Please wait a minute...
Chin. Phys. B, 2021, Vol. 30(12): 120506    DOI: 10.1088/1674-1056/abfcc9
GENERAL Prev   Next  

Stabilization strategy of a car-following model with multiple time delays of the drivers

Weilin Ren(任卫林)1,2,3, Rongjun Cheng(程荣军)1,2,3,†, and Hongxia Ge(葛红霞)1,2,3
1 Faculty of Maritime and Transportation, Ningbo University, Ningbo 315211, China;
2 Jiangsu Province Collaborative Innovation Center for Modern Urban Traffic Technologies, Nanjing 210096, China;
3 National Traffic Management Engineering and Technology Research Centre Ningbo University Subcenter, Ningbo 315211, China
Abstract  An extended car-following model with multiple delays is constructed to describe driver's driving behavior. Through stability analysis, the stability condition of this uncontrolled model is given. To dampen the negative impact of the driver's multiple delays (i.e., stability condition is not satisfied), a novel control strategy is proposed to assist the driver in adjusting vehicle operation. The control strategy consists of two parts:the design of control term as well as the design of the parameters in the term. Bifurcation analysis is performed to illustrate the necessity of the design of parameters in control terms. In the course of the design of parameters in the control term, we improve the definite integral stability method to reduce the iterations by incorporating the characteristics of bifurcation, which can determine the appropriate parameters in the control terms more quickly. Finally, in the case study, we validate the control strategy by utilizing measured data and configuring scenario, which is closer to the actual traffic. The results of validation show that the control strategy can effectively stabilize the unstable traffic flow caused by driver's delays.
Keywords:  car-following model      driver's reaction time delays      improved definite integral method      bifurcation analysis      stabilization strategy  
Received:  19 March 2021      Revised:  18 April 2021      Accepted manuscript online:  29 April 2021
PACS:  05.60.-k (Transport processes)  
  45.70.Vn (Granular models of complex systems; traffic flow)  
  02.30.Oz (Bifurcation theory)  
Fund: Project supported by the Natural Science Foundation of Zhejiang Province, China (Grant No. LY20G010004), the Program of Humanities and Social Science of Education Ministry of China (Grant No. 20YJA630008), the National Key Research and Development Program of China-Traffic Modeling, Surveillance and Control with Connected & Automated Vehicles (Grant No. 2017YFE9134700), and the K.C. Wong Magna Fund in Ningbo University, China.
Corresponding Authors:  Rongjun Cheng     E-mail:

Cite this article: 

Weilin Ren(任卫林), Rongjun Cheng(程荣军), and Hongxia Ge(葛红霞) Stabilization strategy of a car-following model with multiple time delays of the drivers 2021 Chin. Phys. B 30 120506

