60025-X [in English].

4. Mohammad Zaher Serdar, Muammer Koç, Sami G.Al-Ghamdi. (2022). Urban Transportation Networks Resilience: Indicators, Disturbances, and Assessment Methods. Sustainable Cities and Society, 76, 103452. https://doi.org/10.1016/j.scs.2021.103452 [in English].

5. Marcello Montanino, Julien Monteil & Vincenzo Punzo. (2021). From homogeneous to heterogeneous traffic flows: Lp String stability under uncertain model parameters. Transportation Research Part B: Methodological, 146, 136-154. https://doi.org/10.1016/j.trb.2021.01.009 [in English].

6. Saeed Mohammadian, Zuduo Zheng, Md. Mazharul Haque, Ashish Bhaskar. (2021). Performance of continuum models for realworld traffic flows: Comprehensive benchmarking. Transportation Research Part B: Methodological, 147, 132-167. https://doi.org/10.1016/j.trb.2021.03.007 [in English].

7. Ping Jiang, Zhenkun Liu, Lifang Zhang, Jianzhou Wang. (2022). Advanced traffic congestion early warning system based on traffic flow forecasting and extenics evaluation. Applied Soft Computing, 118, 108544. https://doi.org/10.1016/j.asoc.2022.108544 [in English].

8. Trinh Dinh Toan, Wong Y.D. (2021). Fuzzy logic-based methodology for quantification of traffic congestion. Physica A: Statistical Mechanics and its Applications, 570 (15), 125784. https://doi.org/10.1016/j.physa.2021.125784 [in English].

9. Dihua Sun, Dong Chen, Min Zhao, Weining Liu, Linjiang Zheng. (2018). Linear stability and nonlinear analyses of traffic waves for the general nonlinear car-following model with multi-time delays. Physica A: Statistical Mechanics and its Applications, 501 (1), 293-307. https://doi.org/10.1016/j.physa.2018.02.179 [in English].

10. Tao Wang, Yuanshu Zhang, Jing Zhang, Zhen Li, Shubin Li. (2020). New feedback control strategy for optimal velocity traffic model. Physica A: Statistical Mechanics and its Applications, 559 (1), 125053. https://doi.org/10.1016/j.physa.2020.125053 [in English].

11. Ostashevskiy, S.A. (2013). Opredeleniye ponyatiy “upravlyayemost' avtomobiley” i “vozhdeniye mashiny” v sisteme “voditel'-avtomobil'-doroga”. Vestnik KHNADU, Issue 61-62, 300-305 [in English].

12. Markovnina, A.I. & Papunin, A.V. (2019). The study of the influence of intelligent driver assistance systems on the capacity of urban roads. IOP Conf. Series: Journal of Physics: Conf. Series 1177. doi:10.1088/1742-6596/1177/1/012052 [in English].

13. Podoprigora, N., Stepina, P., Dobromirov, V. & Kotikov, J. (2020). Determination of driver’s reaction time in expert studies of road traffic accidents using software and hardware complex. Transportation Research Procedia, Vol. 50, pp. 538-544. https://doi.org/10.1016/j.trpro.2020.10.064 [in English].

14. Mykolaiets, D. & Klen, K. (2020). Fundamentals of the automatic control theory. Calculation work. Kyiv : Igor Sikorsky, Kyiv Polytechnic Institute, 45 p. https://ela.kpi.ua/handle/123456789/38282 [in English].

15. Isidori, A. (2009). Control Theory for Automation: Fundamentals. Springer Handbooks book series (SHB) , pp. 147-172. https://link.springer.com/chapter/10.1007/978-3-540-78831-7_9 [in English].

16. Vojtov, V., Kutiya, О., Berezhnaja, N., Karnaukh, M. & Bilyaeva, O. (2019). Modeling of reliability of logistic systems of urban freight transportation taking into account street congestion. Eastern-European Journal of Enterprise Technologies, Vol. 4, №3 (100), 15-21. DOI: 10.15587/1729-4061.2019.175064 [in English].

17. Muzylyov, D., Shramenko, N. & Karnaukh, M. (2021). Choice of Carrier Behavior Strategy According to Industry 4.0. In: Ivanov V., Trojanowska J., Pavlenko I., Zajac J., Peraković D. (eds). Advances in Design, Simulation and Manufacturing IV. DSMIE 2021. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-77719-7_22 [in English].

