Please wait a minute...
Chin. Phys. B, 2017, Vol. 26(11): 110504    DOI: 10.1088/1674-1056/26/11/110504
GENERAL Prev   Next  

Nonlinear density wave and energy consumption investigation of traffic flow on a curved road

Zhizhan Jin(金智展)1,2,3, Rongjun Cheng(程荣军)1,2,3, 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 Sub-centre, Ningbo 315211, China
Abstract  A new car-following model is proposed based on the full velocity difference model (FVDM) taking the influence of the friction coefficient and the road curvature into account. Through the control theory, the stability conditions are obtained, and by using nonlinear analysis, the time-dependent Ginzburg-Landau (TDGL) equation and the modified Korteweg-de Vries (mKdV) equation are derived. Furthermore, the connection between TDGL and mKdV equations is also given. The numerical simulation is consistent with the theoretical analysis. The evolution of a traffic jam and the corresponding energy consumption are explored. The numerical results show that the control scheme is effective not only to suppress the traffic jam but also to reduce the energy consumption.
Keywords:  car-following model      curved road      energy consumption      time-dependent Ginzburg-Landau (TDGL) equation  
Received:  25 March 2017      Revised:  12 June 2017      Accepted manuscript online: 
PACS:  05.60.-k (Transport processes)  
  05.70.Fh (Phase transitions: general studies)  
  11.90.+t (Other topics in general theory of fields and particles)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11372166), the Scientific Research Fund of Zhejiang Province, China (Grant Nos. LY15A020007 and LY15E080013), the Natural Science Foundation of Ningbo, China (Grant Nos. 2014A610028 and 2014A610022), and the K. C. Wong Magna Fund in Ningbo University, China.
Corresponding Authors:  Hongxia Ge     E-mail:

Cite this article: 

Zhizhan Jin(金智展), Rongjun Cheng(程荣军), Hongxia Ge(葛红霞) Nonlinear density wave and energy consumption investigation of traffic flow on a curved road 2017 Chin. Phys. B 26 110504