[1] Bando M, Hasebe K, Nakayama A, Shibata A and Sugiyama Y 1995 Phys. Rev. E 51 1035
[2] Bando M, Hasebe K, Nakanishi K and Nakayama A 1998 Phys. Rev. E 58 5429
[3] Zhou J, Shi Z K and Cao J L 2014 Phys. A 396 77
[4] Sun D H, Chen D, Zhao M, Liu W N and Zheng L J 2018 Phys. A 501 293
[5] Orosz G, Wilson R E and Krauskopf B 2004 Phys. Rev. E 70 026207
[6] Orosz G, Krauskopf B and Wilson R E 2005 Phys. D 211 277
[7] Orosz G, Wilson R E, Szalai R and Stepan G 2009 Phys. Rev. E 80 046205
[8] Li S K, Yang L X, Gao Z Y and Li K P 2014 ISA T. 53 1739
[9] Jin Y F and Xu M 2016 Phys. A 459 107
[10] Zhou T, Chen D, Zheng L J, Liu W N, He Y C and Liu Z C 2018 Phys. A 512 174
[11] Jin Y F and Meng J W 2020 Commun. Nonlinear Sci. 90 105333
[12] Sun Y Q, Ge H X and Cheng R J 2018 Phys. A 508 349
[13] Jiang R, Wu Q S and Zhu Z J 2001 Phys. Rev. E 64 017101
[14] Treiber M, Hennecke A and Helbing D 2000 Phys. Rev. E 62 1805
[15] Orosz G and Stepan G 2006 Proc. R. Soc. A 462 2643
[16] Ngoduy D and Li T L 2020 Transportmetrica A 17 878
[17] Punzo V, Borzacchiello M T and Ciuffo B 2011 Transport. Res. C-Emer. Techn. 19 1243
[18] Chen C, Li L, Hu J and Geng C 2010 Proceedings of 2010 IEEE International Conference on Vehicular Electronics and Safety, 2010, New York, America, p. 48
[19] Yu S W, Huang M X, Ren J and Shi Z K 2016 Phys. A 449 1
[20] Peng Y, Liu S J and Yu D Z 2020 Phys. A 538 122967
[21] Ma T and Abdulhai B 2002 Transport. Res. Rec. 1800 6
[22] Ossen S J, Hoogendoorn S P and Gorte B G 2006 Transportation Research Record:Journal of the Transportation Research Board, 2006, Washington, p. 121
[1] Bifurcation analysis of visual angle model with anticipated time and stabilizing driving behavior
Xueyi Guan(管学义), Rongjun Cheng(程荣军), and Hongxia Ge(葛红霞). Chin. Phys. B, 2022, 31(7): 070507.
[2] A novel car-following model by sharing cooperative information transmission delayed effect under V2X environment and its additional energy consumption
Guang-Han Peng(彭光含), Te-Ti Jia(贾特提), Hua Kuang(邝华), Hui-Li Tan(谭惠丽), and Tao Chen(陈陶). Chin. Phys. B, 2022, 31(5): 058901.
[3] Modeling the heterogeneous traffic flow considering the effect of self-stabilizing and autonomous vehicles
Yuan Gong(公元) and Wen-Xing Zhu(朱文兴). Chin. Phys. B, 2022, 31(2): 024502.
[4] Extremely hidden multi-stability in a class of two-dimensional maps with a cosine memristor
Li-Ping Zhang(张丽萍), Yang Liu(刘洋), Zhou-Chao Wei(魏周超), Hai-Bo Jiang(姜海波), Wei-Peng Lyu(吕伟鹏), and Qin-Sheng Bi(毕勤胜). Chin. Phys. B, 2022, 31(10): 100503.
[5] Modeling and analysis of car-following behavior considering backward-looking effect
Dongfang Ma(马东方), Yueyi Han(韩月一), Fengzhong Qu(瞿逢重), and Sheng Jin(金盛). Chin. Phys. B, 2021, 30(3): 034501.
[6] Dual mechanisms of Bcl-2 regulation in IP3-receptor-mediated Ca2+ release: A computational study
Hong Qi(祁宏), Zhi-Qiang Shi(史志强), Zhi-Chao Li(李智超), Chang-Jun Sun(孙长君), Shi-Miao Wang(王世苗), Xiang Li(李翔), and Jian-Wei Shuai(帅建伟). Chin. Phys. B, 2021, 30(10): 108704.
[7] Heterogeneous traffic flow modeling with drivers' timid and aggressive characteristics
Cong Zhai(翟聪), Weitiao Wu(巫威眺), and Songwen Luo(罗淞文). Chin. Phys. B, 2021, 30(10): 100507.
[8] Nonlinear density wave and energy consumption investigation of traffic flow on a curved road
Zhizhan Jin(金智展), Rongjun Cheng(程荣军), Hongxia Ge(葛红霞). Chin. Phys. B, 2017, 26(11): 110504.
[9] A new coupled map car-following model considering drivers’ steady desired speed
Zhou Tong (周桐), Sun Di-Hua (孙棣华), Li Hua-Min (李华民), Liu Wei-Ning (刘卫宁). Chin. Phys. B, 2014, 23(5): 050203.
[10] A control method applied to mixed traffic flow for the coupled-map car-following model
Cheng Rong-Jun (程荣军), Han Xiang-Lin (韩祥临), Lo Siu-Ming (卢兆明), Ge Hong-Xia (葛红霞). Chin. Phys. B, 2014, 23(3): 030507.
[11] An improved car-following model with consideration of the lateral effect and its feedback control research
Zheng Ya-Zhou (郑亚周), Zheng Peng-Jun (郑彭军), Ge Hong-Xia (葛红霞). Chin. Phys. B, 2014, 23(2): 020503.
[12] Feedback control scheme of traffic jams based on the coupled map car-following model
Zhou Tong (周桐), Sun Di-Hua (孙棣华), Zhao Min (赵敏), Li Hua-Min (李华民). Chin. Phys. B, 2013, 22(9): 090205.
[13] A new coupled-map car-following model based on a transportation supernetwork framework
Yao Jing (姚静), Huang Jing-Yi (黄婧祎), Chen Guan-Rong (陈关荣), Xu Wei-Sheng (许维胜). Chin. Phys. B, 2013, 22(6): 060208.
[14] Simulation optimization for train movement on single-track railway
Ye Jing-Jing (叶晶晶), Li Ke-Ping (李克平). Chin. Phys. B, 2013, 22(5): 050205.
[15] Modified coupled map car-following model and its delayed feedback control scheme
Ge Hong-Xia(葛红霞) . Chin. Phys. B, 2011, 20(9): 090502.
No Suggested Reading articles found!