Fluid Models in ihe Traffic Flow Theory
AbstractThis 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
R. Ansorge, What does the entropy solution mean in the
traffic flow theory?, Transpn Res.B, Vol24, No 2 (1990),
A. Aw, M. Rascle, Resurrection of second order models of
traffic flow, SIAM J. Appl. Math., Vol 60, No.3 (2000),
J.H. Bick, G.F. Newell, A continuum model for two-directional
traffic flow, Quart. Appl. Math., 18 (1961),
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
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,
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,
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,
I. Prigorgine, F.C. Andrews, A. Boltzmann-like approach
for traffic flow, Operations Research, 8 (1960),
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
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
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