Skip to main content
Log in

A traffic flow model considering influence of car-following and its echo characteristics

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

Taking into account the driving characteristics of vehicles following the vehicle in front on the imported lane of urban signalized intersections, we introduce the acceleration parameters of the vehicle and consider the queue length and volatility of the acceleration that have been affected by the time of fixed signal cycles in the mixed traffic flow. Thereby, we obtain a mixed traffic flow cellular automaton model with the effect of acceleration on the imported lane. Through analyzing the results of numerical simulation, it is found that the maximum queue length and the volatility of acceleration have a great influence on the intersection lane mixed traffic flow with the different time of fixed signal cycles and considerably on traffic arriving strength within a certain range. When the intensity is in specific range, the longer the fixed signal cycle, the shorter the maximum queue length, and the greater the volatility of acceleration, which has smaller queue jam affecting the intersection lane mixed traffic flow. Meanwhile, the improved model can reproduce the evolution and propagation characteristics of gathering–dissipating of the traffic wave in the intersection lane mixed traffic flow.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Kai, N., Schreckenberg, M.: A cellular automaton model for freeway traffic. J. Phys. I Fr. 2(12), 2221–2229 (1992)

  2. Takayasu, M., Takayasu, H.: 1/f noise in a traffic model. Fractals Complex Geom. Patterns Scaling Nat. Soc. 1(4), 860–866 (1993)

    MATH  Google Scholar 

  3. Schadschneider, A., Schreckenberg, M.: Traffic flow models with ‘slow-to-start’ rules. Ann. Phys. 509(7), 541–551 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  4. Li, X.B., Wu, Q.S., Jiang, R.: Cellular automaton model considering the velocity effect of a car on the successive car. Phys. Rev. E 64(6), 066128 (2001)

    Article  Google Scholar 

  5. Knospe, W., Schadschneider, A., Schreckenberg, M., Santen, L.: Towards a realistic microscopic description of highway traffic. J. Phys. A 33(48), L477–L485 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  6. Kerner, B.S., Klenov, S.L., Wolf, D.E.: Cellular automata approach to three-phase traffic theory. J. Phys. A Math. Gen. 35(47), 9971–10013 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  7. Lee, H.K., Barlovic, R., Schreckenberg, M., Kim, D.: Mechanical restriction versus human overreaction triggering congested traffic states. Phys. Rev. Lett. 92(23), 238702 (2004)

    Article  Google Scholar 

  8. Bando, M., Hasebe, K., Nakayama, A., Shibata, A., Sugiyama, Y.: Dynamical model of traffic congestion and numerical simulation. Phys. Rev. E 51(2), 1035–1042 (1994)

    Article  MATH  Google Scholar 

  9. Emmerich, H., Rank, E.: An improved cellular automation model for traffic flow simulation. Phys. Sect. A 234(3), 676–686 (1997)

    Article  Google Scholar 

  10. Dong, L.Y., Yu, X., Dai, S.Q.: One-dimensional cellular automation model of traffic flow based on car-following idea. Appl. Math. Mech-Engl. 23, 363–370 (2002)

  11. Li, K.P., Gao, Z.Y.: Cellular automata model of traffic flow based on car-following model. Chin. Phys. Lett. 21(11), 2120–2123 (2004)

    Article  Google Scholar 

  12. Jiang, R., Hu, M.B., Jia, B., Wang, R.L., Wu, Q.S.: The effects of reaction delay in the Nagel–Schreckenberg traffic flow model. Eur. Phys. J. B 54(2), 267–273 (2006)

    Article  Google Scholar 

  13. Li, Y.F., Zhu, H., Cen, M., Li, Y.G., Li, R., Sun, D.H.: On the stability analysis of microscopic traffic car-following model: a case study. Nonlinear Dyn. 74(1–2), 335–343 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  14. Liu, F.X., Cheng, R.J., Zheng, P.J., Ge, H.X.: TDGL and mKdV equations for car-following model considering traffic jerk. Nonlinear Dyn. 83(1–2), 793–800 (2016)

    Article  Google Scholar 

  15. Lighthill, M.J., Whitham, G.B.: On kinematic waves, II. A theory of traffic flow on long crowded roads. Proc. R. Soc. Math. Phys. Eng. Sci. 299(1178), 317–345 (1955)

