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Nonlinear Follow-the-Leader Models of Traffic Flow

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  1. Zhang, H.M. & Kim, T., 2005. "A car-following theory for multiphase vehicular traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 39(5), pages 385-399, June.
  2. Meng, Y.C. & Lin, Z.Y. & Li, X.Y. & Qiao, D.L. & Guo, M.M. & Zhang, P., 2022. "A semi-discrete model of traffic flow in correspondence with a continuum model under Lagrange coordinate system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 590(C).
  3. Nicola Roveri & Antonio Carcaterra & Leonardo Molinari & Gianluca Pepe, 2020. "Safe and Secure Control of Swarms of Vehicles by Small-World Theory," Energies, MDPI, vol. 13(5), pages 1-28, February.
  4. Dayi Qu & Shaojie Wang & Haomin Liu & Yiming Meng, 2022. "A Car-Following Model Based on Trajectory Data for Connected and Automated Vehicles to Predict Trajectory of Human-Driven Vehicles," Sustainability, MDPI, vol. 14(12), pages 1-16, June.
  5. Guillermo Abramson & Viktoriya Semeshenko & José Roberto Iglesias, 2013. "Cooperation and Defection at the Crossroads," PLOS ONE, Public Library of Science, vol. 8(4), pages 1-8, April.
  6. Georgia Perakis & Guillaume Roels, 2006. "An Analytical Model for Traffic Delays and the Dynamic User Equilibrium Problem," Operations Research, INFORMS, vol. 54(6), pages 1151-1171, December.
  7. Jin, Wen-Long, 2012. "The traffic statics problem in a road network," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1360-1373.
  8. Hongxia Ge & Siteng Li & Chunyue Yan, 2021. "An Extended Car-Following Model Based on Visual Angle and Electronic Throttle Effect," Mathematics, MDPI, vol. 9(22), pages 1-17, November.
  9. Jan Paszkowski & Marcus Herrmann & Matthias Richter & Andrzej Szarata, 2021. "Modelling the Effects of Traffic-Calming Introduction to Volume–Delay Functions and Traffic Assignment," Energies, MDPI, vol. 14(13), pages 1-18, June.
  10. R.E. Wilson & J.A. Ward, 2010. "Car-following models: fifty years of linear stability analysis -- a mathematical perspective," Transportation Planning and Technology, Taylor & Francis Journals, vol. 34(1), pages 3-18, July.
  11. Alireza Mostafizi & Haizhong Wang & Dan Cox & Lori A. Cramer & Shangjia Dong, 2017. "Agent-based tsunami evacuation modeling of unplanned network disruptions for evidence-driven resource allocation and retrofitting strategies," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 88(3), pages 1347-1372, September.
  12. Zhang, Xiangzhou & Shi, Zhongke & Chen, Jianzhong & Ma, lijing, 2023. "A bi-directional visual angle car-following model considering collision sensitivity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
  13. Nakata, Makoto & Yamauchi, Atsuo & Tanimoto, Jun & Hagishima, Aya, 2010. "Dilemma game structure hidden in traffic flow at a bottleneck due to a 2 into 1 lane junction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(23), pages 5353-5361.
  14. Jiao, Shuaiyang & Zhang, Shengrui & Zhou, Bei & Zhang, Lei & Xue, Liyuan, 2021. "Dynamic performance and safety analysis of car-following models considering collision sensitivity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 564(C).
  15. Michael Z. F. Li, 2008. "A Generic Characterization of Equilibrium Speed-Flow Curves," Transportation Science, INFORMS, vol. 42(2), pages 220-235, May.
  16. Tang, Yuan & Xue, Yu & Huang, Mu-Yang & Wen, Qi-Yun & Cen, Bing-Ling & Chen, Dong, 2023. "Bifurcation analysis and control strategy for a car-following model considering jerk behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 618(C).
  17. Sun, Lu & Jafaripournimchahi, Ammar & Kornhauser, Alain & Hu, Wushen, 2020. "A new higher-order viscous continuum traffic flow model considering driver memory in the era of autonomous and connected vehicles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
  18. Wang, Xiujuan & Peng, Mingshu, 2019. "Rich dynamics in some discrete-time car-following models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
  19. Kalathil, Dileep & Kurzhanskiy, Alex A. & Varaiya, Pravin, 2017. "Sustainable Operation of Arterial Networks," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt5js550jt, Institute of Transportation Studies, UC Berkeley.