Citations

  1. Ishii, M., Hibiki, T. (2006). Two-Fluid Model. In: Thermo-Fluid Dynamics of Two-Phase Flow. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-29187-1_9
  2. Martin Luther Mfenjou, Ado Adamou Abba Ari, Wahabou Abdou, François Spies Kolyang. (2018). Methodology and trends for an intelligent transport system in developing countries. Sustainable Computing: Informatics and Systems. Vol. 19. P. 96-111 https://doi.org/10.1016/j.suscom.2018.08.002.
  3. Ingridvan SCHAGEN, Theo JANSSEN. (2000). MANAGING ROAD TRANSPORT RISKS: Sustainable Safety in the Netherlands. IATSS Research, Volume 24, Issue 2, Pages 18-27 https://doi.org/10.1016/S0386-1112(14)60025-X
  4. Mohammad Zaher Serdar, Muammer Koç, Sami G.Al-Ghamdi. (2022). Urban Transportation Networks Resilience: Indicators, Disturbances, and Assessment Methods. Sustainable Cities and Society, Volume 76, 103452 https://doi.org/10.1016/j.scs.2021.103452
  5. Marcello Montanino, Julien Monteil, Vincenzo Punzo. (2021). From homogeneous to heterogeneous traffic flows: Lp String stability under uncertain model parameters. Transportation Research Part B: Methodological, Volume 146, Pages 136-154 https://doi.org/10.1016/j.trb.2021.01.009
  6. Saeed Mohammadian, Zuduo Zheng, Md. Mazharul Haque, Ashish Bhaskar. (2021). Performance of continuum models for realworld traffic flows: Comprehensive benchmarking. Transportation Research Part B: Methodological, Volume 147, Pages 132-167 https://doi.org/10.1016/j.trb.2021.03.007
  7. Ping Jiang, Zhenkun Liu, Lifang Zhang, Jianzhou Wang. (2022). Advanced traffic congestion early warning system based on traffic flow forecasting and extenics evaluation. Applied Soft Computing, Volume 118, 108544 https://doi.org/10.1016/j.asoc.2022.108544
  8. Trinh Dinh Toan, Wong Y.D. (2021). Fuzzy logic-based methodology for quantification of traffic congestion. Physica A: Statistical Mechanics and its Applications, Volume 570, 15, 125784 https://doi.org/10.1016/j.physa.2021.125784
  9. Dihua Sun, Dong Chen, Min Zhao, Weining Liu, Linjiang Zheng. (2018). Linear stability and nonlinear analyses of traffic waves for the general nonlinear car-following model with multi-time delays. Physica A: Statistical Mechanics and its Applications, Volume 501, 1, Pages 293-307 https://doi.org/10.1016/j.physa.2018.02.179
  10. Tao Wang, Yuanshu Zhang, Jing Zhang, Zhen Li, Shubin Li. (2020). New feedback control strategy for optimal velocity traffic model. Physica A: Statistical Mechanics and its Applications, Volume 559, 1, 125053 https://doi.org/10.1016/j.physa.2020.125053
  11. Осташевский С.А. (2013). Определение понятий «управляемость автомобилей» и «вождение машины» в системе «водитель-автомобиль-дорога». Вестник ХНАДУ. Вып.61-62. С. 300-305.
  12. Markovnina A.I., Papunin A.V. (2019). The study of the influence of intelligent driver assistance systems on the capacity of urban roads. IOP Conf. Series: Journal of Physics: Conf. Series 1177. doi:10.1088/1742-6596/1177/1/012052
  13. Podoprigora N., Stepina P., Dobromirov V., Kotikov J. (2020). Determination of driver’s reaction time in expert studies of road traffic accidents using software and hardware complex. Transportation Research Procedia, vol. 50, pp. 538-544. https://doi.org/10.1016/j.trpro.2020.10.064
  14. Mykolaiets D., Klen K. (2020). Fundamentals of the automatic control theory. Calculation work. Kyiv : Igor Sikorsky, Kyiv Polytechnic Institute, 45 p. https://ela.kpi.ua/handle/123456789/38282
  15. Isidori A. (2009). Control Theory for Automation: Fundamentals. Springer Handbooks book series (SHB) , pp. 147-172. https://link.springer.com/chapter/10.1007/978-3-540-78831-7_9
  16. Vojtov V., Kutiya О., Berezhnaja N., Karnaukh M., Bilyaeva O. (2019). Modeling of reliability of logistic systems of urban freight transportation taking into account street congestion. Eastern-European Journal of Enterprise Technologies. Vol. 4, no. 3 (100), рр. 15-21. DOI: 10.15587/1729-4061.2019.175064.
  17. Muzylyov D., Shramenko N., Karnaukh M. (2021) Choice of Carrier Behavior Strategy According to Industry 4.0. In: Ivanov V., Trojanowska J., Pavlenko I., Zajac J., Peraković D. (eds) Advances in Design, Simulation and Manufacturing IV. DSMIE 2021. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-77719-7_22
Copyright (c) 2023 Viktor Vojtov, Andrey Кravtsov, Mykola Karnaukh, Oleksiy Goryayinov, Anna Kozenok, Inna Babych