An Extended Multilane Lattice Hydrodynamic Model Considering the Predictive Effect of Drivers under Connected Vehicle Environment
Publication: Journal of Transportation Engineering, Part A: Systems
Volume 149, Issue 10
Abstract
As the main road pattern, multilane roads are prevalent on high-grade highways. In a connected vehicle environment, drivers can perceive the full view of traffic information on each lane, which provides more opportunities for flexibly changing lanes on multilane highways. In addition, drivers can predict the traffic status on short notice and regulate the vehicle’s operating state in advance. This study determined the predictive effect of drivers in a multilane scenario using the lattice hydrodynamic model. The stability criteria of the proposed model were deduced via the reductive perturbation method; when the stability conditions do not hold, the modified Korteweg–de Vries (mKdV) equation can be deduced. By solving this above equation, we derived the kink–antikink soliton wave solution, which can be used to analyze and explain the formation and evolution process of traffic jams. The results show that the number of lanes and the prediction time of drivers considerably affect the stability of traffic flow. Simulation examples verified that when the predictive time is fixed and the number of lanes increases from 1 to 4, the fluctuation amplitude of traffic density decreases from 0.2 to 0.08 even with exogenous initial disturbance; when the number of lanes is fixed, the density fluctuation amplitude decreases as the predictive time increases; and when the predictive time increases to 0.7, the fluctuation amplitude of traffic density approximates to 0 and is a uniform flow.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This work is jointly supported by the Guangdong Basic and Applied Research Foundation (Project Nos. 2022A1515010948, 2019A1515111200, 2019A1515110837, and 2023A1515011696), and the National Science Foundation of China (Project Nos. 72071079 and 52272310).
Author contributions: Cong Zhai: conceptualization, methodology, funding acquisition, validation, formal analysis, investigation, and writing—review and editing; Weitiao Wu: conceptualization, methodology, formal analysis, writing—review and editing, and funding acquisition; and Yingping Xiao: writing—review and editing, and funding acquisition.
References
Cao, J. L., and Z. K. Shi. 2016. “Analysis of a novel two lane lattice model on a gradient road with the consideration of relative current.” Commun. Nonlinear Sci. Numer. Simul. 33 (Apr): 1–18. https://doi.org/10.1016/j.cnsns.2015.08.025.
Cheng, R. J., H. Lyu, Y. X. Zheng, and H. X. Ge. 2022. “Modeling and stability analysis of cyberattack effect on heterogeneous intelligent traffic flow.” Physica A 604 (Oct): 127941. https://doi.org/10.1016/j.physa.2022.127941.
Ge, H. X., Y. Cui, K. Q. Zhu, and R. J. Cheng. 2015. “The control method for the lattice hydrodynamic model.” Commun. Nonlinear Sci. Numer. Simul. 22 (May): 903–908. https://doi.org/10.1016/j.cnsns.2014.09.014.
Gupta, A. K., S. Sharma, and P. Redhu. 2015. “Effect of multi-phase optimal velocity function on jamming transition in a lattice hydrodynamic model with passing.” Nonlinear Dyn. 80 (May): 1091–1108. https://doi.org/10.1007/s11071-015-1929-0.
Huang, L., C. Zhai, H. W. Wang, R. H. Zhang, Z. J. Qiu, and J. P. Wu. 2020. “Cooperative adaptive cruise control and exhaust emission evaluation under heterogeneous connected vehicle network environment in urban city.” J. Environ. Manage. 256 (May): 109975. https://doi.org/10.1016/j.jenvman.2019.109975.
Jiang, C. T., R. J. Cheng, and H. X. Ge. 2018. “An improved lattice hydrodynamic model considering the ‘backward looking’ effect and the traffic interruption probability.” Nonlinear Dyn. 91 (Jan): 777–784. https://doi.org/10.1007/s11071-017-3908-0.
Jiang, C. T., R. J. Cheng, and H. X. Ge. 2019. “Mean-field flow difference model with consideration of on-ramp and off-ramp.” Physica A 513 (Jan): 465–476. https://doi.org/10.1016/j.physa.2018.09.026.
