Journal of Jilin University(Engineering and Technology Edition) ›› 2026, Vol. 56 ›› Issue (2): 393-406.doi: 10.13229/j.cnki.jdxbgxb.20240754

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Stability analysis of homogeneous and heterogeneous traffic flows considering curved conditions

Hong-xing ZHAO1(),Shu-ying LIU1,Jiang-long NIE2,Rui-yan LIANG3,Rui-chun HE1()   

  1. 1.School of Traffic and Transportation,Lanzhou Jiaotong University,Lanzhou 730070,China
    2.Construction Business Department of State Grid Gansu Electric Power Company,Lanzhou 730000,China
    3.Digital Business Department of State Grid Gansu Electric Power Company,Lanzhou 730000,China
  • Received:2024-07-08 Online:2026-02-01 Published:2026-03-17
  • Contact: Rui-chun HE E-mail:zhaohx@mail.lzjtu.cn;tranman@163.com

Abstract:

To study the following characteristics and stability conditions of vehicles on curved roads, this paper builds upon an intelligent driver model (IDM), integrating considerations of factors such as curve radius and super-elevation, and incorporating road mechanics to establish an extended model. By analyzing the influence of curves on traffic flow stability, the study derives stability conditions applicable to both homogeneous and heterogeneous traffic flows comprising human driven vehicles (HDVs), automated vehicles (AVs), and connected automated vehicles (CAVs). Parameter sensitivity analyses and numerical validations are conducted. The findings indicate that traffic flow stability is highest under Condition 2 (R=250?m,ie=8%). Increasing equilibrium speeds enhances traffic flow stability, while increasing free-flow speeds is detrimental to stability. Moreover, as CAVs penetration rates increase, the stability of mixed traffic flows gradually improves, although increasing maximum platoon sizes may destabilize traffic flows. In homogeneous traffic flows, lower speeds are advantageous for stability at low speeds; for high-speed conditions, stability is optimized at speeds of 29.9 m/s for HDVs, 26.8 m/s for AVs, and 26.9 m/s for CAVs. In mixed traffic flows, stability can be maintained when the penetration rates of CAVs exceed 0.72.

Key words: intelligent transportation, car-following model, numerical simulation, homogeneous and heterogeneous traffic flows, curved roads

CLC Number: 

  • U463.6

Table 1

Parameter values"

参数IDMA-IDMC-IDM
l/m555
a/(m·s-2133
b/(m·s-2222
vf/(m·s-133.333.333.3
s0/m222
T/s1.51.21.0

Fig.1

Homogeneous traffic flow under different conditions"

Fig.2

Heterogeneous traffic flow under different conditions"

Fig.3

Heterogeneous traffic flows under different maximum platoon size"

Fig.4

Heterogeneous traffic flow under different free-flow speed"

Fig.5

Heterogeneous traffic flow under different equilibrium speeds"

Fig.6

Space-time evolution of the headway for different conditions (HDVs)"

Fig.7

Headway profiles for different conditions (HDVs)"

Fig.8

Space-time evolution of the headway for different conditions (AVs)"

Fig.9

Headway profiles for different conditions (AVs)"

Fig.10

Space-time evolution of the headway for different conditions (CAVs)"

Fig.11

Headway profiles for different conditions (CAVs)"

Fig.12

Space-time evolution of the headway for heterogeneous traffic flows under different conditions"

Fig.13

Headway profiles for heterogeneous traffic flows under different conditions"

Fig.14

Space-time evolution of the headway for different penetration rates of CAVs"

Fig.15

Headway profiles for different penetration rates of CAVs"

