Two-phase fluids model for freeway traffic flow and its application to simulate evolution of solitons in traffic

Journal of Transportation Engineering

Volumn 129, Issue 1, 2003, Pages 51-56

  Zhu, Zuojin ^a   Wu, Tongqiang ^b  

^a UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

Simulation; Traffic flow; Two phase flow

Indexed keywords

COMPUTER SIMULATION; HIGHWAY TRAFFIC CONTROL; MATHEMATICAL MODELS; PROBLEM SOLVING; VEHICLES;

FREEWAY TRAFFIC FLOW;

MOTOR TRANSPORTATION;

FLUID FLOW; TRAFFIC MANAGEMENT;

EID: 0037249479     PISSN: 0733947X     EISSN: None     Source Type: Journal    
DOI: 10.1061/(ASCE)0733-947X(2003)129:1(51)     Document Type: Article

References (23)

1. Ardekani, S., and Herman, R. (1987). "Urban network-wide traffic variables and their relations." Transp. Sci., 21(1), 1-16.
2. Bick, J. H., and Newell, G. F. (1960). "A continuum model for traffic flow on an undivided freeway." Q. Appl. Math., 18(2), 191-204.
3. Chang, M. F., and Herman, R. (1981). "Trip time versus stop time and fuel consumption characteristics in cities." Transp. Sci., 15, 183-209.
4. Chen, X. N. (1988). "The diffraction, reflection, and radiation of soliton and its relevant viscous decay." PhD thesis, Shanghai Jiao Tong Univ., Shanghai, P.R. China.
5. Daganzo, C. (1995a). "A finite difference approximation of the kinematic wave model of traffic flow." Transp. Res., Part B: Methodol., 29(4), 261-276.
6. Daganzo, C. (1995b). "Requiem for second order approximations of traffic flow." Transp. Res., Part B: Methodol., 24(4), 277-286.
7. Daganzo, C. (1997). Fundamentals of transportation and traffic flow, Elsevier, New York, 66-149.
8. Davis, S. F. (1988). "Simplified second-order Godunov-type methods." J. Sci. Statist. Comput., 9, 445-473.
9. De, S. C. (1956). "Kinematic wave theory of bottlenecks of varying capacity." Proc. Cambridge Philos. Soc., 52(3), 564-572.
10. Hirota, R. (1973). "Exact envelope solutions of a nonlinear wave equation." J. Math. Phys., 14, 805-809.
11. Herman, R., and Ardekani, S. (1984). "Characterizing traffic conditions in urban areas." Transp. Sci., 18(2), 101-140.
12. Herman, R., and Ardekani, S. (1985). "The influence of stops on vehicle fuel consumption in urban traffic." Transp. Sci., 19(1), 1-12.
13. Herman, R., and Prigogine. (1979). "A two-fluid approach to town traffic." Science, 204, 148-151.
14. Kortewg, D. J., and Devries, G. (1895). "On the change of form of long waves advancing in a rectangular channel and on a new type of long stationary waves." Philos. Mag., 39, 422-443.
15. Lighthill, M. J., and Whitham, G. B. (1955). "On kinematic waves. II: A theory of traffic flow on long crowded roads." Proc. R. Soc., 229A, 317-345.
16. Richards, P. I. (1956). "Shock waves on the freeway." Oper. Res., 4, 42-51.
17. Remoisenet, P. C. (1999). "Waves called solitons." Concepts and experiments, 3rd Ed., Springer, New York, 1-12.
18. Roe, P. C. (1981). "Approximate Riemann solvers, parameter vectors, and difference schemes." J. Comput. Phys., 43, 357-372.
19. Shui, H. S. (1998). Finite difference in one dimensional fluid mechanics, National Defense, Beijing, 343-551.
20. Singer, P. C. (1996). "Signal processing and communication with solitons." PhD thesis, Massachusetts Institute of Technology, Cambridge, Mass.
21. Yee, H. C. (1987). "Construction of explicit and implicit symmetric TVD schemes and their applications." J. Comput. Phys., 68, 151-179.
22. Zabusky, N. J., and Kruskal, M. D. (1965). "Interaction of solitons in a collisionless plasma and the recurrence of initial states." Phys. Rev. Lett., 15, 240-243.
23. Zhang, H. M. (1999). "A mathematical theory of traffic hysteresis." Transp. Res., Part B: Methodol., 33, 1-23.