    Article  MathSciNet  MATH  Google Scholar 

  16. Richards, P.I.: Shock waves on the highway. Oper. Res. 4(1), 42–51 (1956)

    Article  MathSciNet  Google Scholar 

  17. Kang, Y.S.: Delay, stop and queue estimation for uniform and random traffic arrivals at fixed-time signalized intersections. The Faculty of the Virginia Polytechnic Institute and State University, Blacksburg (2000)

  18. Dion, F., Rakha, H., Kang, Y.S.: Comparison of delay estimates at under-saturated and over-saturated pre-timed signalized intersections. Transp. Res. Part B Methodol. 38(2), 99–122 (2004)

  19. Li, X.G., Gao, Z.Y., Jia, B., Zhao, X.M.: Modeling the interaction between motorized vehicle and bicycle by using cellular automata model. Int. J. Mod. Phys. C 20(02), 209–222 (2009)

    Article  MATH  Google Scholar 

  20. Fukamachi, M., Nagatani, T.: Sidle effect on pedestrian counter flow. Phys. A Stat. Mech. Appl. 377(1), 269–278 (2007)

    Article  Google Scholar 

  21. Jiang, R., Wu, Q.S.: A stopped time dependent randomization cellular automata model for traffic flow controlled by traffic light. Phys. A Stat. Mech. Appl. 364(C), 493–496 (2006)

    Article  Google Scholar 

  22. Sasaki, M., Nagatani, T.: Transition and saturation of traffic flow controlled by traffic lights. Phys. A Stat. Mech. Appl. 325(3–4), 531–546 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  23. Ruskin, H.J., Deo, P.: Urban signalised intersections: impact of vehicle heterogeneity and driver type on cross-traffic manoeuvres. Phys. A Stat. Mech. Appl. 405, 140–150 (2014)

    Article  Google Scholar 

  24. Tang, T.Q., Shi, W.F., Shang, H.Y., Wang, Y.P.: An extended car-following model with consideration of the reliability of inter-vehicle communication. Measurement 58, 286–293 (2014)

  25. Tang, T.Q., Shi, W.F., Shang, H.Y., Wang, Y.P.: A new car-following model with consideration of inter-vehicle communication. Nonlinear Dyn. 76, 2017–2023 (2014)

  26. Wang, T., Gao, Z.Y., Zhao, X.M.: Multiple velocity difference model and its stability analysis. Acta Phys. Sin. 55, 0634 (2006)

    Google Scholar 

  27. Yu, S.W., Shi, Z.K.: An extended car-following model at signalized intersections. Phys. A 407, 152–159 (2014)

  28. Yu, S.W., Shi, Z.K.: Dynamics of connected cruise control systems considering velocity changes with memory feedback. Measurement 64, 34–48 (2015)

  29. Yu, S.W., Shi, Z.K.: An improved car-following model considering relative velocity fluctuation. Commun. Nonlinear Sci. Numer. Simul. 36, 319–326 (2016)

  30. Yu, S.W., Shi, Z.K.: The effects of vehicular gap changes with memory on traffic flow in cooperative adaptive cruise control strategy. Phys. A 428, 206–223 (2015)

  31. Yu, S.W., Liu, Q.L., Li, X.H.: Full velocity difference and acceleration model for a car-following theory. Commun. Nonlinear Sci. Numer. Simul. 18, 1229–1234 (2013)

  32. Ge, J., Orosz, G.: Dynamics of connected vehicle systems with delayed acceleration feedback. Transp. Res. Part C 46, 46–64 (2014)

    Article  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 51468034) and the Colleges and Universities Fundamental Scientific Research Expenses Project of Gansu Province, China (Grant No. 214148) and the Natural Science Foundation of Gansu Province, China (Grant No. 1508RJZA112) and the Universities Scientific Research Project of Gansu Province Education Department (Grant No. 2015A-051).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yongsheng Qian.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Qian, Y., Zeng, J., Wang, N. et al. A traffic flow model considering influence of car-following and its echo characteristics. Nonlinear Dyn 89, 1099–1109 (2017). https://doi.org/10.1007/s11071-017-3502-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-017-3502-5

Keywords

Navigation