Stability analysis for heterogeneous traffic flow with lane-change disturbance
Abstract
Stability analysis and benefit estimation have substantial implications for lane-change decision-making to reduce delay and variation. Connected platoons drive with minor headway to increase capacity, whereas dividing or reforming platoons significantly impacts traveling efficiency. Therefore, this article focuses on the instability of the platoon caused by an en-route lane-change. Construction of platoon forming, combination rules, and car-following models for various vehicle types are presented to describe driving behaviours. Then, a velocity adjustment and a model for lane-change preparation and recovery are proposed. In addition, a group of stability recognition indexes and related stability evaluation factors are presented. Experiments involving numerical comparisons of the proposed factors are conducted to demonstrate the propagation properties of the instability and reveal the fluctuation degree. The variation duration, velocity variation range, and total delay are the primary indicators for evaluating lane-change feasibility. The models and findings can be applied effectively in practice to determine the optimal time and location for en-route lane-change and to assist with traffic management and lane selection at the entrance.
Keyword : heterogeneous traffic flow, lane-change, cooperative adaptive cruise control platoons, stability analysis, disturbance propagation, fluctuation degree
How to Cite
Li, H., Pu, Y., Chen, L., & Luo, X. (2024). Stability analysis for heterogeneous traffic flow with lane-change disturbance. Transport, 39(1), 37–53. https://doi.org/10.3846/transport.2024.20544
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
Ali, Y.; Zheng, Z.; Haque, M. M. 2018. Connectivity’s impact on mandatory lane-changing behaviour: evidences from a driving simulator study, Transportation Research Part C: Emerging Technologies 93: 292–309. https://doi.org/10.1016/j.trc.2018.06.008
Ali, Y.; Zheng, Z.; Haque, M. M. 2021. Modelling lane-changing execution behaviour in a connected environment: a grouped random parameters with heterogeneity-in-means approach, Communications in Transportation Research 1: 100009. https://doi.org/10.1016/j.commtr.2021.100009
Cao, Z.; Lu, L.; Chen, C.; Chen, X. 2021. Modeling and simulating urban traffic flow mixed with regular and connected vehicles, IEEE Access 9: 10392–10399. https://doi.org/10.1109/ACCESS.2021.3050199
Chang, X.; Li, H. J.; Rong, J.; Zhao, X.; Li, A. 2020. Analysis on traffic stability and capacity for mixed traffic flow with platoons of intelligent connected vehicles, Physica A: Statistical Mechanics and its Applications 557: 124829. https://doi.org/10.1016/j.physa.2020.124829
Chen, Y.; Kong, D.; Sun, L.; Zhang, T.; Song, Y. 2022. Fundamental diagram and stability analysis for heterogeneous traffic flow considering human-driven vehicle driver’s acceptance of cooperative adaptive cruise control vehicles, Physica A: Statistical Mechanics and its Applications 589: 126647. https://doi.org/10.1016/j.physa.2021.126647
Ciuffo, B.; Punzo, V.; Montanino, M. 2012. Thirty years of Gipps’ car-following model: applications, developments, and new features, Transportation Research Record: Journal of the Transportation Research Board 2315: 89–99. https://doi.org/10.3141/2315-10
Davis, L. C. 2013. Optimality and oscillations near the edge of stability in the dynamics of autonomous vehicle platoons, Physica A: Statistical Mechanics and its Applications 392(17): 3755–3764. https://doi.org/10.1016/j.physa.2013.03.054
Flores, C.; Milanés, V. 2018. Fractional-order-based ACC/CACC algorithm for improving string stability, Transportation Research Part C: Emerging Technologies 95: 381–393. https://doi.org/10.1016/j.trc.2018.07.026
Ge, J. I.; Orosz, G. 2014. Dynamics of connected vehicle systems with delayed acceleration feedback, Transportation Research Part C: Emerging Technologies 46: 46–64. https://doi.org/10.1016/j.trc.2014.04.014
