Numerical Simulation of Freeway Traffic Flow
Publication: Journal of Transportation Engineering
Volume 123, Issue 6
Abstract
A new high-order continuum model is presented in this paper. This high-order model exhibits smooth solutions rather than discontinuities, is able to describe the amplification of small disturbances on heavy traffic, and allows fluctuations of speed around the equilibrium values. Furthermore, unlike some earlier high-order models, it does not result in negative speeds at the tail of congested regions and disturbance propagation speeds greater than the flow speed. The model takes into account the relaxation time as a function of density and, in the equilibrium limit, it is consistent with the simple continuum model. A Riemann-problem-based numerical method is proposed for the solution of the new high-order model. Modeling of interrupted flow behavior such as merging, diverging, and weaving is also investigated. Based on the new high order model, the proposed numerical method and the modeling of interrupted flow, a versatile code is developed for the numerical simulation of freeway traffic flow that includes several freeway geometries. We compare the high-order model with the simple continuum model and the proposed numerical method with the Lax method based on 30-s and 5-min field data. The model is tested in interrupted flow situations (e.g., pipeline, merging, diverging, and weaving areas). A comparison of numerical results with limited field data shows that the high-order model performs better than the simple continuum model and describes better than a previously proposed method.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Aiken, R. C. (1985). Stiff computation. Oxford University Press, New York, England.
2.
Chapman, S., and Cowling, T. G. (1970). The mathematical theory of nonuniform gases, 3rd Ed., Cambridge Univ. Press, Cambridge, England.
3.
Daganzo, C. F. (1995). “Requiem for second order fluid approximations of traffic flow.”Transp. Res., 29B, 277–286.
4.
Harten, A., Lax, P. D., and van Leer, B.(1983). “On upstream differencing and Godunov-type schemes for hyperbolic conservation laws.”SIAM Rev., 25(1), 35–61.
5.
Highway capacity manual. (1985). Transportation Research Board, Washington, D.C.
6.
Kühne, R. (1984). “Macroscopic freeway model for dense traffic—stop-start waves and incident detection.”9th Int. Symp. on Transp. and Traffic Theory, I. Volmuller and R. Hamerslag, eds., VNU Science Press, Utrecht, The Netherlands, 21–42.
7.
Lighthill, M. H., and Whitham, G. B. (1955). “On kinematic waves II: a theory of traffic flow on long crowded roads.”Proc., R. Soc. London Ser. A. 229, 317–345.
8.
Liu, G.-Q. (1997). “Development, implementation and testing of high-order traffic flow models for freeways,” PhD dissertation, Dept. of Civil & Mineral Engrg., Univ. of Minnesota, Minneapolis, MN.
9.
Lyrintzis, A. S., Liu, G.-Q., and Michalopoulos, P. G. (1994b). “Development and comparative evaluation of high-order traffic flow models.”Transp. Res. Rec. 1457, Washington D.C., 174–183.
10.
Lyrintzis, A. S., Michalopoulos, P. G., and Liu, G.-Q. (1995). “Development of advanced traffic flow models and implementation in parallel processing.”Final Rep., Minnesota Dept. of Transp., Minneapolis, Minn.
11.
Lyrintzis, A. S., Yi, P., Michalopoulos, P. G., and Beskos, E.(1994a). “Development and field testing of advanced continuum traffic flow models for congested freeways.”J. Transp. Engrg., ASCE, 120(3), 461–477.
12.
Michalopoulos, P. G., and Lin, J. (1985). “A freeway simulation program for microcomputers.”Proc., 1st Nat. Conf. on Microcomp. in Urban Transp., ASCE, New York, N.Y., 330–341.
13.
Michalopoulos, P. G, Kwon, E., and Kang. J.-G. (1991a). “Enhancement and field testing of a dynamic freeway simulation program.”Transp. Res. Rec. 1320, Washington D.C., 203–215.
14.
Michalopoulos, P. G., Yi, P., and Lyrintzis, A. S. (1993a). “Continuum modeling of traffic dynamics for congested freeways.”Transp. Res., 27B, 315–332.
15.
Michalopoulos, P. G., Yi, P., and Lyrintzis, A. S. (1993b). “Development of an improved high order continuum traffic flow model.”Transp. Res. Rec. 1365, Washington D.C., 125–132.
16.
Michalopoulos, P. G., Yi, P., Beskos, D. E., and Lyrintzis, A. S. (1991b). “Continuum modeling of traffic dynamics.”Proc., 2nd Int. Conf. on Appl. of Advanced Tech. in Transp. Engrg., Minneapolis, Minn., 36–40.
17.
Michalopoulos, P. G., Kwon, E., Lee, C.-F., Mahadevan, G., and Kang, J.-G. (1992). “Development of an integrated simulation package for freeway design, operations and adaptive traffic management, phase 1: Enhancement of the KRONOS simulation program.”Final Rep., Ctr. for Transp. Studies, Univ. of Minnesota, Minneapolis, Minn.
18.
Papageorgiou, M. (1983). “A hierarchical control system for freeway traffic.”Transp. Res, 17B, 251–261.
19.
Papageorgiou, M., Blosseville, J. M., and Hadj-Salem, H. (1989). “Macroscopic modelling of traffic flow on the boulevard peripherique in Paris.”Transp. Res, 23B, 29–47.
20.
Payne, H. J. (1971). “Models of freeway traffic and control.”Proc., Math. Models of Public Sys. Simulation Council Ser. 1, G. A. Bekey, ed., 51–61.
21.
Payne H. J. (1979). “FREFLO: A macroscopic simulation model of freeway traffic.”Transp. Res. Rec. 722, Washington D.C., 68–77.
22.
Phillips, W. F. (1979). “A kinetic model for traffic flow with continuum implications.”Transp. Planning Technol. 5(3), 131–138.
23.
Press, W., et al. (1994). Numerical recipes in C. Cambridge University Press, London, England.
24.
Ross, P. (1988). “Traffic dynamics.”Transp. Res., 22B, 421–435.
25.
Whitham, G. B. (1974). Linear and nonlinear waves. John Wiley & Sons, Inc., New York, N.Y.
Information & Authors
Information
Published In
Journal of Transportation Engineering
Volume 123 • Issue 6 • November 1997
Pages: 503 - 513
Copyright
Copyright © 1997 American Society of Civil Engineers.
History
Published online: Nov 1, 1997
Published in print: Nov 1997
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.