  20. Daiheng Ni & John D. Leonard & Chaoqun Jia & Jianqiang Wang, 2016. "Vehicle Longitudinal Control and Traffic Stream Modeling," Transportation Science, INFORMS, vol. 50(3), pages 1016-1031, August.
  21. Jiajun Shen & Guangchuan Yang, 2020. "Crash Risk Assessment for Heterogeneity Traffic and Different Vehicle-Following Patterns Using Microscopic Traffic Flow Data," Sustainability, MDPI, vol. 12(23), pages 1-18, November.
  22. McCrea, Jennifer & Moutari, Salissou, 2010. "A hybrid macroscopic-based model for traffic flow in road networks," European Journal of Operational Research, Elsevier, vol. 207(2), pages 676-684, December.
  23. Hongxing Zhao & Ruichun He & Xiaoyan Jia, 2019. "Estimation and Analysis of Vehicle Exhaust Emissions at Signalized Intersections Using a Car-Following Model," Sustainability, MDPI, vol. 11(14), pages 1-25, July.
  24. Jiang, Rui & Wu, Qing-Song & Zhu, Zuo-Jin, 2002. "A new continuum model for traffic flow and numerical tests," Transportation Research Part B: Methodological, Elsevier, vol. 36(5), pages 405-419, June.
  25. Jinhua Tan & Li Gong & Xuqian Qin, 2019. "Global Optimality under Internet of Vehicles: Strategy to Improve Traffic Safety and Reduce Energy Dissipation," Sustainability, MDPI, vol. 11(17), pages 1-16, August.
  26. Viacheslav Morozov & Artur I. Petrov & Vladimir Shepelev & Mohammed Balfaqih, 2024. "Ideology of Urban Road Transport Chaos and Accident Risk Management for Sustainable Transport Systems," Sustainability, MDPI, vol. 16(6), pages 1-32, March.
  27. Jin, Wen-Long, 2010. "A kinematic wave theory of lane-changing traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 1001-1021, September.
  28. Wang, Jinghui & Lv, Wei & Jiang, Yajuan & Qin, Shuangshuang & Li, Jiawei, 2021. "A multi-agent based cellular automata model for intersection traffic control simulation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 584(C).
  29. van Lint, J.W.C. & Calvert, S.C., 2018. "A generic multi-level framework for microscopic traffic simulation—Theory and an example case in modelling driver distraction," Transportation Research Part B: Methodological, Elsevier, vol. 117(PA), pages 63-86.
  30. Kun Zhang & Yu Xue & Hao-Jie Luo & Qiang Zhang & Yuan Tang & Bing-Ling Cen, 2023. "Cyber-attacks on the optimal velocity and its variation by bifurcation analyses," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(12), pages 1-19, December.
  31. Rehborn, Hubert & Klenov, Sergey L. & Palmer, Jochen, 2011. "An empirical study of common traffic congestion features based on traffic data measured in the USA, the UK, and Germany," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4466-4485.
  32. Zheng, Liang & Jin, Peter J. & Huang, Helai, 2015. "An anisotropic continuum model considering bi-directional information impact," Transportation Research Part B: Methodological, Elsevier, vol. 75(C), pages 36-57.
  33. Hilliges, Martin & Weidlich, Wolfgang, 1995. "A phenomenological model for dynamic traffic flow in networks," Transportation Research Part B: Methodological, Elsevier, vol. 29(6), pages 407-431, December.
  34. Peng, Yong & Liu, Shijie & Yu, Dennis Z., 2020. "An improved car-following model with consideration of multiple preceding and following vehicles in a driver’s view," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
  35. Zhang, Xiaoyan & Jarrett, David F., 1997. "Stability analysis of the classical car-following model," Transportation Research Part B: Methodological, Elsevier, vol. 31(6), pages 441-462, November.
  36. Jiang, Rui & Hu, Mao-Bin & Zhang, H.M. & Gao, Zi-You & Jia, Bin & Wu, Qing-Song, 2015. "On some experimental features of car-following behavior and how to model them," Transportation Research Part B: Methodological, Elsevier, vol. 80(C), pages 338-354.
  37. Toan, Trinh Dinh & Lam, Soi Hoi & Wong, Yiik Diew & Meng, Meng, 2022. "Development and validation of a driving simulator for traffic control using field data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 596(C).
