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Chin. Phys. B, 2021, Vol. 30(12): 120506    DOI: 10.1088/1674-1056/abfcc9
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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
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