Macroscopic Model on Driver Physiological and Psychological Behavior at changes in Traffic

  • Zawar Hussain Khan University of Engineering and Technology, Peshawar, Pakistan
  • T. Aaron Gulliver University of Victoria, British Columbia, Canada
  • Khizar Azam University of Engineering and Technology, Peshawar, Pakistan
  • Khurram Shehzad Khattak University of Engineering and Technology, Peshawar, Pakistan
Keywords: Macroscopic traffic, physiological and psychological response, Payne-Witham (PW) model, Roe decomposition

Abstract

A model is presented which can accurately characterize macroscopic traffic evolution. This model is based on analogies with the ideal gas law. A traffic constant is proposed which considers both physiological and psychological driver behavior. Physiological behavior is the time taken to observe and process local traffic conditions and then initiate actions while psychological behavior includes the attitude and awareness of a driver. Thus, the traffic constant encompasses the perception, awareness, attitude, and reaction of a driver. The proposed model is evaluated for changes in traffic flow caused by an inactive bottleneck. The results are compared with those for the Payne-Whitham (PW) model. This shows that the temporal and spatial evolution of traffic with the proposed model is more realistic.

References

1. Aw, A., & Rascle, M., (2000), “Resurrection of “second order” models of traffic flow”, SIAM Journal Applied Mathematics, Vol. 60, Issue 3, pp. 916–938.
2. Bellomo, N., & Dogbe, C., (2011), “On the modelling of traffic and crowds: A survey of models, speculations, and perspectives”, SIAM Review., Vol. 53, Issue 3, pp. 409–463.
3. Berg, P., Mason, A., & Woods, A., (2000), “Continuum approach to car-following models”, Physics Review E, Vol. 61, Issue 2, pp. 1056–1066.
4. Daganzo, C. F., (1995), “Requiem for second-order fluid approximations of traffic flow”, Transportation Research B, Vol. 29, Issue 4, pp. 277–286.
5. Castillo, J. M. D., Pintado, P., & Benitez, F. G., (1994), “The reaction time of drivers and the stability of traffic flow”, Transportation. Research B, Vol. 28, Issue 1, pp. 35–60.
6. Fengchum, S., Hui, W., & Hong, L., (2011), “A mesoscopic model for bicycle flow”, Proc. Chinese Control Conf., pp. 5574–557, Yantai, China.
7. Greenshields, B. D., (1935), “A study in highway capacity”, Proceedings of Highway Research Board, Vol. 14, pp. 448–477.
8. Gupta, A. K., & Katiyar, V. K., (2006), “A new anisotropic continuum model for traffic flow”, Physics Review A, Vol. 368, Issue 2, pp. 551–559.
9. Harten, A., & Hayman, J. M., (1983), “Self adjusting grid methods for one dimensional hyperbolic conservation laws”, Journal of Computational Physics, Vol. 50, pp. 253–269.
10. Helbing, D., (1995), “Improved fluid dynamic model for vehicular traffic”, Physics Review E, Vol. 51, Issue 4, pp. 3164–3169.
11. Jin, W., (2003), “Traffic flow models and their numerical solutions”, Ph.D. dissertation, Department of Mathematics, University of California, Davis, CA.
12. Jin, W., & Zhang, H. M., (2001), “Solving the Payne-Whitham traffic flow model as a hyperbolic system of conservation laws with relaxation”, Technical Report UCD-ITS–Zhang–2001–1, University of California, Davis, CA.
13. Kerner, B. S., & Konhuser, P., (1993), “Cluster effects in initially homogeneous traffic flow”, Physics Review E, Vol. 48, Issue 4, pp. 2335–2338.
14. Klar, A., & Wegener, R., (2000), “Kinetic derivation of macroscopic anticipation models for vehicular traffic”, SIAM Journal of Applied Mathematics, Vol. 60, Issue 5, pp. 1749–1766.
15. Kachroo, P., (2007), “Optimal and feedback control for hyperbolic conservation laws”, Ph.D. dissertation, University of Virginia, Blacksburg, VA.
16. Khan, Z., & Gulliver, T. A., (2019), “A macroscopic traffic model based on anticipation”, Arabian Journal for Science and Engineering, Vol. 44, Issue 5, pp. 5151-5163.
17. Kermani, M. J., & Plett, E. G., (2001), “Modified entropy correction formula for the Roe scheme”, American Institute of Aeronautics and Astronautics, Paper 2011-0083, pp. 1–11.
18. Lighthill, M. J., & Whitham, J. B., (1955), “On kinematic waves II: A theory of traffic flow on long crowded roads”, Proceedings of Royal Society A, Vol. 229, pp. 317–345.
19. LeVeque, R. J., (2nd. Ed.) (1992), “Numerical Methods for Conservation Laws”, Lectures in Math., ETH Zürich, Birkhäuser: Basel, Switzerland.
