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Feedback control for the lattice hydrodynamics model with drivers’ reaction time

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Abstract

In this paper, a new lattice hydrodynamic model (LH model) of traffic flow under consideration of reaction time of drivers and a corresponding feedback control scheme are proposed. Based on the model, stability analysis is conducted through linear stability analysis of transfer function. The obtained phase diagram indicates that the reaction time of driver can affect the instability region of traffic flow. Under the action of a feedback control, the unstable region is shrunken to reach suppressing jams. The numerical simulations are performed to validate the effect of reaction time of driver in the new LH model. The study results confirm that the reaction time of driver significantly affects the unstability of traffic system, and the feedback control can suppress traffic jams. Furthermore, it is found that the traffic system from the chaotic traffic state to periodic steady one is successfully realizing the control of traffic system.

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References

  1. Chowdhury, D., Santen, L., Schadschneider, A., Schreckenberg, M.: Statistical physics of vehicular traffic and some related systems. Phys. Rep. 329, 199–329 (2000)

    Article  MathSciNet  Google Scholar 

  2. Helbing, D.: Traffic and related self-driven many-particle systems. Rev. Mod. Phys. 73, 1067–1141 (2001)

    Article  Google Scholar 

  3. Kerner, B.S.: The Physics of Traffic. Springer, Berlin (2004)

    Book  Google Scholar 

  4. Bando, M., Hasebe, K., Nakayama, A.: Dynamical model of traffic congestion and numerical simulation. Phys. Rev. E 51, 1035–1042 (1995)

    Article  Google Scholar 

  5. Nagatani, T.: The physics of traffic jams. Rep. Progr. Phys. 65, 1331–1386 (2002)

    Article  Google Scholar 

  6. Tang, T.Q., Li, C.Y., Huang, H.J.: A new car-following model with the consideration of the driver’s forecast effect. Phys. Lett. A. 374, 3951–3956 (2010)

    Article  MATH  Google Scholar 

  7. Tang, T.Q., Li, J.G., Yang, S.C., Shang, H.Y.: Effects of on-ramp on the fuel consumption of the vehicles on the main road under car-following model. Phys. A 419, 293–300 (2015)

    Article  Google Scholar 

  8. Nagatani, T.: Modified KdV equation for jamming transition in the continuum models of traffic. Phys. A 261, 599–607 (1998)

    Article  MathSciNet  Google Scholar 

  9. Nagatani, T.: TDGL and MKdV equations for jamming transition in the lattice models of traffic. Phys. A 264, 581–592 (1999)

    Article  Google Scholar 

  10. Ge, H.X., Cheng, R.J.: The “backward looking” effect in the lattice hydrodynamic model. Phys. A 387, 6952–6958 (2008)

    Article  Google Scholar 

  11. Tang, T.Q., Huang, H.J., Xue, Y.: An improved two-lane traffic flow lattice model. Acta Phys. Sin. 55, 4026–4031 (2006). (in Chinese)

    Google Scholar 

  12. Gupta, A.K., Redhu, P.: Analyses of a modified two-lane lattice model by considering the density difference effect. Commun. Nonliear Sci. Numer. Simulat. 19, 1600–1610 (2014)

    Article  Google Scholar 

  13. Ge, H.X., Zheng, P.J., Lo, S.M., Cheng, R.J.: TDGL equation in lattice hydrodynamic model considering driver’s physical delay. Nonlinear Dyn. 76, 441–445 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  14. Kang, Y.R., Sun, D.H.: Lattice hydrodynamic traffic flow model with explicit drivers physical delay. Nonlinear Dyn. 71, 531–537 (2013)

    Article  MathSciNet  Google Scholar 

  15. Redhu, P., Gupta, A.K.: Jamming transitions and the effect of interruption probability in a lattice traffic flow model with passing. Phys. A 421, 249–260 (2014)

    Article  Google Scholar 

  16. Gupta, A.K., Redhu, P.: Analyses of the driver’s anticipation effect in a new lattice hydrodynamic traffic flow model with passing. Nonlinear Dyn. 76, 1001–1011 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  17. Gupta, A.K., Sharma, S., Redhu, P.: Effect of multi-phase optimal velocity function on jamming transition in a lattice hydrodynamic model with passing. Nonlinear Dyn. 80, 1091–1108 (2015)

    Article  Google Scholar 

  18. Gupta, A.K., Sharma, S., Redhu, P.: Analyses of lattice traffic flow model on a gradient highway. Commun. Theor. Phys. 62, 393–404 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  19. Redhu, P., Gupta, A.K.: Effect of forward looking sites on a multi-phase lattice hydrodynamic model. Phys. A. 445, 150–160 (2016)

    Article  MathSciNet  Google Scholar 

  20. Gupta, A.K., Redhu, P.: Jamming transition of a two-dimensional traffic dynamics with consideration of optimal current difference. Phys. Lett. A 377, 2027–2033 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  21. Redhu, P., Gupta, A.K.: Phase transition in a two-dimensional triangular flow with consideration of optimal current difference effect. Nonlinear Dyn. 78, 957–968 (2014)

    Article  MathSciNet  Google Scholar 

  22. Peng, G.H., Cai, X.H., Cao, B.F., Liu, C.Q.: Non-lane-based lattice hydrodynamic model of traffic flow considering the lateral effects of the lane width. Phys. Lett. A 375, 2823–2827 (2011)