Gipps, P. G. 1981. A behavioural car-following model for computer simulation, Transportation Research Part B: Methodological 15(2): 105–111. https://doi.org/10.1016/0191-2615(81)90037-0
Gregurić, M.; Kušić, K.; Ivanjko, E. 2022. Impact of deep reinforcement learning on variable speed limit strategies in connected vehicles environments, Engineering Applications of Artificial Intelligence 112: 104850. https://doi.org/10.1016/j.engappai.2022.104850
Guo, H.; Keyvan-Ekbatani, M.; Xie, K. 2022. Lane-change detection and prediction using real-world connected vehicle data, Transportation Research Part C: Emerging Technologies 142: 103785. https://doi.org/10.1016/j.trc.2022.103785
Kesting, A.; Treiber, M.; Schönhof, M.; Helbing, D. 2008. Adaptive cruise control design for active congestion avoidance, Transportation Research Part C: Emerging Technologies 16(6): 668–683. https://doi.org/10.1016/j.trc.2007.12.004
Konishi, K.; Kokame, H.; Hirata, K. 2000. Decentralized delayed-feedback control of an optimal velocity traffic model, European Physical Journal B: Condensed Matter and Complex Systems 15(4): 715–722. https://doi.org/10.1007/s100510051176
Lee, S.; Heydecker, B. G.; Kim, J.; Park, S. 2018. Stability analysis on a dynamical model of route choice in a connected vehicle environment, Transportation Research Part C: Emerging Technologies 94: 67–82. https://doi.org/10.1016/j.trc.2017.10.019
Lee, D.; Lee, S.; Chen, Z.; Park, B. B.; Shim, D. H. 2021. Design and field evaluation of cooperative adaptive cruise control with unconnected vehicle in the loop, Transportation Research Part C: Emerging Technologies 132: 103364. https://doi.org/10.1016/j.trc.2021.103364
Liu, H.; Kan, X.; Shladover, S. E.; Lu, X.-Y.; Ferlis, R. E. 2018a. Impact of cooperative adaptive cruise control on multilane freeway merge capacity, Journal of Intelligent Transportation Systems: Technology, Planning, and Operations 22(3): 263–275. https://doi.org/10.1080/15472450.2018.1438275
Liu, H.; Kan, X.; Shladover, S. E.; Lu, X.-Y.; Ferlis, R. E. 2018b. Modeling impacts of cooperative adaptive cruise control on mixed traffic flow in multi-lane freeway facilities, Transportation Research Part C: Emerging Technologies 95: 261–279. https://doi.org/10.1016/j.trc.2018.07.027
Marsden, G.; McDonald, M.; Brackstone, M. 2001. Towards an understanding of adaptive cruise control, Transportation Research Part C: Emerging Technologies 9(1): 33–51. https://doi.org/10.1016/S0968-090X(00)00022-X
Milanés, V.; Shladover, S. E. 2014. Modeling cooperative and autonomous adaptive cruise control dynamic responses using experimental data, Transportation Research Part C: Emerging Technologies 48: 285–300. https://doi.org/10.1016/j.trc.2014.09.001
Newell, G. F. 2002. A simplified car-following theory: a lower order model, Transportation Research Part B: Methodological 36(3): 195–205. https://doi.org/10.1016/S0191-2615(00)00044-8
Ploeg, J.; Semsar-Kazerooni, E.; Lijster, G.; Van de Wouw, N.; Nijmeijer, H. 2015. Graceful degradation of cooperative adaptive cruise control, IEEE Transactions on Intelligent Transportation Systems 16(1): 488–497. https://doi.org/10.1109/TITS.2014.2349498
Qin, Y.; Wang, H. 2023. Stabilizing mixed cooperative adaptive cruise control traffic flow to balance capacity using car-following model, Journal of Intelligent Transportation Systems: Technology, Planning, and Operations 27(1): 57–79. https://doi.org/10.1080/15472450.2021.1985490
Schmidt, K. W. 2017. Cooperative adaptive cruise control for vehicle following during lane-changes, IFAC-PapersOnLine 50(1): 12582–12587. https://doi.org/10.1016/j.ifacol.2017.08.2199
Sharma, A.; Zheng, Z.; Kim, J.; Bhaskar, A.; Haque, M. M. 2021. Assessing traffic disturbance, efficiency, and safety of the mixed traffic flow of connected vehicles and traditional vehicles by considering human factors, Transportation Research Part C: Emerging Technologies 124: 102934. https://doi.org/10.1016/j.trc.2020.102934
Shladover, S. E.; Su, D.; Lu, X.-Y. 2012. Impacts of cooperative adaptive cruise control on freeway traffic flow, Transportation Research Record: Journal of the Transportation Research Board 2324: 63–70. https://doi.org/10.3141/2324-08
