Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2014, Article ID 539459, 7 pages
http://dx.doi.org/10.1155/2014/539459
Research Article

The Burgers Equation for a New Continuum Model with Consideration of Driver’s Forecast Effect

1College of Automation, Northwestern Polytechnical University, Xi’an, Shaanxi 710129, China
2School of Science, Northwestern Polytechnical University, Xi’an, Shaanxi 710129, China

Received 18 June 2014; Revised 12 August 2014; Accepted 12 August 2014; Published 24 August 2014

Academic Editor: Weichao Sun

Copyright © 2014 Lei Yu and Bingchang Zhou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. T. Ezaki and K. Nishinari, “Cluster size distribution in 1D-CA traffic models,” Journal of Physics A, vol. 45, no. 4, Article ID 045101, 2012. View at Publisher · View at Google Scholar · View at Scopus
  2. W.-X. Zhu and R.-L. Yu, “Nonlinear analysis of traffic flow on a gradient highway,” Physica A: Statistical Mechanics and Its Applications, vol. 391, no. 4, pp. 954–965, 2012. View at Publisher · View at Google Scholar · View at Scopus
  3. B. S. Kerner, “Physics of traffic gridlock in a city,” Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, vol. 84, Article ID 045102, 4 pages, 2011. View at Publisher · View at Google Scholar · View at Scopus
  4. X. M. Zhao, D. F. Xie, B. Jia, R. Jiang, and Z. Y. Gao, “Disorder structure of free-flow and global jams in the extended BML model,” Physics Letters A, vol. 375, no. 7, pp. 1142–1147, 2011. View at Publisher · View at Google Scholar · View at Scopus
  5. D. Yang, J. Jin, B. Ran, Y. Pu, and F. Yang, “Modeling and analysis of car-truck heterogeneous traffic flow based on intelligent driver car-following model,” in Proceedings of the 92nd Annual Meeting on Transportation Research Board (TRB '13), Washington, Wash, USA, January 2013.
  6. T. Nagatani, “Jamming and freezing transitions in CA model for facing pedestrian traffic with a soft boundary,” Physics Letters A, vol. 374, no. 15-16, pp. 1686–1689, 2010. View at Publisher · View at Google Scholar · View at Scopus
  7. S. Masukura, T. Nagatani, and K. Tanaka, “Jamming transitions induced by a slow vehicle in traffic flow on a multi-lane highway,” Journal of Statistical Mechanics: Theory and Experiment, vol. 2009, no. 4, Article ID P04002, 2009. View at Publisher · View at Google Scholar · View at Scopus
  8. T. Nagatani, “The physics of traffic jams,” Reports on Progress in Physics, vol. 65, no. 9, pp. 1331–1386, 2002. View at Publisher · View at Google Scholar · View at Scopus
  9. M. Bando, K. Hasebe, A. Nakayama, A. Shibata, and Y. Sugiyama, “Dynamical model of traffic congestion and numerical simulation,” Physical Review E, vol. 51, no. 2, pp. 1035–1042, 1995. View at Publisher · View at Google Scholar · View at Scopus
  10. D. Helbing and B. Tilch, “Generalized force model of traffic dynamics,” Physical Review E, vol. 58, no. 1, pp. 133–138, 1998. View at Google Scholar · View at Scopus
  11. Y. Xue, L. Y. Dong, Y. W. Yuan, and S. Q. Dai, “The effect of the relative velocity on traffic flow,” Communications in Theoretical Physics, vol. 38, no. 2, pp. 230–234, 2002. View at Publisher · View at Google Scholar · View at Scopus
  12. M. J. Lighthill and G. B. Whitham, “On kinematic waves: II. A theory of traffic flow on long crowed roads,” Proceedings of the Royal Society A, vol. 229, no. 1178, pp. 317–345, 1955. View at Publisher · View at Google Scholar
  13. P. I. Richards, “Shock waves on the highway,” Operations Research, vol. 4, pp. 42–51, 1956. View at Publisher · View at Google Scholar · View at MathSciNet
  14. H. J. Payne, “Models of freeway traffic and control,” in Mathematical Models of Public Systems, G. A. Bekey, Ed., vol. 1 of Simulation Councils Proceedings Series, pp. 51–61, 1971. View at Google Scholar