  38. Calvert, Simeon C. & Schakel, Wouter J. & van Lint, J.W.C., 2020. "A generic multi-scale framework for microscopic traffic simulation part II – Anticipation Reliance as compensation mechanism for potential task overload," Transportation Research Part B: Methodological, Elsevier, vol. 140(C), pages 42-63.
  39. Kaur, Ramanpreet & Sharma, Sapna, 2018. "Modeling and simulation of driver’s anticipation effect in a two lane system on curved road with slope," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 110-120.
  40. Jin, Wen-Long, 2016. "On the equivalence between continuum and car-following models of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 543-559.
  41. Jiang, Rui & Wu, Qing-Song, 2003. "Study on propagation speed of small disturbance from a car-following approach," Transportation Research Part B: Methodological, Elsevier, vol. 37(1), pages 85-99, January.
  42. Li, Xiaopeng & Ouyang, Yanfeng, 2011. "Characterization of traffic oscillation propagation under nonlinear car-following laws," Transportation Research Part B: Methodological, Elsevier, vol. 45(9), pages 1346-1361.
  43. Coifman, Benjamin, 2014. "Revisiting the empirical fundamental relationship," Transportation Research Part B: Methodological, Elsevier, vol. 68(C), pages 173-184.
  44. Jin, Wen-Long & Yan, Qinglong, 2019. "A formulation of unifiable multi-commodity kinematic wave model with relative speed ratios," Transportation Research Part B: Methodological, Elsevier, vol. 128(C), pages 236-253.
  45. Piotr Gołębiowski & Jolanta Żak & Ilona Jacyna-Gołda, 2020. "Approach to the Proecological Distribution of the Traffic Flow on the Transport Network from the Point of View of Carbon Dioxide," Sustainability, MDPI, vol. 12(17), pages 1-16, August.
  46. Li, Xiaopeng & Wang, Xin & Ouyang, Yanfeng, 2012. "Prediction and field validation of traffic oscillation propagation under nonlinear car-following laws," Transportation Research Part B: Methodological, Elsevier, vol. 46(3), pages 409-423.
  47. Newell, G. F., 2002. "A simplified car-following theory: a lower order model," Transportation Research Part B: Methodological, Elsevier, vol. 36(3), pages 195-205, March.
  48. Denos C. Gazis, 2002. "The Origins of Traffic Theory," Operations Research, INFORMS, vol. 50(1), pages 69-77, February.
  49. Li, Xiangchen & Luo, Xia & He, Mengchen & Chen, Siwei, 2018. "An improved car-following model considering the influence of space gap to the response," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 536-545.
  50. Cheng, Qixiu & Liu, Zhiyuan & Lin, Yuqian & Zhou, Xuesong (Simon), 2021. "An s-shaped three-parameter (S3) traffic stream model with consistent car following relationship," Transportation Research Part B: Methodological, Elsevier, vol. 153(C), pages 246-271.
  51. Jin, Wen-Long, 2012. "A kinematic wave theory of multi-commodity network traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 46(8), pages 1000-1022.
  52. Faryal Ali & Zawar Hussain Khan & Khurram Shehzad Khattak & Thomas Aaron Gulliver & Akhtar Nawaz Khan, 2022. "A Microscopic Heterogeneous Traffic Flow Model Considering Distance Headway," Mathematics, MDPI, vol. 11(1), pages 1-20, December.
  53. Nelson, Paul, 1995. "On deterministic developments of traffic stream models," Transportation Research Part B: Methodological, Elsevier, vol. 29(4), pages 297-302, August.
  54. Tian, Junfang & Zhu, Chenqiang & Chen, Danjue & Jiang, Rui & Wang, Guanying & Gao, Ziyou, 2021. "Car following behavioral stochasticity analysis and modeling: Perspective from wave travel time," Transportation Research Part B: Methodological, Elsevier, vol. 143(C), pages 160-176.
  55. Shanchuan Yu & Yu Chen & Lang Song & Zhaoze Xuan & Yi Li, 2023. "Modelling and Mitigating Secondary Crash Risk for Serial Tunnels on Freeway via Lighting-Related Microscopic Traffic Model with Inter-Lane Dependency," IJERPH, MDPI, vol. 20(4), pages 1-29, February.
  56. Wang, Qiao & Song, Weiguo & Zhang, Jun & Wang, Shujie & Wu, Chunlin & Lo, Siuming, 2019. "Understanding single-file movement with ant experiments and a multi-grid CA model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 1-13.