Sun, Jie; Zheng, Z.; Sun, Jian. 2020. The relationship between car following string instability and traffic oscillations in finite-sized platoons and its use in easing congestion via connected and automated vehicles with IDM based controller, Transportation Research Part B: Methodological 142: 58–83. https://doi.org/10.1016/j.trb.2020.10.004
Tian, B.; Wang, G.; Xu, Z.; Zhang, Y.; Zhao, X. 2021. Communication delay compensation for string stability of CACC system using LSTM prediction, Vehicular Communications 29: 100333. https://doi.org/10.1016/j.vehcom.2021.100333
Treiber, M.; Hennecke, A.; Helbing, D. 2000. Congested traffic states in empirical observations and microscopic simulations, Physical Review E 62(2): 1805–1824. https://doi.org/10.1103/PhysRevE.62.1805
Wang, H.; Qin, Y.; Wang, W.; Chen, J. 2019. Stability of CACC-manual heterogeneous vehicular flow with partial CACC performance degrading, Transportmetrica B: Transport Dynamics 7(1): 788–813. https://doi.org/10.1080/21680566.2018.1517058
Wang, H.; Lai, J.; Zhang, X.; Zhou, Y.; Li, S.; Hu, J. 2022a. Make space to change lane: a cooperative adaptive cruise control lane-change controller, Transportation Research Part C: Emerging Technologies 143: 103847. https://doi.org/10.1016/j.trc.2022.103847
Wang, T.; Cheng, R.; Wu, Y. 2022b. Stability analysis of heterogeneous traffic flow influenced by memory feedback control signal, Applied Mathematical Modelling 109: 693–708. https://doi.org/10.1016/j.apm.2022.05.026
Wang, X.; Liu, M.; Ci, Y.; Wu, L. 2022c. Effect of front two adjacent vehicles’ velocity information on car-following model construction and stability analysis, Physica A: Statistical Mechanics and its Applications 607: 128196. https://doi.org/10.1016/j.physa.2022.128196
Ward, J. A. 2009. Heterogeneity, Lane-Changing and Instability in Traffic: a Mathematical Approach. PhD Dissertation. University of Bristol, Bristol, UK. 126 p.
Yao, Z.; Hu, R.; Jiang, Y.; Xu, T. 2020. Stability and safety evaluation of mixed traffic flow with connected automated vehicles on expressways, Journal of Safety Research 75: 262–274. https://doi.org/10.1016/j.jsr.2020.09.012
Zhang, J.; Xu, K.; Li, G.; Li, S.; Wang, T. 2021a. Dynamics of traffic flow affected by the future motion of multiple preceding vehicles under vehicle-connected environment: modeling and stabilization, Physica A: Statistical Mechanics and its Applications 565: 125538. https://doi.org/10.1016/j.physa.2020.125538
Zhang, L.; Zhang, M.; Wang, J.; Li, X.; Zhu, W. 2021b. Internet connected vehicle platoon system modeling and linear stability analysis, Computer Communications 174: 92–100. https://doi.org/10.1016/j.comcom.2021.04.015
Zhou, L.; Ruan, T.; Ma, K.; Dong, C.; Wang, H. 2021. Impact of CAV platoon management on traffic flow considering degradation of control mode, Physica A: Statistical Mechanics and its Applications 581: 126193. https://doi.org/10.1016/j.physa.2021.126193
Ali, Y.; Zheng, Z.; Haque, M. M. 2021. Modelling lane-changing execution behaviour in a connected environment: a grouped random parameters with heterogeneity-in-means approach, Communications in Transportation Research 1: 100009. https://doi.org/10.1016/j.commtr.2021.100009
Cao, Z.; Lu, L.; Chen, C.; Chen, X. 2021. Modeling and simulating urban traffic flow mixed with regular and connected vehicles, IEEE Access 9: 10392–10399. https://doi.org/10.1109/ACCESS.2021.3050199
Chang, X.; Li, H. J.; Rong, J.; Zhao, X.; Li, A. 2020. Analysis on traffic stability and capacity for mixed traffic flow with platoons of intelligent connected vehicles, Physica A: Statistical Mechanics and its Applications 557: 124829. https://doi.org/10.1016/j.physa.2020.124829
Chen, Y.; Kong, D.; Sun, L.; Zhang, T.; Song, Y. 2022. Fundamental diagram and stability analysis for heterogeneous traffic flow considering human-driven vehicle driver’s acceptance of cooperative adaptive cruise control vehicles, Physica A: Statistical Mechanics and its Applications 589: 126647. https://doi.org/10.1016/j.physa.2021.126647