    Article  MATH  Google Scholar 

  23. Peng, G.H.: A study of wide moving jams in a new lattice model of traffic flow with the consideration of the driver anticipation effect and numerical simulation. Phys. A 391, 5971–5977 (2012)

    Article  Google Scholar 

  24. Tian, H.H., He, H.D., Wei, Y.F., Xue, Y., Lu, W.Z.: Lattice hydrodynamic model with bidirectional pedestrian flow. Phys. A 388, 2895–2902 (2009)

    Article  MathSciNet  Google Scholar 

  25. Xue, Y., Tian, H.H., He, H.D., Lu, W.Z., Wei, Y.F.: Jamming transitions and density wave in two-dimensional bidirectional pedestrian flow. Eur. Phys. J. B 69, 289–295 (2009)

    Article  Google Scholar 

  26. May, A.D.: Traffic Flow Fundamentals. Prentice Hall, New York (1990)

    Google Scholar 

  27. Davis, L.C.: Modifications of the optimal velocity traffic model to include delay due to driver reaction time. Phys. A 319, 557–567 (2003)

    Article  MATH  Google Scholar 

  28. Treiber, M., Kesting, A., Helbing, D.: Delays, inaccuracies and anticipation in microscopic traffic model. Phys. A 360, 71–88 (2006)

    Article  Google Scholar 

  29. Kesting, A., Treiber, M.: How reaction time, update time, and adaptation time influence the stability of traffic flow. Comput. Aided Civ. Infrastruct. Eng. 23, 125–137 (2008)

    Article  Google Scholar 

  30. Orosz, G., Wilson, R.E., Krauskopf, B.: Global bifurcation investigation of an optimal velocity traffic model with driver reaction time. Phys. Rev. E 70, 026207(1)–026207(10) (2004)

    Article  MathSciNet  Google Scholar 

  31. Orosz, G., Krauskopf, B., Wilson, R.E.: Bifurcations and multiple traffic jams in a car-following model with reaction-time delay. Phys. D 211, 277–293 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  32. Ngoduy, D.: Generalized macroscopic traffic model with time delay. Nonlinear Dyn. 77, 289–296 (2014)

    Article  MathSciNet  Google Scholar 

  33. Ngoduy, D.: Linear stability of a generalized multi-anticipative car following model with time delays. Commun. Nonlinear Sci. Numer. Simul. 22, 420–426 (2015)

    Article  Google Scholar 

  34. Konishi, K., Kokame, H., Hirata, K.: Coupled map car-following model and its delayed-feedback control. Phys. Rev. E 60, 4000–4007 (1999)

    Article  Google Scholar 

  35. Konishi, K., Kokame, H., Hirata, K.: Decentralized delayed-feedback control of an optimal velocity traffic model. Eur. Phys. J. B 15, 715–722 (2000)

  36. Zhao, X., Gao, Z.: A control method for congested traffic induced by bottlenecks in the coupled map car-following model. Phys. A 366, 513–522 (2006)

    Article  Google Scholar 

  37. Ge, H.X., Yu, J., Lo, S.M.: A control method for congested traffic in the car-following model. Chin. Phys. Lett. 29, 050502-3 (2012)

    Google Scholar 

  38. Ge, H.X., Cui, Y., Zhu, K.Q., Cheng, R.J.: The control method for the lattice hydrodynamic model. Commun. Nonlinear. Sci. Numer. Simulat. 22, 903–908 (2015)

    Article  Google Scholar 

  39. Jin, Y., Hu, H.: Stabilization of traffic flow in optimal velocity model via delayed-feedback control. Commun. Nonliear Sci. Numer. Simulat. 18, 1027–1034 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  40. Redhu, P., Gupta, A.K.: Delayed-feedback control in a lattice hydrodynamic model. Commun. Nonlinear Sci. Numer. Simulat. 27, 263–270 (2015)

    Article  MathSciNet  Google Scholar 

  41. Zhang, L.D., Zhu, W.X.: Delay-feedback control strategy for reducing \({\rm CO}_2\) emission of traffic flow system. Phys. A 428, 481–491 (2015)

    Article  MathSciNet  Google Scholar 

  42. Shaowei, Y., Zhongke, S.: The effects of vehicular gap changes with memory on traffic flow in cooperative adaptive cruise control strategy. Phys. A 428, 206–223 (2015)

    Article  Google Scholar 

Download references

Acknowledgements

The project supported by the National Natural Science Foundation of China (Grant Nos. 11262003 and 11302125) and the Graduate Student Innovative Foundation of Guangxi Zhuang Autonomous Region (No. YCSZ2012013).

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Authors and Affiliations

  1. Institute of Physical Science and Engineering, Guangxi University, Nanning, 53004, China

    Yu Xue, Yan Guo & Yin Shi

  2. Key Lab Relativist Astrophys, Nanning, 530004, Guangxi, People’s Republic of China

    Yu Xue & Liang-zhong Lv

  3. Logistics Research Center, Shanghai Maritime University, Shanghai, 200135, China

    Hong-di He

Authors
  1. Yu Xue
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  2. Yan Guo
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  3. Yin Shi
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  4. Liang-zhong Lv
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  5. Hong-di He
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Correspondence to Yu Xue.

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Xue, Y., Guo, Y., Shi, Y. et al. Feedback control for the lattice hydrodynamics model with drivers’ reaction time. Nonlinear Dyn 88, 145–156 (2017). https://doi.org/10.1007/s11071-016-3235-x

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  • DOI: https://doi.org/10.1007/s11071-016-3235-x

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