  57. Saifuzzaman, Mohammad & Zheng, Zuduo & Mazharul Haque, Md. & Washington, Simon, 2015. "Revisiting the Task–Capability Interface model for incorporating human factors into car-following models," Transportation Research Part B: Methodological, Elsevier, vol. 82(C), pages 1-19.
  58. Tamra Heberling & Lisa Davis & Jakub Gedeon & Charles Morgan & Tomáš Gedeon, 2016. "A Mechanistic Model for Cooperative Behavior of Co-transcribing RNA Polymerases," PLOS Computational Biology, Public Library of Science, vol. 12(8), pages 1-38, August.
  59. Treiber, Martin & Kanagaraj, Venkatesan, 2015. "Comparing numerical integration schemes for time-continuous car-following models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 183-195.
  60. Corli, Andrea & Fan, Haitao, 2023. "String stability in traffic flows," Applied Mathematics and Computation, Elsevier, vol. 443(C).
  61. Daniel (Jian) Sun & Lily Elefteriadou, 2014. "A Driver Behavior-Based Lane-Changing Model for Urban Arterial Streets," Transportation Science, INFORMS, vol. 48(2), pages 184-205, May.
  62. Wang, Xiao & Jiang, Rui & Li, Li & Lin, Yi-Lun & Wang, Fei-Yue, 2019. "Long memory is important: A test study on deep-learning based car-following model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 786-795.
  63. Tian, Junfang & Li, Guangyu & Treiber, Martin & Jiang, Rui & Jia, Ning & Ma, Shoufeng, 2016. "Cellular automaton model simulating spatiotemporal patterns, phase transitions and concave growth pattern of oscillations in traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 560-575.
  64. Xin Chang & Xingjian Zhang & Haichao Li & Chang Wang & Zhe Liu, 2022. "A Survey on Mixed Traffic Flow Characteristics in Connected Vehicle Environments," Sustainability, MDPI, vol. 14(13), pages 1-22, June.
  65. Yifan Pan & Yongjiang Wang & Baobin Miao & Rongjun Cheng, 2022. "Stabilization Strategy of a Novel Car-Following Model with Time Delay and Memory Effect of the Driver," Sustainability, MDPI, vol. 14(12), pages 1-20, June.
  66. Maosheng Li & Jing Fan & Jaeyoung Lee, 2023. "Modeling Car-Following Behavior with Different Acceptable Safety Levels," Sustainability, MDPI, vol. 15(7), pages 1-23, April.
  67. Zhang, H. M., 1998. "A theory of nonequilibrium traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 32(7), pages 485-498, September.
  68. Ponnu, Balaji & Coifman, Benjamin, 2015. "Speed-spacing dependency on relative speed from the adjacent lane: New insights for car following models," Transportation Research Part B: Methodological, Elsevier, vol. 82(C), pages 74-90.
  69. Faryal Ali & Zawar Hussain Khan & Khurram Shehzad Khattak & Thomas Aaron Gulliver & Ahmed B. Altamimi, 2023. "A Microscopic Traffic Model Incorporating Vehicle Vibrations Due to Pavement Condition," Mathematics, MDPI, vol. 11(24), pages 1-24, December.
  70. Li, Xiaopeng & Cui, Jianxun & An, Shi & Parsafard, Mohsen, 2014. "Stop-and-go traffic analysis: Theoretical properties, environmental impacts and oscillation mitigation," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 319-339.
  71. Guang Yu & Shuo Liu & Qiangqiang Shangguan, 2021. "Optimization and Evaluation of Platooning Car-Following Models in a Connected Vehicle Environment," Sustainability, MDPI, vol. 13(6), pages 1-20, March.
  72. Jia, Yanfeng & Qu, Dayi & Song, Hui & Wang, Tao & Zhao, Zixu, 2022. "Car-following characteristics and model of connected autonomous vehicles based on safe potential field," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 586(C).
  73. Lei Tang & Jingchi Jia & Zongtao Duan & Jingyu Ma & Xin Wang & Weiwei Kong, 2020. "Tracking and climbing behavior recognition of heavy-duty trucks on roadways," International Journal of Distributed Sensor Networks, , vol. 16(2), pages 15501477209, February.
  74. Coifman, Benjamin, 2015. "Empirical flow-density and speed-spacing relationships: Evidence of vehicle length dependency," Transportation Research Part B: Methodological, Elsevier, vol. 78(C), pages 54-65.
  75. Mendes, G.A. & da Silva, L.R. & Herrmann, H.J., 2012. "Traffic gridlock on complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 362-370.