20. Leer, B. V., Thomas, J. L., Roe, P. L., & Newsome, R. W., (1987) “A comparison of numerical flux formulas for the Euler and Navier-Stokes equations”, American Inst. Aeronautics and Astronautics, Paper 87-1104, pp. 36–41.
21. Li, T., (2007), “Instability and formation of clustering solutions of traffic flow”, Bulletin of Institute of Mathematics Academia Sinica (New Series), Vol. 2, Issue 2, pp. 281–295.
22. Morgan, J. V., (2002), “Numerical methods for macroscopic traffic models”, Ph.D. dissertation, Department of Mathematics, University of Reading, Berkshire, UK.
23. Muralidharan, A. (2012), “Tools for modelling and control of freeway network”, Ph.D. dissertation, Department of Mechanical Engineering., University of California, Berkeley, USA.
24. Nakrachi, A., Hayat, S., & Popescu, D., (2012), “An energy concept for macroscopic traffic flow modelling”, European Transport. Research. Review., Vol. 4, Issue 2, pp. 57–66.
25. Payne, H. J., (1971), “Models of freeway traffic and control”, Simulation Council Proceedings, Vol. 1, Issue 1, pp. 51–61.
26. Papageorgiou, M., (1998), “Some remarks on macroscopic traffic modelling”, Transportation Research A, Vol. 32, Issue 5, pp. 323–329.
27. Papageorgiou, M., Blosseville, J.-M., & Hadj-Salem, H., (1990), “Modelling and real-time control of traffic flow on the southern part of Boulevard Peripherique in Paris, Part-1: Modelling”, Transportation Research A, Vol. 24, Issue 5, pp. 345–359.
28. Richards, P. I., (1956), “Shock waves on the highway”, Operations Research, Vol. 4, Issue 1, pp. 42–51.
29. Roe, P. L., (1981), “Approximate Riemann solvers, parameter vectors, and difference schemes”, Journal of Computational Physics, Vol. 43, Issue 2, pp. 357–372.
30. Strang, G., (4th Ed.) (2009), “Introduction to Applied Mathematics”, Wellesley: Cambridge Press, MA.
31. Tang, T. Q., Huang, H. J., Gao, Z. Y., & Wong, S. C., (2007), “Interaction of waves in the speed-gradient traffic flow model”, Physica A, Vol. 380, Issue 1, pp. 481–489.
32. Vorraa, T., & Brignone, A., (2008), “Modelling traffic in detail with mesoscopic models: Opening powerful new possibilities for traffic analyses”, WIT Trans. The Built Environment, Vol. 101, pp. 659–666.
33. Whitham, G. B., (1974), “Linear and Nonlinear Waves”, New York: Wiley.
34. Yokoya, Y., Asano, Y., & Uchida, N. (2008), “Qualitative change of traffic flow induced by driver response”, Proceedings of IEEE International Conference on Systems, Man and Cybernetics, Singapore, pp. 2315–2320.
35. Zhang, H. M., (2002), “A non-equilibrium traffic model devoid of gas-like behaviour”, Transportation Research B, Vol. 36, Issue 3, pp. 275–290.
36. Zhang, H., (1998), “A theory of non-equilibrium traffic flow”, Transportation Research B, Vol. 32, Issue 7, pp. 485–498.
37. Khan, Z., Gulliver, T. A., Khattak, K. S., & Qazi, A., (2019), “A macroscopic traffic flow based on reaction velocity”, Iranian Journal of Science and Technology-Transactions of Civil Engineering, doi:10.1007/s40996-019-00266-y.
38. Khan, Z. H., Imran, W., Azeem, S., Gulliver, T. A., & Aslam M. S., (2019), “A macroscopic traffic model based on driver reaction and traffic stimuli”, Applied Sciences, Vol. 9, Issue 14, 2848.
39. Khan, Z. Gulliver, T.A., Nasir, H., Rehman, A., & Shahzada, K., (2019), “A macroscopic traffic model based on driver physiological response”, Journal of Engineering Mathematics, Vol. 115, Issue 1, pp. 21-41.
40. Khan, Z., Shah, S.A.A., & Gulliver, T.A., (2018), “A macroscopic traffic flow model based on weather conditions”, Chinese Journal of Physics B, Vol. 27, Issue 7, art. 070202.
41. Khan, Z. & Gulliver, T.A., (2018), “A macroscopic traffic model for traffic flow harmonization”, European Transport Research Review, Vol. 10, art. 30.
42. Imran, W., Khan, Z. H., Gulliver, T. A., Khattak, K. S., & Nasir, H., (2020), “A macroscopic traffic model for heterogeneous flow”, Chinese Journal of Physics, Vol. 63, Issue 1, pp. 419-435.
43. Siebel, F. & Mauser, W., (2006), “On the fundamental diagram of traffic flow”, SIAM Journal on Applied Mathematics, Vol. 66, Issue 4, pp. 1150-1162.
44. Khan, Z., (2016), “Traffic modelling for intelligent transportation systems”, Ph.D. dissertation, Department of Electrical and Computer Engineering, University of Victoria, BC, Canada.
Published
2019-12-31
How to Cite
Khan, Z., Gulliver, T. A., Azam, K., & Khattak, K. S. (2019, December 31). Macroscopic Model on Driver Physiological and Psychological Behavior at changes in Traffic. JOURNAL OF ENGINEERING AND APPLIED SCIENCES, 38(2). https://doi.org/https://doi.org/10.25211/jeas.v38i2.3150