Jiang, Y. S., S. C. Wang, Z. H. Yao, B. Zhao, and Y. Wang. 2021. “A cellular automata model for mixed traffic flow considering the driving behavior of connected automated vehicle platoons.” Physica A 582 (Nov): 126262. https://doi.org/10.1016/j.physa.2021.126262.
Kaur, D., and S. Sharma. 2020. “A new two-lane lattice model by considering predictive effect in traffic flow.” Physica A 539 (Feb): 122913. https://doi.org/10.1016/j.physa.2019.122913.
Kaur, R., and S. Sharma. 2017. “Analysis of driver’s characteristics on a curved road in a lattice model.” Physica A 471 (Apr): 59–67. https://doi.org/10.1016/j.physa.2016.11.116.
Kaur, R., and S. Sharma. 2018a. “Analyses of lattice hydrodynamic model using delayed feedback control with passing.” Physica A 510 (Nov): 446–455. https://doi.org/10.1016/j.physa.2018.06.118.
Kaur, R., and S. Sharma. 2018b. “Modeling and simulation of driver’s anticipation effect in a two lane system on curved road with slope.” Physica A 499 (Jun): 110–120. https://doi.org/10.1016/j.physa.2017.12.101.
Kuang, H., F. L. Yang, M. T. Wang, G. H. Peng, and X. L. Li. 2021. “Multi-anticipative average flux effect in the lattice hydrodynamic model.” IEEE Access 9 (Feb): 2169–3536. https://doi.org/10.1109/ACCESS.2021.3060080.
Li, L. X., R. J. Cheng, and H. X. Ge. 2021. “New feedback control for a novel two-dimensional lattice hydrodynamic model considering driver’s memory effect.” Physica A 561 (Jan): 125295. https://doi.org/10.1016/j.physa.2020.125295.
Lyu, H., T. Wang, R. J. Cheng, and H. X. Ge. 2022. “Improved longitudinal control strategy for connected and automated truck platoon against cyberattacks.” IET Intel. Transport Syst. 16 (12): 1710–1725. https://doi.org/10.1049/itr2.12181.
Ma, G. Y., M. H. Ma, S. D. Liang, Y. S. Wang, and Y. Z. Zhang. 2020. “An improved car following model accounting for the time-delayed velocity difference and backward-looking effect.” Commun. Nonlinear Sci. Numer. Simul. 85 (Jun): 105221. https://doi.org/10.1016/j.cnsns.2020.105221.
Ma, M., W. Wang, S. Liang, J. Xiao, and C. Wu. 2023. “Improved car-following model for connected vehicles considering backward-looking effect and motion information of multiple vehicles.” J. Transp. Eng. 149 (2): 04022148. https://doi.org/10.1061/JTEPBS.TEENG-7430.
Madaan, N., and S. Sharma. 2021. “A lattice model accounting for multi-lane traffic system.” Physica A 564 (Feb): 125446. https://doi.org/10.1016/j.physa.2020.125446.
Madaan, N., and S. Sharma. 2022. “Influence of driver’s behavior with empirical lane changing on the traffic dynamics.” Eur. Phys. J. B 95 (1): 6. https://doi.org/10.1140/epjb/s10051-021-00270-0.
Mayakuntla, S. K., and A. Verma. 2019. “Cell transmission modelling of heterogeneous disordered traffic.” J. Transp. Eng. 145 (7): 04019027. https://doi.org/10.1061/JTEPBS.0000248.
Mei, Y. R., X. Q. Zhao, Y. Q. Qian, S. Z. Xu, and Z. P. Li. 2021. “Effect of self-stabilizing control in lattice hydrodynamic model with on-ramp and off-ramp.” Physica A 575 (Aug): 126048. https://doi.org/10.1016/j.physa.2021.126048.
Natagani, T. 1998. “Modified KdV equation for jamming transition in the continuum models of traffic.” Physica A 261 (3–4): 599–607. https://doi.org/10.1016/S0378-4371(98)00347-1.
Natagani, T. 1999a. “Jamming transition in traffic flow on triangular lattice.” Physica A 271 (1–2): 200–221. https://doi.org/10.1016/S0378-4371(99)00196-X.
Natagani, T. 1999b. “Jamming transition in a two-dimensional traffic flow model.” Phys. Rev. E 59 (5): 4857–4864. https://doi.org/10.1103/PhysRevE.59.4857.