  76. Kaufman, Arie, 1982. "Continuous simulation of a car-following equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 24(1), pages 88-94.
  77. Xiangquan Chen & Zhizhou Wu & Yunyi Liang, 2023. "Modeling Mixed Traffic Flow with Connected Autonomous Vehicles and Human-Driven Vehicles in Off-Ramp Diverging Areas," Sustainability, MDPI, vol. 15(7), pages 1-14, March.
  78. Wang, Yi & Szeto, W.Y. & Han, Ke & Friesz, Terry L., 2018. "Dynamic traffic assignment: A review of the methodological advances for environmentally sustainable road transportation applications," Transportation Research Part B: Methodological, Elsevier, vol. 111(C), pages 370-394.
  79. Cheng, Qixiu & Lin, Yuqian & Zhou, Xuesong (Simon) & Liu, Zhiyuan, 2024. "Analytical formulation for explaining the variations in traffic states: A fundamental diagram modeling perspective with stochastic parameters," European Journal of Operational Research, Elsevier, vol. 312(1), pages 182-197.
  80. Xiangyang Cao & Bingzhong Zhou & Qiang Tang & Jiaqi Li & Donghui Shi, 2018. "Urban Wasteful Transport and Its Estimation Methods," Sustainability, MDPI, vol. 10(12), pages 1-15, December.
  81. Li, Xiaopeng & Peng, Fan & Ouyang, Yanfeng, 2010. "Measurement and estimation of traffic oscillation properties," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 1-14, January.
  82. Coifman, Benjamin & Ponnu, Balaji, 2020. "Adjacent lane dependencies modulating wave velocity on congested freeways-An empirical study," Transportation Research Part B: Methodological, Elsevier, vol. 142(C), pages 84-99.
  83. Fang, Yaling & Shi, Zhongke, 2015. "Chaos analysis and delayed-feedback control in a discrete dynamic coupled map traffic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 422(C), pages 40-46.
  84. Kai Nagel & Peter Wagner & Richard Woesler, 2003. "Still Flowing: Approaches to Traffic Flow and Traffic Jam Modeling," Operations Research, INFORMS, vol. 51(5), pages 681-710, October.
  85. Muhammad Tanveer & Faizan Ahmad Kashmiri & Hassan Naeem & Huimin Yan & Xin Qi & Syed Muzammil Abbas Rizvi & Tianshi Wang & Huapu Lu, 2020. "An Assessment of Age and Gender Characteristics of Mixed Traffic with Autonomous and Manual Vehicles: A Cellular Automata Approach," Sustainability, MDPI, vol. 12(7), pages 1-22, April.
  86. Chandle Chae & Youngho Kim, 2023. "Investigation of Following Vehicles’ Driving Patterns Using Spectral Analysis Techniques," Sustainability, MDPI, vol. 15(13), pages 1-15, July.
  87. Auwal Alhassan Musa & Salim Idris Malami & Fayez Alanazi & Wassef Ounaies & Mohammed Alshammari & Sadi Ibrahim Haruna, 2023. "Sustainable Traffic Management for Smart Cities Using Internet-of-Things-Oriented Intelligent Transportation Systems (ITS): Challenges and Recommendations," Sustainability, MDPI, vol. 15(13), pages 1-15, June.
  88. Wen-Long Jin, 2021. "A Link Queue Model of Network Traffic Flow," Transportation Science, INFORMS, vol. 55(2), pages 436-455, March.
  89. Shang, Pengjian & Li, Xuewei & Kamae, Santi, 2005. "Chaotic analysis of traffic time series," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 121-128.
  90. Piyush Dhawankar & Prashant Agrawal & Bilal Abderezzak & Omprakash Kaiwartya & Krishna Busawon & Maria Simona Raboacă, 2021. "Design and Numerical Implementation of V2X Control Architecture for Autonomous Driving Vehicles," Mathematics, MDPI, vol. 9(14), pages 1-24, July.
  91. Jin, Wen-Long, 2017. "A Riemann solver for a system of hyperbolic conservation laws at a general road junction," Transportation Research Part B: Methodological, Elsevier, vol. 98(C), pages 21-41.
  92. Jin, Wen-Long & Recker, Wilfred W. & Wang, Xiubin B., 2016. "Instantaneous multihop connectivity of one-dimensional vehicular ad hoc networks with general distributions of communication nodes," Transportation Research Part B: Methodological, Elsevier, vol. 91(C), pages 159-177.
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