Some recent developments in traffic flow theory

This paper attempts to give a qualitative assessment of some recent developments related to the continuum modeling of vehicular traffic flow. Our objectives are threefold: 1) to establish a unified view on the discussed theories; 2) to compare their predictions with available observations; and 3) to find out their limitations and postulate new research directions in traffic flow. Our discussion begins with a brief introduction on continuum traffic flow theories and ends with a note on further directions of research in this area.

[1]  Michael J. Cassidy,et al.  Validation of the Incremental Transfer Model , 1999 .

[2]  M. Cassidy.  BIVARIATE RELATIONS IN NEARLY STATIONARY HIGHWAY TRAFFIC , 1998 .

[3]  M J Lighthill,et al.  On kinematic waves II. A theory of traffic flow on long crowded roads , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[4]  H. Greenberg.  An Analysis of Traffic Flow , 1959 .

[5]  Gordon F. Newell,et al.  INSTABILITY IN DENSE HIGHWAY TRAFFIC: A REVIEW. , 1965 .

[6]  Carlos F. Daganzo,et al.  THE CELL TRANSMISSION MODEL, PART II: NETWORK TRAFFIC , 1995 .

[7]  Reinhart D Kuhne.  FREEWAY CONTROL AND INCIDENT DETECTION USING A STOCHASTIC CONTINUUM THEORY OF TRAFFIC FLOW , 1989 .

[8]  R. B. Potts,et al.  Car-Following Theory of Steady-State Traffic Flow , 1959 .

[9]  J. M. D. Castillo,et al.  The reaction time of drivers and the stability of traffic flow , 1994 .

[10]  J. M. D. Castillo,et al.  ON THE FUNCTIONAL FORM OF THE SPEED-DENSITY RELATIONSHIP--II: EMPIRICAL INVESTIGATION , 1995 .

[11]  Carlos F. Daganzo,et al.  A BEHAVIORAL THEORY OF MULTI-LANE TRAFFIC FLOW. PART I, LONG HOMOGENEOUS FREEWAY SECTIONS , 1999 .

[12]  C. Daganzo.  Requiem for second-order fluid approximations of traffic flow , 1995 .

[13]  B D Greenshields,et al.  A study of traffic capacity , 1935 .

[14]  H. M. Zhang.  Analyses of the stability and wave properties of a new continuum traffic theory , 1999 .

[15]  H. M. Zhang.  STRUCTURAL PROPERTIES OF SOLUTIONS ARISING FROM A NONEQUILIBRIUM TRAFFIC FLOW THEORY , 2000 .

[16]  B. Kerner.  EXPERIMENTAL FEATURES OF SELF-ORGANIZATION IN TRAFFIC FLOW , 1998 .

[17]  H. M. Zhang.  A NON-EQUILIBRIUM TRAFFIC MODEL DEVOID OF GAS-LIKE BEHAVIOR , 2002 .

[18]  L. Chambers.  Linear and Nonlinear Waves , 2000, The Mathematical Gazette.

[19]  Harold J Payne,et al.  MODELS OF FREEWAY TRAFFIC AND CONTROL. , 1971 .

[20]  Carlos F. Daganzo,et al.  A continuum theory of traffic dynamics for freeways with special lanes , 1997 .

[21]  H. M. Zhang,et al.  Anisotropic property revisited––does it hold in multi-lane traffic? , 2003 .

[22]  R S Foote,et al.  TRAFFIC FLOW IN TUNNELS , 1958 .

[23]  H. M. Zhang,et al.  A NOTE ON HIGHWAY CAPACITY , 2001 .

[24]  E R Case,et al.  EVALUATION OF DYNAMIC FREEWAY FLOW MODEL BY USING FIELD DATA (DISCUSSION AND CLOSURE) , 1983 .

[25]  H. M. Zhang.  New Perspectives on Continuum Traffic Flow Models , 2001 .

[26]  Joseph L. Schofer,et al.  A STATISTICAL ANALYSIS OF SPEED-DENSITY HYPOTHESES. IN VEHICULAR TRAFFIC SCIENCE , 1967 .

[27]  L. C. Edie.  Car-Following and Steady-State Theory for Noncongested Traffic , 1961 .

[28]  P. I. Richards.  Shock Waves on the Highway , 1956 .

[29]  H. M. Zhang.  A mathematical theory of traffic hysteresis , 1999 .

[30]  J Treiterer,et al.  THE HYSTERESIS PHENOMENON IN TRAFFIC FLOW , 1974 .

[31]  C. Daganzo.  The Cell Transmission Model: Network Traffic , 1994 .

[32]  H. M. Zhang.  A theory of nonequilibrium traffic flow , 1998 .

[33]  Markos Papageorgiou,et al.  SOME REMARKS ON MACROSCOPIC TRAFFIC FLOW MODELLING , 1998 .

[34]  Carlos F. Daganzo,et al.  A SIMPLE PHYSICAL PRINCIPLE FOR THE SIMULATION OF FREEWAYS WITH SPECIAL LANES AND PRIORITY VEHICLES , 1997 .

[35]  Chin Jian Leo,et al.  Numerical simulation of macroscopic continuum traffic models , 1992 .