Research Article
BibTex RIS Cite

Controllability of the Main Road with an On-Ramp Section in Freeway Traffic Flow

Year 2023, Volume: 12 Issue: 3, 642 - 648, 28.09.2023
https://doi.org/10.17798/bitlisfen.1264187

Abstract

This study examines the controllability issue pertaining to the main road with a single on-ramp segment within the context of freeway traffic flow. In this regard, a finite-dimensional nonlinear model is formulated by integrating variable speed limit (VSL) and ramp metering (RM) techniques with the controllability property of the system derived under continuous VSL and RM controllers. This allows us to simultaneously control the density of the main line and reduce the queue density of the merging sector. In the numerical experiment, numerical simulations are conducted on a sample model of a main road to investigate the null controllability of the system and validate the theoretical findings. The numerical findings suggest that it is possible to achieve a consistent queue length for the on-ramp section through the implementation of suitable VSL and RM controls. Therefore, the primary accomplishment of this study is to effectively regulate the traffic flow on the main road segment by managing the density of vehicles within a specified timeframe while also considering the queue density of the on-ramp section

References

  • [1] T.V. Baby, V. Bhattacharyya, P.K. Shahri, A.H. Ghasemi, and B. HomChaudhuri, “A suggestion based fuel efficient control framework for connected and automated vehciles in heterogeneous urban traffic”, Transportation Research Part C: Emerging Technologies, 134, 103476, 2022.
  • [2] S.R. Klomp, V.L. Knoop, H. Taale, and S.P. Hoogendoorn, “Ramp metering with microscopic gap detection algorithm design and empirical acceleration verification”, Transportation Research Record, vol. 2676, no. 1, pp. 91-104, 2021.
  • [3] S. Li, and D. Cao, “Variable speed limit strategies’ analysis with cell transmission model on freeway” Modern Physics Letters B, vol. 31, no. 24, 1750219, 2017.
  • [4] H. Zhang, S. G. Ritchie and W. W. Recker, “Some general results on the optimal ramp control problem”, Transportation Research Part C: Emerging Technologies, vol. 4, no. 2, pp. 51-69, 1996.
  • [5] Y. Di, W. Zhang, H. Ding, X. Zheng, and H. Bai, “Integrated Control for Mixed CAV and CV Traffic Flow in Expressway Merge Zones Combined with Variable Speed Limit, Ramp Metering, and Lane Changing”, Journal of Transportation Engineering, Part A: Systems, vol. 149, no. 2, 04022140, 2023.
  • [6] G. Gomes, and R. Horowitz, “Optimal freeway ramp metering using the asymmetric cell transmission model”, Transportation Research Part C: Emerging Technologies, vol. 14, no. 4, pp. 244–262, 2006.
  • [7] C. Gu, C. Wu, Y. Wu, and B. Wiwatanapataphee, “Distributionally robust ramp metering under traffic demand uncertainty”, Transportmetrica B: Transport Dynamics, vol. 10, no. 1, pp.652-666, 2022.
  • [8] C. Gu, T. Zhou, and C. Wu, “Deep Koopman Traffic Modeling for Freeway Ramp Metering”, IEEE Transactions on Intelligent Transportation Systems, pp. 1-13, 2023.
  • [9] N. Yuan, M. Ma, S. Liang, W. Wang, and H. Zhang, “Optimal control method of freeway based on tollbooths lane configuration and variable speed limit control”, Physica A: Statistical Mechanics and its Applications, vol. 603, 127801, 2022.
  • [10] J. Wang, Y. Zheng, Q. Xu, J. Wang, and K. Li, “Controllability analysis and optimal control of mixed traffic flow with human-driven and autonomous vehicles,” IEEE Transactions on Intelligent Transportation Systems, vol. 22, no. 12, pp. 7445-7459, 2020.
  • [11] A. Bayen, J. M. Coron, N. De Nitti, A. Keimer, and L. Pflug, “Boundary controllability and asymptotic stabilization of a nonlocal traffic flow model”, Vietnam Journal of Mathematics, vol. 49, no. 3, pp. 957-985, 2021.
  • [12] S. Agarwal and P. Kachroo, “Controllability and observability analysis for intelligent transportation systems”, Transportation in Developing Economies, vol. 5, no. 1, 2, 2019
  • [13] M. Rinaldi, “Controllability of transportation networks”, Transportation Research Part B: Methodological, vol. 118, pp. 381-406, 2018.
  • [14] A. Hamidoğlu and E. N. Mahmudov, “On construction of sampling patterns for preserving observability/controllability of linear sampled-data systems”, International Journal of Control, vol. 95, no. 1, pp. 206-217, 2022.
  • [15] A. Hamidoğlu, “Null controllability of heat equation with switching controls under Robin’s boundary condition”, Hacettepe Journal of Mathematics and Statistics, vol. 45, no. 2, pp. 373-379, 2016.
  • [16] A. Hamidoglu, “Null controllability of heat equation with switching pointwise controls”, Transactions of NAS of Azerbaijan, Issue Mathematics, Series of Physical-Technical and Mathematical Sciences, vol. 35, no. 4, pp. 52-60, 2015.
  • [17] A. Hamidoglu, “Switching lumped controls”, Proceedings of the Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, vol. 41, no. 2, pp. 83-90, 2015.
  • [18] E. D. Sontag, “Kalman’s controllability rank condition: from linear to nonlinear”, Mathematical system theory: The influence of RE Kalman, pp. 453-462, 1991.
  • [19] D. Lukes, “Global controllability of nonlinear systems”, SIAM Journal on Control, vol. 10, no. 1, pp. 112–126, 1972.
  • [20] P. I. Richards, “Shock waves on the highway”, Operations research, vol. 4, no. 1, pp. 42-51, 1956.
Year 2023, Volume: 12 Issue: 3, 642 - 648, 28.09.2023
https://doi.org/10.17798/bitlisfen.1264187