  15. R. Jiang, Q. Wu, and Z. Zhu, “A new continuum model for traffic flow and numerical tests,” Transportation Research Part B: Methodological, vol. 36, no. 5, pp. 405–419, 2002. View at Publisher · View at Google Scholar · View at Scopus
  16. D. C. Gazis, R. Herman, and R. B. Potts, “Car-following theory of steady-state traffic flow,” Operations Research, vol. 7, pp. 499–505, 1959. View at Publisher · View at Google Scholar · View at MathSciNet
  17. Z. Ou, “Density waves in the continuum analog of the full velocity difference model,” Physica A: Statistical Mechanics and its Applications, vol. 387, no. 8-9, pp. 1799–1806, 2008. View at Publisher · View at Google Scholar · View at Scopus
  18. D. A. Kurtze and D. C. Hong, “Traffic jams, granular flow, and soliton selection,” Physical Review E, vol. 52, no. 1, pp. 218–221, 1995. View at Publisher · View at Google Scholar · View at Scopus
  19. X. Zhou, Z. Liu, and J. Luo, “The density wave in a car-following model,” Journal of Physics A: Mathematical and General, vol. 35, no. 20, pp. 4495–4500, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. L. Yu, T. Li, and Z. K. Shi, “Density waves in a traffic flow model with reaction-time delay,” Physica A, vol. 389, no. 13, pp. 2607–2616, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. T. Q. Tang, H. J. Huang, and H. Y. Shang, “A new macro model for traffic flow with the consideration of the driver's forecast effect,” Physics Letters, Section A: General, Atomic and Solid State Physics, vol. 374, no. 15-16, pp. 1668–1672, 2010. View at Publisher · View at Google Scholar · View at Scopus
  22. B. S. Kerner and P. Konhäuser, “Cluster effect in initially homogeneous traffic flow,” Physical Review E, vol. 48, no. 4, pp. R2335–R2338, 1993. View at Publisher · View at Google Scholar · View at Scopus
  23. J. M. D. Castillo and F. G. Benítez, “On the functional form of the speed-density relationship-I: general theory,” Transportation Research Part B, vol. 29, no. 5, pp. 373–389, 1995. View at Publisher · View at Google Scholar · View at Scopus
  24. B. S. Kerner, “Synchronized flow as a new traffic phase and related problems for traffic flow modelling,” Mathematical and Computer Modelling, vol. 35, no. 5-6, pp. 481–508, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  25. W. C. Sun, H. J. Gao, and O. Kaynak, “Finite frequency H control for vehicle active suspension systems,” IEEE Transactions on Control Systems Technology, vol. 19, no. 2, pp. 416–422, 2011. View at Publisher · View at Google Scholar · View at Scopus
  26. W. Sun, Z. Zhao, and H. Gao, “Saturated adaptive robust control for active suspension systems,” IEEE Transactions on Industrial Electronics, vol. 60, no. 9, pp. 3889–3896, 2013. View at Publisher · View at Google Scholar · View at Scopus
  27. W. C. Sun, H. J. Gao, and O. Kaynak, “Adaptive backstepping control for active suspension systems with hard constraints,” IEEE/ASME Transactions on Mechatronics, vol. 18, no. 3, pp. 1072–1079, 2013. View at Publisher · View at Google Scholar · View at Scopus
  28. G. D. Tian, M. C. Zhou, J. W. Chu, and Y. M. Liu, “Probability evaluation models of product disassembly cost subject to random removal time and different removal labor cost,” IEEE Transactions on Automation Science and Engineering, vol. 9, no. 2, pp. 288–295, 2012. View at Publisher · View at Google Scholar · View at Scopus
  29. G. Tian, J. Chu, Y. Liu, H. Ke, X. Zhao, and G. Xu, “Expected energy analysis for industrial process planning problem with fuzzy time parameters,” Computers and Chemical Engineering, vol. 35, no. 12, pp. 2905–2912, 2011. View at Publisher · View at Google Scholar · View at Scopus
  30. B. Wang, G. D. Tian, Y. Liang, and T. G. Qiang, “Reliability modeling and evaluation of electric vehicle motor by using fault tree and extended stochastic Petri nets,” Journal of Applied Mathematics, vol. 2014, Article ID 638013, 9 pages, 2014. View at Google Scholar