Ciuffo, B.; Punzo, V.; Montanino, M. 2012. Thirty years of Gipps’ car-following model: applications, developments, and new features, Transportation Research Record: Journal of the Transportation Research Board 2315: 89–99. https://doi.org/10.3141/2315-10
Davis, L. C. 2013. Optimality and oscillations near the edge of stability in the dynamics of autonomous vehicle platoons, Physica A: Statistical Mechanics and its Applications 392(17): 3755–3764. https://doi.org/10.1016/j.physa.2013.03.054
Flores, C.; Milanés, V. 2018. Fractional-order-based ACC/CACC algorithm for improving string stability, Transportation Research Part C: Emerging Technologies 95: 381–393. https://doi.org/10.1016/j.trc.2018.07.026
Ge, J. I.; Orosz, G. 2014. Dynamics of connected vehicle systems with delayed acceleration feedback, Transportation Research Part C: Emerging Technologies 46: 46–64. https://doi.org/10.1016/j.trc.2014.04.014
Gipps, P. G. 1981. A behavioural car-following model for computer simulation, Transportation Research Part B: Methodological 15(2): 105–111. https://doi.org/10.1016/0191-2615(81)90037-0
Gregurić, M.; Kušić, K.; Ivanjko, E. 2022. Impact of deep reinforcement learning on variable speed limit strategies in connected vehicles environments, Engineering Applications of Artificial Intelligence 112: 104850. https://doi.org/10.1016/j.engappai.2022.104850
Guo, H.; Keyvan-Ekbatani, M.; Xie, K. 2022. Lane-change detection and prediction using real-world connected vehicle data, Transportation Research Part C: Emerging Technologies 142: 103785. https://doi.org/10.1016/j.trc.2022.103785
Kesting, A.; Treiber, M.; Schönhof, M.; Helbing, D. 2008. Adaptive cruise control design for active congestion avoidance, Transportation Research Part C: Emerging Technologies 16(6): 668–683. https://doi.org/10.1016/j.trc.2007.12.004
Konishi, K.; Kokame, H.; Hirata, K. 2000. Decentralized delayed-feedback control of an optimal velocity traffic model, European Physical Journal B: Condensed Matter and Complex Systems 15(4): 715–722. https://doi.org/10.1007/s100510051176
Lee, S.; Heydecker, B. G.; Kim, J.; Park, S. 2018. Stability analysis on a dynamical model of route choice in a connected vehicle environment, Transportation Research Part C: Emerging Technologies 94: 67–82. https://doi.org/10.1016/j.trc.2017.10.019
Lee, D.; Lee, S.; Chen, Z.; Park, B. B.; Shim, D. H. 2021. Design and field evaluation of cooperative adaptive cruise control with unconnected vehicle in the loop, Transportation Research Part C: Emerging Technologies 132: 103364. https://doi.org/10.1016/j.trc.2021.103364
Liu, H.; Kan, X.; Shladover, S. E.; Lu, X.-Y.; Ferlis, R. E. 2018a. Impact of cooperative adaptive cruise control on multilane freeway merge capacity, Journal of Intelligent Transportation Systems: Technology, Planning, and Operations 22(3): 263–275. https://doi.org/10.1080/15472450.2018.1438275
Liu, H.; Kan, X.; Shladover, S. E.; Lu, X.-Y.; Ferlis, R. E. 2018b. Modeling impacts of cooperative adaptive cruise control on mixed traffic flow in multi-lane freeway facilities, Transportation Research Part C: Emerging Technologies 95: 261–279. https://doi.org/10.1016/j.trc.2018.07.027
Marsden, G.; McDonald, M.; Brackstone, M. 2001. Towards an understanding of adaptive cruise control, Transportation Research Part C: Emerging Technologies 9(1): 33–51. https://doi.org/10.1016/S0968-090X(00)00022-X
Milanés, V.; Shladover, S. E. 2014. Modeling cooperative and autonomous adaptive cruise control dynamic responses using experimental data, Transportation Research Part C: Emerging Technologies 48: 285–300. https://doi.org/10.1016/j.trc.2014.09.001
Newell, G. F. 2002. A simplified car-following theory: a lower order model, Transportation Research Part B: Methodological 36(3): 195–205. https://doi.org/10.1016/S0191-2615(00)00044-8
Ploeg, J.; Semsar-Kazerooni, E.; Lijster, G.; Van de Wouw, N.; Nijmeijer, H. 2015. Graceful degradation of cooperative adaptive cruise control, IEEE Transactions on Intelligent Transportation Systems 16(1): 488–497. https://doi.org/10.1109/TITS.2014.2349498