Abstract

References

  • [1] T.V. Baby, V. Bhattacharyya, P.K. Shahri, A.H. Ghasemi, and B. HomChaudhuri, “A suggestion based fuel efficient control framework for connected and automated vehciles in heterogeneous urban traffic”, Transportation Research Part C: Emerging Technologies, 134, 103476, 2022.
  • [2] S.R. Klomp, V.L. Knoop, H. Taale, and S.P. Hoogendoorn, “Ramp metering with microscopic gap detection algorithm design and empirical acceleration verification”, Transportation Research Record, vol. 2676, no. 1, pp. 91-104, 2021.
  • [3] S. Li, and D. Cao, “Variable speed limit strategies’ analysis with cell transmission model on freeway” Modern Physics Letters B, vol. 31, no. 24, 1750219, 2017.
  • [4] H. Zhang, S. G. Ritchie and W. W. Recker, “Some general results on the optimal ramp control problem”, Transportation Research Part C: Emerging Technologies, vol. 4, no. 2, pp. 51-69, 1996.
  • [5] Y. Di, W. Zhang, H. Ding, X. Zheng, and H. Bai, “Integrated Control for Mixed CAV and CV Traffic Flow in Expressway Merge Zones Combined with Variable Speed Limit, Ramp Metering, and Lane Changing”, Journal of Transportation Engineering, Part A: Systems, vol. 149, no. 2, 04022140, 2023.
  • [6] G. Gomes, and R. Horowitz, “Optimal freeway ramp metering using the asymmetric cell transmission model”, Transportation Research Part C: Emerging Technologies, vol. 14, no. 4, pp. 244–262, 2006.
  • [7] C. Gu, C. Wu, Y. Wu, and B. Wiwatanapataphee, “Distributionally robust ramp metering under traffic demand uncertainty”, Transportmetrica B: Transport Dynamics, vol. 10, no. 1, pp.652-666, 2022.
  • [8] C. Gu, T. Zhou, and C. Wu, “Deep Koopman Traffic Modeling for Freeway Ramp Metering”, IEEE Transactions on Intelligent Transportation Systems, pp. 1-13, 2023.
  • [9] N. Yuan, M. Ma, S. Liang, W. Wang, and H. Zhang, “Optimal control method of freeway based on tollbooths lane configuration and variable speed limit control”, Physica A: Statistical Mechanics and its Applications, vol. 603, 127801, 2022.
  • [10] J. Wang, Y. Zheng, Q. Xu, J. Wang, and K. Li, “Controllability analysis and optimal control of mixed traffic flow with human-driven and autonomous vehicles,” IEEE Transactions on Intelligent Transportation Systems, vol. 22, no. 12, pp. 7445-7459, 2020.
  • [11] A. Bayen, J. M. Coron, N. De Nitti, A. Keimer, and L. Pflug, “Boundary controllability and asymptotic stabilization of a nonlocal traffic flow model”, Vietnam Journal of Mathematics, vol. 49, no. 3, pp. 957-985, 2021.
  • [12] S. Agarwal and P. Kachroo, “Controllability and observability analysis for intelligent transportation systems”, Transportation in Developing Economies, vol. 5, no. 1, 2, 2019
  • [13] M. Rinaldi, “Controllability of transportation networks”, Transportation Research Part B: Methodological, vol. 118, pp. 381-406, 2018.
  • [14] A. Hamidoğlu and E. N. Mahmudov, “On construction of sampling patterns for preserving observability/controllability of linear sampled-data systems”, International Journal of Control, vol. 95, no. 1, pp. 206-217, 2022.
  • [15] A. Hamidoğlu, “Null controllability of heat equation with switching controls under Robin’s boundary condition”, Hacettepe Journal of Mathematics and Statistics, vol. 45, no. 2, pp. 373-379, 2016.
  • [16] A. Hamidoglu, “Null controllability of heat equation with switching pointwise controls”, Transactions of NAS of Azerbaijan, Issue Mathematics, Series of Physical-Technical and Mathematical Sciences, vol. 35, no. 4, pp. 52-60, 2015.
  • [17] A. Hamidoglu, “Switching lumped controls”, Proceedings of the Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, vol. 41, no. 2, pp. 83-90, 2015.
  • [18] E. D. Sontag, “Kalman’s controllability rank condition: from linear to nonlinear”, Mathematical system theory: The influence of RE Kalman, pp. 453-462, 1991.
  • [19] D. Lukes, “Global controllability of nonlinear systems”, SIAM Journal on Control, vol. 10, no. 1, pp. 112–126, 1972.
  • [20] P. I. Richards, “Shock waves on the highway”, Operations research, vol. 4, no. 1, pp. 42-51, 1956.
There are 20 citations in total.

Details

Primary Language English
Subjects Calculus of Variations, Mathematical Aspects of Systems Theory and Control Theory
Journal Section Araştırma Makalesi
Authors

Ali Hamidoğlu 0000-0003-3584-8848

Early Pub Date September 23, 2023
Publication Date September 28, 2023
Submission Date March 13, 2023
Acceptance Date September 13, 2023
Published in Issue Year 2023 Volume: 12 Issue: 3

Cite

IEEE A. Hamidoğlu, “Controllability of the Main Road with an On-Ramp Section in Freeway Traffic Flow”, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 12, no. 3, pp. 642–648, 2023, doi: 10.17798/bitlisfen.1264187.

Bitlis Eren University
Journal of Science Editor
Bitlis Eren University Graduate Institute
Bes Minare Mah. Ahmet Eren Bulvari, Merkez Kampus, 13000 BITLIS