[1] Tang T Q, Huang H J and Shang H Y 2010 Chin. Phys. B 19 050517
[2] Dong L Y, Dong K L and Xiang L 2016 Chin. Phys. B 25 098901
[3] Liu Y, Chai C C, Yang Y T, Sun J and Li Z P 2016 Chin. Phys. B 25 048504
[4] Zheng Y Z, Cheng R J, Lo S M and Ge H X 2016 Chin. Phys. B 25 060506
[5] Ge H X, Zheng P J, Lo S M and Cheng R J 2014 Nonlinear Dyn. 76 441
[6] Wang Y and Chen Y Y 2015 Chin. Phys. B 24 038902
[7] Peng G H and Cheng R J 2013 Phys. A 392 3563
[8] Tang T Q, He J, Wu Y H and Caccetta L 2014 Phys. A 396 164
[9] Liang Y J and Xue Y 2010 Acta Phys. Sin. 59 5325(in Chinese)
[10] Yu S W and Shi Z K 2015 Nonlinear Dyn. 82 731
[11] Zhu H B and Dai S Q 2008 Phys. A 387 3290
[12] Ge H X, Zheng P J, Wang W and Cheng R J 2015 Phys. A 433 274
[13] Li Z P, Li W Z, Xu S Z, Qian Y Q and Sun J 2015 Phys. A 436 729
[14] Zheng Y Z, Zheng P J and Ge H X 2014 Chin. Phys. B 23 020503
[15] Cheng R J and Cheng Y M 2016 Chin. Phys. B 25 020203
[16] Jiang R, Wu Q S and Jia B 2008 Phys. D 237 467
[17] Peng G H, He H D and Lu W Z 2015 Nonlinear Dyn. 81 417
[18] Jiang R, Hu M B, Zhang H M, Gao Z Y, Jia B and Wu Q S 2015 Transp. Rese. Part. B 80 338
[19] Zhu W X and Zhang L D 2016 Phys. A 449 265
[20] Helbing D 2009 Eur. Phys. J. B 69 539
[21] Peng G H, Lu W Z and He H D 2016 Mod. Phys. Lett. B 30 1650327
[22] Li Y F, Sun D H, Liu W N, Zhang M, Zhao M, Liao X Y and Tang L 2011 Nonlinear Dyn. 66 15
[23] Li Z P and Liu Y C 2006 Chin. Phys. B 15 1570
[24] Tang T Q, Huang H J, Wong S C and Jiang R 2009 Chin. Phys. B 18 975
[25] Tang T Q, Li C Y and Huang H J 2010 Phys. Lett. A 374 3951
[26] Ge H X, Meng X P, Ma J and Lo S M 2012 Phys. Lett. A 377 9
[27] Jiang R and Wu Q S 2007 Phys. A 375 297
[28] Li L, Wang F, Jiang R, Hu J M and Ji Y 2010 Phys. B 19 020513
[29] Nagatani T 1999 Phys. A 264 581
[30] Li Q D, Dong L Y and Dai S Q 2009 Acta Phys. Sin. 58 7584(in Chinese)
[31] Nagatani T 1999 Phys. Rev. E 59 4857
[32] Peng G H, Cai X H, Liu C Q and Tuo M X 2012 Phys. Lett. A 376 447
[33] Tian H H, Xue Y, Kan S J and Liang Y J 2009 Acta Phys. Sin. 58 4506(in Chinese)
[34] Li Z P, Liu F Q and Sun J 2011 Chin. Phys. B 20 088901
[35] Lv F, Zhu H B and Ge H X 2014 Nonlinear Dyn. 77 1245
[36] Wen J A, Tian H H and Xue Y 2010 Acta Phys. Sin. 59 3817(in Chinese)
[37] Nagatani T 1998 Phys. A 261 599
[38] Zhou J and Shi Z K 2015 Nonlinear Dyn. 81 1247
[39] Tian H H, Hu H D, Wei Y F, Xue Y and Lu W Z 2009 Phys. A 388 2895
[40] Ge H X, Cheng R J and Lo S M 2013 Chin. Phys. B 22 070507
[41] Bando M, Haseba K, Nakayama A, Shibata A and Sugiyama Y 1995 Phys. Rev. E 51 1035
[42] Helbing D and Tilch B 1998 Phys. Rev. E 58 133
[43] Jiang R, Wu Q S and Zhu Z J 2001 Phys. Rev. E 64 017101
[44] Ge H X, Dai S Q and Dong L Y 2008 Chin. Phys. B 17 23
[45] Zhang L D, Jia L and Zhu W X 2012 Acta Phys. Sin. 61 7(in Chinese)
[46] Zhu W X and Zhang L D 2012 Phys. A 391 4597
[47] Xue Y, Kang S J, Lu W Z and He H D 2014 Phys. A 398 172
[1] 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.
[2] A new coupled map car-following model considering drivers’ steady desired speed
Zhou Tong, Sun Di-Hua, Li Hua-Min, Liu Wei-Ning. Chin. Phys. B, 2014, 23(5): 050203.
[3] A control method applied to mixed traffic flow for the coupled-map car-following model
Cheng Rong-Jun, Han Xiang-Lin, Lo Siu-Ming, Ge Hong-Xia. Chin. Phys. B, 2014, 23(3): 030507.
[4] An improved car-following model with consideration of the lateral effect and its feedback control research
Zheng Ya-Zhou, Zheng Peng-Jun, Ge Hong-Xia. Chin. Phys. B, 2014, 23(2): 020503.
[5] Feedback control scheme of traffic jams based on the coupled map car-following model
Zhou Tong, Sun Di-Hua, Zhao Min, Li Hua-Min. Chin. Phys. B, 2013, 22(9): 090205.
[6] A new coupled-map car-following model based on a transportation supernetwork framework
Yao Jing, Huang Jing-Yi, Chen Guan-Rong, Xu Wei-Sheng. Chin. Phys. B, 2013, 22(6): 060208.
[7] Simulation optimization for train movement on single-track railway
Ye Jing-Jing, Li Ke-Ping. Chin. Phys. B, 2013, 22(5): 050205.
[8] Modified coupled map car-following model and its delayed feedback control scheme
Ge Hong-Xia. Chin. Phys. B, 2011, 20(9): 090502.
[9] Efficiency promotion for an on-ramp system based on intelligent transportation system information
Xie Dong-Fan, Gao Zi-You, Zhao Xiao-Mei. Chin. Phys. B, 2010, 19(8): 080515.
[10] The relationship between energy consumption and train delay in railway traffic
Li Ke-Ping, Fan Hong-Qiang. Chin. Phys. B, 2010, 19(10): 100511.
[11] Simulating train movement in railway traffic using a car-following model
Li Ke-Ping, Guan Li-Jia. Chin. Phys. B, 2009, 18(6): 2200-2204.
[12] A new car-following model with consideration of the traffic interruption probability
Tang Tie-Qiao, Huang Hai-Jun, Wong S. C., Jiang Rui. Chin. Phys. B, 2009, 18(3): 975-983.
[13] A control method for congested traffic in the coupled map car-following model
Shen Fei-Ying, Ge Hong-Xia, Zhang Hui, Yu Han-Mei, Lei Li. Chin. Phys. B, 2009, 18(10): 4208-4216.
[14] Phase transition on speed limit traffic with slope
Li Xing-Li, Song Tao, Kuang Hua, Dai Shi-Qiang. Chin. Phys. B, 2008, 17(8): 3014-3020.
[15] The effect of ACC vehicles to mixed traffic flow consisting of manual and ACC vehicles
Xie Dong-Fan, Gao Zi-You, Zhao Xiao-Mei. Chin. Phys. B, 2008, 17(12): 4440-4445.
No Suggested Reading articles found!