[1] Marsden G, Mcdonald M, Brackstone M. Towards an understanding of adaptive cruise control[J]. Transportation Research Part C, 2001, 9(1): 33-51.
[2] Xiao L Y, Gao F. A comprehensive review of the development of adaptive cruise control systems[J]. Vehicle System Dynamics, 2010, 48(10): 1167-1192.
[3] Makridis M, Mattas K, Anesiadou A, et al. OpenACC: An open database of car-following experiments to study the properties of commercial ACC systems[J]. Transportation Research Part C: Emerging Technologies, 2021, 125: No.103047.
[4] Shang M F, Stern R E. Impacts of commercially available adaptive cruise control vehicles on highway stability and throughput[J]. Transportation Research Part C: Emerging Technologies, 2021, 122: No.102897.
[5] Wissam K, Soyoung A. A strategic approach to handle performance uncertainties in autonomous vehicle's car-following behavior[J]. Transportation Research Part C: Emerging Technologies, 2024, 160: No.104499.
[6] 张毅, 姚丹亚, 李力, 等. 智能车路协同系统关键技术与应用[J]. 交通运输系统工程与信息, 2021, 21(5): 40-51.
Zhang Yi, Yao Dan-ya, Li Li, et al. Technologies and applications for intelligent vehicle-infrastructure cooperation systems[J]. Journal of Transportation Systems Engineering and Information Technology,2021, 21(5): 40-51.
[7] Jiang Y S, Ren T T, Ma Y Q, et al. Traffic safety evaluation of mixed traffic flow considering the maximum platoon size of connected automated vehicles[J]. Physica A, 2023, 612: No.128452.
[8] Ge Y M, Jiang R, Sun H J, et al. Environmental impact estimation of mixed traffic flow involving CAVs and Human-driven vehicles considering the non-equilibrium state[J]. Transportation Research Part C: Emerging Technologies, 2024, 161: No.104542.
[9] Luo L H, Liu Y, Feng Y H, et al. Stabilizing traffic flow by autonomous vehicles: stability analysis and implementation considerations[J]. Transportation Research Part C: Emerging Technologies, 2024, 158:No.104449.
[10] Qin Y Y, Luo Q Z, Wang H.Stability analysis and connected vehicles management for mixed traffic flow with platoons of connected automated vehicles[J]. Transportation Research Part C, 2023, 157: No.104370.
[11] Wang S T, Zhu W X, Ma X L.Mixed traffic system with multiple vehicle types and autonomous vehicle platoon: modeling, stability analysis and control strategy[J]. Physica A, 2023, 632: No.129293.
[12] 宋成举, 贾洪飞, 秦昊溥. 网联车混入条件下混合交通流跟驰稳定性[J]. 吉林大学学报: 工学版, 2024, 54(2): 419-426.
Song Cheng-ju, Jia Hong-fei, Qin Hao-bo. Car following stability in mixed traffic flow with CAVs mixing[J]. Journal of Jilin University (Engineering and Technology Edition), 2024, 54(2): 419-426.
[13] 郝威, 龚雅馨, 张兆磊, 等. 面向高速公路混合交通流的车辆协同合流策略[J]. 交通运输系统工程与信息,2023, 23(1): 224-235.
Hao Wei, Gong Ya-xin, Zhang Zhao-lei, et al. Cooperative merging strategy for freeway ramp in a mixed traffic environment[J]. Journal of Transportation Systems Engineering and Information Technology, 2023, 23(1): 224-235.
[14] 马万经, 李金珏, 俞春辉. 智能网联混合交通流交叉口控制: 研究进展与前沿[J]. 中国公路学报, 2023, 36(2): 22-40.
Ma Wan-jing, Li Jin-yu, Yu Chun-hui. Intersection control in mixed traffic with connected automated vehicles: a review of recent developments and research frontiers[J].China Journal of Highway and Transport,2023, 36(2): 22-40.
[15] Zhang Y, Yang X F. Discrete macroscopic traffic flow model considering the lane-changing behaviors in the mixed traffic environment[J]. Transportation Research Part C: Emerging Technologies, 2024, 164:No.104672.
[16] Shang Y, Zhu F, Jiang R, et al. Trajectory planning at a signalized road section in a mixed traffic environment considering lane-changing of CAVs and stochasticity of HDVs[J]. Transportation Research Part C: Emerging Technologies, 2024, 158: No.104441.
[17] Treiber M, Hennecke A, Helbing D.Congested traffic states in empirical observations and microscopic simulations[J]. Phys Rev E, 2000, 62(2): 1805.
[18] Vanderwerf J, Shladover S, Kourjanskaia N, et al.Modeling effects of driver control assistance systems on traffic[J]. Transportation Research Record, 2001, 1748(1): 167-174.
[19] Kesting A, Treiber M, Schoenhof M, et al. Adaptive cruise control design for active congestion avoidance[J]. Transportation Research Part C: Emerging Technologies, 2008, 16: 668-683.
[20] Kesting A, Treiber M, Helbing D.Enhanced intelligent driver model to access the impact of driving strategies on traffic capacity[J]. Philosophical Transactions of the Royal Society A, 2010, 368(1928): 4585-4605.
[21] Yi Z W, Lu W Q, Xu L H, et al. Intelligent back looking distance driver model and stability analysis for connected and automated vehicles[J]. Journal of Central South University, 2020, 27(11): 3499-3512.