Qin, Y.; Wang, H. 2023. Stabilizing mixed cooperative adaptive cruise control traffic flow to balance capacity using car-following model, Journal of Intelligent Transportation Systems: Technology, Planning, and Operations 27(1): 57–79. https://doi.org/10.1080/15472450.2021.1985490
Schmidt, K. W. 2017. Cooperative adaptive cruise control for vehicle following during lane-changes, IFAC-PapersOnLine 50(1): 12582–12587. https://doi.org/10.1016/j.ifacol.2017.08.2199
Sharma, A.; Zheng, Z.; Kim, J.; Bhaskar, A.; Haque, M. M. 2021. Assessing traffic disturbance, efficiency, and safety of the mixed traffic flow of connected vehicles and traditional vehicles by considering human factors, Transportation Research Part C: Emerging Technologies 124: 102934. https://doi.org/10.1016/j.trc.2020.102934
Shladover, S. E.; Su, D.; Lu, X.-Y. 2012. Impacts of cooperative adaptive cruise control on freeway traffic flow, Transportation Research Record: Journal of the Transportation Research Board 2324: 63–70. https://doi.org/10.3141/2324-08
Sun, Jie; Zheng, Z.; Sun, Jian. 2020. The relationship between car following string instability and traffic oscillations in finite-sized platoons and its use in easing congestion via connected and automated vehicles with IDM based controller, Transportation Research Part B: Methodological 142: 58–83. https://doi.org/10.1016/j.trb.2020.10.004
Tian, B.; Wang, G.; Xu, Z.; Zhang, Y.; Zhao, X. 2021. Communication delay compensation for string stability of CACC system using LSTM prediction, Vehicular Communications 29: 100333. https://doi.org/10.1016/j.vehcom.2021.100333
Treiber, M.; Hennecke, A.; Helbing, D. 2000. Congested traffic states in empirical observations and microscopic simulations, Physical Review E 62(2): 1805–1824. https://doi.org/10.1103/PhysRevE.62.1805
Wang, H.; Qin, Y.; Wang, W.; Chen, J. 2019. Stability of CACC-manual heterogeneous vehicular flow with partial CACC performance degrading, Transportmetrica B: Transport Dynamics 7(1): 788–813. https://doi.org/10.1080/21680566.2018.1517058
Wang, H.; Lai, J.; Zhang, X.; Zhou, Y.; Li, S.; Hu, J. 2022a. Make space to change lane: a cooperative adaptive cruise control lane-change controller, Transportation Research Part C: Emerging Technologies 143: 103847. https://doi.org/10.1016/j.trc.2022.103847
Wang, T.; Cheng, R.; Wu, Y. 2022b. Stability analysis of heterogeneous traffic flow influenced by memory feedback control signal, Applied Mathematical Modelling 109: 693–708. https://doi.org/10.1016/j.apm.2022.05.026
Wang, X.; Liu, M.; Ci, Y.; Wu, L. 2022c. Effect of front two adjacent vehicles’ velocity information on car-following model construction and stability analysis, Physica A: Statistical Mechanics and its Applications 607: 128196. https://doi.org/10.1016/j.physa.2022.128196
Ward, J. A. 2009. Heterogeneity, Lane-Changing and Instability in Traffic: a Mathematical Approach. PhD Dissertation. University of Bristol, Bristol, UK. 126 p.
Yao, Z.; Hu, R.; Jiang, Y.; Xu, T. 2020. Stability and safety evaluation of mixed traffic flow with connected automated vehicles on expressways, Journal of Safety Research 75: 262–274. https://doi.org/10.1016/j.jsr.2020.09.012
Zhang, J.; Xu, K.; Li, G.; Li, S.; Wang, T. 2021a. Dynamics of traffic flow affected by the future motion of multiple preceding vehicles under vehicle-connected environment: modeling and stabilization, Physica A: Statistical Mechanics and its Applications 565: 125538. https://doi.org/10.1016/j.physa.2020.125538
Zhang, L.; Zhang, M.; Wang, J.; Li, X.; Zhu, W. 2021b. Internet connected vehicle platoon system modeling and linear stability analysis, Computer Communications 174: 92–100. https://doi.org/10.1016/j.comcom.2021.04.015
Zhou, L.; Ruan, T.; Ma, K.; Dong, C.; Wang, H. 2021. Impact of CAV platoon management on traffic flow considering degradation of control mode, Physica A: Statistical Mechanics and its Applications 581: 126193. https://doi.org/10.1016/j.physa.2021.126193