Fluid Models in ihe Traffic Flow Theory

  • Sanja Marušić
Keywords: Traffic flow, fluid models, L WR model, second order models, shock waves.

Abstract

This paper presents a survey of results concerning continuum(fluid) models in the the01y of traffic flow. We begin withthe basic LWR model from 1955-56 and describe the benefitsand deficiencies of that model. Ajte1wards we present somenew models developed over the peliod from 1971 (Payne) until1999 (Aw and Rascle) in attempt of correcting the deficienciesof classical L WR model

References

R. Ansorge, What does the entropy solution mean in the

traffic flow theory?, Transpn Res.B, Vol24, No 2 (1990),

-143.

A. Aw, M. Rascle, Resurrection of second order models of

traffic flow, SIAM J. Appl. Math., Vol 60, No.3 (2000),

-938.

J.H. Bick, G.F. Newell, A continuum model for two-directional

traffic flow, Quart. Appl. Math., 18 (1961),

-204.

C.F. Daganzo, Fundamentals of Transportation and

Traffic Operations, Pergamon, Amsterdam, 1996.

C.F. Daganzo, Requiem for second order fluid approximation

to traffic flow, Transpn. Res. B, Vol 29, No 4

(1995), 277-286.

C.F. Daganzo, A continuum themy of traffic dynamics

for freeways with special lanes, Transpn Res. B, Vol 31,

No 2 (1997), 83-102.

N.D. Fowkes, J.J. Mahony, An Introduction to Mathematical

Modelling, Wiley, New York, 1994.

R. Haberman, Mechanical Vibrations, Population Dynamics

and Traffic Flow, SIAM, Philadelphia, 1998.

D. Helbing, Verkehrsynamik, Springer Verlag, Berlin,

H. Holden, N.H. Risebro, A mathematical model of

traffic flow on a network of unidirectional roads, SIAM J.

Math. Anal., Vol26, No 4 (1995), 999-1017.

E. Godlewski, P .A. Raviart, Hyperbolic systems of conseJvation

laws, Ellipses, Paris, 1991.

C.J. Leo, R.L. Pretty, Numerical simulation of macroscopic

continuum traffic models, Transpn Res. B, Vol

, No 3 (1992), 207-220.

R.J. LeVeque, Numelical Methods for ConseJVation

Laws, Birkhauser, Basel, 1992.

M.J. Lighthill, J.B. Whitham, On kinematic waves. I:

Flow movement in long rivers. II· A theory of traffic flow

on long crowded roads, Proc. Royal Soc. Edinburgh. A,

(1955), 281-345.

P.G. Michalopoulos, D.E. Beskos, J.K. Lin, Analysis of

interrupted traffic flow by finite difference methods.

Transpn Res. B, 18B (1984), 409-421.

P.G. Michalopulos, P.Yi, A.S. Lyrintzis, Continuum

modelling of traffic dynamics for congested freeways,

Transpn Rs. B, Vol 27, No 4 (1993), 315-332.

C.S. Morawetz, Nonlinear Waves and Shocks, Springer,

Berlin, 1981.

H.J. Payne, Models of freeway traffic and control, Simulation

Councils Pros. Series: Mathematical Models of

Public Systems, Vol 1, No 1 (1971), ed. G. A Bakey,

-61.

I. Prigorgine, F.C. Andrews, A. Boltzmann-like approach

for traffic flow, Operations Research, 8 (1960),

-797.

P.I. Richards, Shock waves on the highway, Operations

Research, 4 (1956), 42-51.

A.J. Roberts, One-Dimensional Introduction to Continuum

Mechanics, World Scientific, Singapore, 1994.

K.K. Sanwal, K.Petty, J.Walrand,An extended macroscopic

modelfortrafficflow, Transpn Res. B, Vol30, No

(1996), 1-9.

H. M. Zhang, A theory of nonequilibrium traffic flow,

Transpn Res. B, Vol 32, No 7 (1998), 485-498.

X. Zhang, F.J. Jarret, Stability analysis of the classical

car-following model, Transpn Res. B, Vol 31, No 6

(1997), 441-462.

How to Cite
1.
Marušić S. Fluid Models in ihe Traffic Flow Theory. Promet [Internet]. 1 [cited 2024Mar.28];12(1):7-14. Available from: http://traffic.fpz.hr/index.php/PROMTT/article/view/729
Section
Older issues