Natagani, T. 1999c. “Jamming transition of high-dimensional traffic dynamics.” Physica A 272 (May): 592–611. https://doi.org/10.1016/S0378-4371(99)00296-4.
Natagani, T. 1999d. “Jamming transitions and the modified Korteweg-de Vries equation in a two-lane traffic flow.” Physica A 265 (Mar): 297–310. https://doi.org/10.1016/S0378-4371(98)00563-9.
Natagani, T. 1999e. “TDGL and mKdV equations for jamming transition in the lattice model of traffic.” Physica A 264 (3): 581–592. https://doi.org/10.1016/S0378-4371(98)00466-X.
Peng, G. H., T. T. Jia, H. Kuang, and H. L. Tan. 2022. “Energy consumption in a new lattice hydrodynamic model based on the delayed effect of collaborative information transmission under V2X environment.” Physica A 585 (Aug): 126443. https://doi.org/10.1016/j.physa.2021.126443.
Peng, G. H., H. Kuang, and K. Z. Bai. 2019a. “The impact of the individual difference on traffic flow under honk environment in lattice hydrodynamic model.” Physica A 526 (Jul): 120772. https://doi.org/10.1016/j.physa.2019.04.008.
Peng, G. H., H. Kuang, and L. Qing. 2018. “Feedback control method in lattice hydrodynamic model under honk environment.” Physica A 509 (Nov): 651–656. https://doi.org/10.1016/j.physa.2018.06.080.
Peng, G. H., C. Q. Liu, and M. X. Tuo. 2015a. “Influence of the traffic interruption probability on traffic stability in lattice model for two-lane freeway.” Physica A 436 (Oct): 952–959. https://doi.org/10.1016/j.physa.2015.05.055.
Peng, G. H., W. Z. Lu, and H. D. He. 2015b. “Impact of the traffic interruption probability of optimal current on traffic congestion in lattice model.” Physica A 425 (May): 27–33. https://doi.org/10.1016/j.physa.2015.01.045.
Peng, G. H., H. Z. Zhao, and X. Q. Li. 2019b. “The impact of self-stabilization on traffic stability considering the current lattice’s historic flux for two-lane freeway.” Physica A 515 (Feb): 31–37. https://doi.org/10.1016/j.physa.2018.09.173.
Qi, X. Y., H. X. Ge, and R. J. Cheng. 2019. “Analysis of a novel lattice hydrodynamic model considering density integral and ‘backward looking’ effect.” Physica A 525 (Jul): 714–723. https://doi.org/10.1016/j.physa.2019.03.030.
Redhu, P., and A. K. Gupta. 2014. “Phase transition in a two-dimensional triangular flow with consideration of optimal current difference effect.” Nonlinear Dyn. 78 (Oct): 957–968. https://doi.org/10.1007/s11071-014-1489-8.
Redhu, P., and A. K. Gupta. 2015. “Delayed-feedback control in a lattice hydrodynamic model.” Commun. Nonlinear Sci. Numer. Simul. 27 (Oct): 263–270. https://doi.org/10.1016/j.cnsns.2015.03.015.
Sharma, S. 2015. “Lattice hydrodynamic modeling of two-lane traffic flow with timid and aggressive driving behavior.” Physica A 421 (Mar): 401–411. https://doi.org/10.1016/j.physa.2014.11.003.
Sharma, S. 2016. “Modeling and analyses of driver’s characteristics in a traffic system with passing.” Nonlinear Dyn. 86 (Nov): 2093–2104. https://doi.org/10.1007/s11071-016-3018-4.
Sun, F. X., A. H. F. Chow, S. M. Lo, and H. X. Ge. 2018. “A two-lane lattice hydrodynamic model with heterogeneous lane changing rates.” Physica A 511 (Dec): 389–400. https://doi.org/10.1016/j.physa.2018.08.012.
Wang, T., R. D. Zang, K. Y. Xu, and J. Zhang. 2019. “Analysis of predictive effect on lattice hydrodynamic traffic flow model.” Physica A 526 (Jul): 120711. https://doi.org/10.1016/j.physa.2019.03.076.