[22] 王树凤, 王世皓, 王新凯. 基于改进跟驰模型的混合车辆编队研究[J]. 公路, 2023, 68(6): 289-297.
Wang Shu-feng, Wang Shi-hao, Wang Xin-kai. Research on hybrid vehicle formation based on improved car-following[J]. Highway, 2023, 68(6): 289-297.
[23] Cui Z Y, Wang X N, Ci Y S, et al. Modeling and analysis of car-following models incorporating multiple lead vehicles and acceleration information in heterogeneous traffic flow[J]. Physica A, 2023, 630:129259.
[24] 蒲云, 徐银, 刘海旭, 等. 考虑多车影响的智能网联车跟驰模型[J]. 吉林大学学报: 工学版, 2024, 54(5):1285-1292.
Pu Yun, Xu Yin, Liu Hai-xu, et al. An improved car-following model for connected and automated vehicles considering impact of multiple vehicles[J]. Journal of Jilin University (Engineering and Technology Edition), 2024, 54(5): 1285-1292.
[25] Zhu W X, Zhang L D. Friction coefficient and radius of curvature effects upon traffic flow on a curved road[J]. Physica A, 2012, 20(391): 4597-4605.
[26] Cheng R J, Wang Y H. An extended lattice hydrodynamic model considering the delayed feedback control on a curved road[J]. Physica A, 2019, 513: 510-517.
[27] 陈秀锋, 高艳艳, 石英杰, 等. 基于最优速度的弯道跟驰模型及其稳定性分析[J]. 重庆交通大学学报: 自然科学版, 2020, 39(1): 126-130.
Chen Xiu-feng, Gao Yan-yan, Shi Ying-jie, et al. Curve car following model based on optimal velocity and its stability analysis[J]. Journal of Chongqing Jiaotong University (Natural Science), 2020, 39(1): 126-130.
[28] Zhai C, Wu W W, Xiao Y P.Cooperative car-following control with electronic throttle and perceived headway errors on gyroidal roads[J]. Applied Mathematical Modeling, 2022, 108: 770-786.
[29] Wang Z, Zhu W X.Modeling and stability analysis of traffic flow considering electronic throttle dynamics on a curved road with slope[J]. Physical A: Statistical Mechanics and its Applications, 2022, 597: No.127225.
[30] 罗瑞发, 郝慧君, 徐桃让, 等. 考虑时延的网联车混合交通流基本图模型[J]. 华南理工大学学报: 自然科学版, 2023, 51(1): 106-113.
Luo Rui-fa, Hao Hui-jun, Xu Tao-rang, et al. Fundamental diagram model of mixed traffic flow of connected vehicles considering time delay[J]. Journal of South China University of Technology (Natural Science Edition), 2023, 51(1): 106-113.
[31] 吴德华, 陈荣峰. 智能网联客货混合交通流特性及集聚换道策略[J]. 吉林大学学报: 工学版, 2025, 55(8):2588-2596.
Wu De-hua, Chen Rong-feng. Characteristics and agglomeration lane-changing strategies of intelligent connected passenger and freight mixed traffic flow [J]. Journal of Jilin University (Engineering and Technology Edition), 2020, 55(8): 2588-2596.
[32] 覃频频, 吴锋民, 覃光毅, 等. 考虑道路几何条件的ACC系统上层速度控制模型[J]. 机械设计与制造, 2021(5): 235-240.
Qin Pin-pin, Wu Feng-min, Qin Guang-yi, et al. The upper-layer speed control model of adaptive cruise control (ACC) system considering road geometry[J]. Machinery Design & Manufacture, 2021(5): 235-240.
[33] 许金良, 曾卓, 穆明浩, 等. 考虑制动、 荷载转移、纵坡的雨天小客车弯道安全车速模型[J]. 重庆交通大学学报: 自然科学版, 2024, 43(2): 75-83.
Xu Jin-liang, Zeng Zhuo, Mu Ming-hao, et al. Safe speed model of passenger cars on bends in rainy days considering braking, load transfer and longitudinal slope[J]. Journal of Chongqing Jiaotong University(Natural Science), 2024, 43(2): 75-83.
[34] Qin Y Y, Luo Q Z, Wang H. Stability analysis and connected vehicles management for mixed traffic flow with platoons of connected automated vehicles[J]. Transportation Research Part C: Emerging Technologies, 2023, 157: No.104370.
[35] Wilson R E. Mechanisms for spatio-temporal pattern formation in highway traffic models[J]. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2008, 366(1872):2017-2032.
[36] . 公路路线设计规范 [S].
[37] Ward J A. Heterogeneity, lane-changing and instability in traffic: a mathematical approach[J]. Pure mathematics12C-Applied Mathematics, 2009, 1: 40050067.
[38] Yao Z B, Wu Y X, Wang Y, et al.Analysis of the impact of maximum platoon size of CAVs on mixed traffic flow: an analytical and simulation method[J]. Transportation Research Part C: Emerging Technologies, 2023, 147: 103989.
[39] Zhou J Z, Zhu F. Modeling the fundamental diagram of mixed human-driven and connected automated vehicles[J]. Transportation Research Part C: Emerging Technologies, 2020, 115: 102614.
[40] Zhou J Z, Zhu F.Analytical analysis of the effect of maximum platoon size of connected and automated vehicles[J]. Transportation Research Part C: Emerging Technologies, 2021, 122: 102882.
[41] Zhang X Z, Shi Z K, Yu S W, et al.A new car-following model considering driver's desired visual angle on sharp curves[J]. Physica A: Statistical Mechanics and its Applications, 2023, 615: 128551.
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