Zhai, C., and W. T. Wu. 2018. “Stability analysis of two-lane lattice hydrodynamic model considering lane-changing and memorial effects.” Mod. Phys. Lett. B 32 (20): 1850233. https://doi.org/10.1142/S0217984918502330.
Zhai, C., and W. T. Wu. 2019. “Lattice hydrodynamic model-based feedback control method with traffic interruption probability.” Mod. Phys. Lett. B 33 (23): 1950273. https://doi.org/10.1142/S0217984919502737.
Zhai, C., and W. T. Wu. 2020. “Lattice hydrodynamic modelling with continuous self-delayed traffic flux integral and overtaking effect.” Mod. Phys. Lett. B 34 (5): 2050071. https://doi.org/10.1142/S0217984920500712.
Zhai, C., and W. T. Wu. 2021a. “A continuous traffic flow model considering predictive headway variation and preceding vehicle’s taillight effect.” Physica A 584 (Dec): 126364. https://doi.org/10.1016/j.physa.2021.126364.
Zhai, C., and W. T. Wu. 2021b. “Designing continuous delay feedback control for lattice hydrodynamic model under cyber-attacks and connected vehicle environment.” Commun. Nonlinear Sci. Numer. Simul. 95 (Apr): 105667. https://doi.org/10.1016/j.cnsns.2020.105667.
Zhai, C., and W. T. Wu. 2021c. “Self-delayed feedback car-following control with the velocity uncertainty of preceding vehicles on gradient roads.” Nonlinear Dyn. 106 (4): 3379–3400. https://doi.org/10.1007/s11071-021-06970-7.
Zhai, C., and W. T. Wu. 2022. “A continuum model considering the uncertain velocity of preceding vehicles on gradient highways.” Physica A 588 (Feb): 126561. https://doi.org/10.1016/j.physa.2021.126561.
Zhai, C., W. T. Wu, and Y. P. Xiao. 2022. “Cooperative car-following control with electronic throttle and perceived headway errors on gyroidal roads.” Appl. Math. Modell. 108 (Aug): 770–786. https://doi.org/10.1016/j.apm.2022.04.010.
Zhang, G. 2018. “The self-stabilization effect of lattice’s historical flow in a new lattice hydrodynamic model.” Nonlinear Dyn. 91 (2): 809–817. https://doi.org/10.1007/s11071-017-3911-5.
Zhou, Z. M., M. Zhao, D. Chen, Y. C. Zhang, and D. H. Sun. 2019. “An extended mean-field lattice hydrodynamic model with consideration of the average effect of multi-lattice interaction.” IEEE Access 7 (Nov): 2169–3536. https://doi.org/10.1109/ACCESS.2019.2952416.
Zhu, C. Q., S. Q. Zhong, and S. F. Ma. 2019. “Two lane lattice hydrodynamic model considering the empirical lane changing rate.” Commun. Nonlinear Sci. Numer. Simul. 73 (Jul): 229–243. https://doi.org/10.1016/j.cnsns.2019.02.010.
Information & Authors
Information
Published In
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Dec 8, 2022
Accepted: May 23, 2023
Published online: Jul 31, 2023
Published in print: Oct 1, 2023
Discussion open until: Dec 31, 2023
ASCE Technical Topics:
- Driver behavior
- Engineering fundamentals
- Fluid dynamics
- Fluid mechanics
- Highway and road management
- Highway transportation
- Highways and roads
- Hydrodynamics
- Hydrologic engineering
- Hydrologic models
- Infrastructure
- Lattices
- Models (by type)
- Structural engineering
- Structural systems
- Traffic engineering
- Traffic flow
- Traffic management
- Traffic models
- Transportation engineering
- Vehicles
- Water and water resources
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited by
- Cong Zhai, Kening Li, Ronghui Zhang, Tao Peng, Changfu Zong, Phase diagram in multi-phase heterogeneous traffic flow model integrating the perceptual range difference under human-driven and connected vehicles environment, Chaos, Solitons & Fractals, 10.1016/j.chaos.2024.114791, 182, (114791), (2024).
- Sunita Yadav, Poonam Redhu, Analysis of passing behavior on car-following model under the influence of cyberattacks, Nonlinear Dynamics, 10.1007/s11071-024-09348-7, 112, 9, (7269-7289), (2024).