A kinematic wave theory of multi-commodity network traffic flow

[1]  R. Courant,et al.  Über die partiellen Differenzengleichungen der mathematischen Physik , 1928 .

[2]  J. G. Wardrop,et al.  Some Theoretical Aspects of Road Traffic Research , 1952 .

[3]  J. Wardrop.  ROAD PAPER. SOME THEORETICAL ASPECTS OF ROAD TRAFFIC RESEARCH. , 1952 .

[4]  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.

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

[6]  I. Bohachevsky,et al.  Finite difference method for numerical computation of discontinuous solutions of the equations of fluid dynamics , 1959 .

[7]  D. Gazis,et al.  Nonlinear Follow-the-Leader Models of Traffic Flow , 1961 .

[8]  Stella C. Dafermos,et al.  Traffic assignment problem for a general network , 1969 .

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

[10]  George A. Bekey,et al.  Mathematical models of public systems , 1971 .

[11]  G. Whitham,et al.  Linear and Nonlinear Waves , 1976 .

[12]  Deepak K. Merchant,et al.  A Model and an Algorithm for the Dynamic Traffic Assignment Problems , 1978 .

[13]  S. Osher,et al.  Stable and entropy satisfying approximations for transonic flow calculations , 1980 .

[14]  Gordon F. Newell,et al.  Traffic flow on transportation networks , 1980 .

[15]  Warren B. Powell,et al.  A transportation network evacuation model , 1982 .

[16]  Bram van Leer,et al.  On the Relation Between the Upwind-Differencing Schemes of Godunov, Engquist–Osher and Roe , 1984 .

[17]  P. G. Gipps,et al.  A MODEL FOR THE STRUCTURE OF LANE-CHANGING DECISIONS , 1986 .

[18]  P. Lax.  Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves , 1987 .

[19]  Markos Papageorgiou,et al.  Dynamic modeling, assignment, and route guidance in traffic networks , 1990 .

[20]  R. Ansorge.  What does the entropy condition mean in traffic flow theory , 1990 .

[21]  Carlos F. Daganzo,et al.  Properties of link travel time functions under dynamic loads , 1995 .

[22]  H. Holden,et al.  A mathematical model of traffic flow on a network of unidirectional roads , 1995 .

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

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

[25]  Carlos F. Daganzo,et al.  THE NATURE OF FREEWAY GRIDLOCK AND HOW TO PREVENT IT. , 1995 .

[26]  C Buisson,et al.  STRADA, a discretized macroscopic model of vehicular traffic flow in complex networks based on the Godunov scheme , 1996 .

[27]  J. Lebacque.  THE GODUNOV SCHEME AND WHAT IT MEANS FOR FIRST ORDER TRAFFIC FLOW MODELS , 1996 .

[28]  A. Lyrintzis,et al.  Modelling of freeway merging and diverging flow dynamics , 1996 .

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

[30]  Michael Florian,et al.  The continuous dynamic network loading problem : A mathematical formulation and solution method , 1998 .

[31]  Denis Serre,et al.  Unstable Godunov Discrete Profiles for Steady Shock Waves , 1998 .

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

[33]  Peter Hidas,et al.  MODELLING LANE CHANGING AND MERGING IN MICROSCOPIC TRAFFIC SIMULATION , 2002 .

[34]  W. Y. Szeto,et al.  A cell-based variational inequality formulation of the dynamic user optimal assignment problem , 2002 .

[35]  Markos Papageorgiou,et al.  Freeway ramp metering: an overview , 2002, IEEE Trans. Intell. Transp. Syst..

[36]  R. LeVeque.  Finite Volume Methods for Hyperbolic Problems: Characteristics and Riemann Problems for Linear Hyperbolic Equations , 2002 .

[37]  Wen-Long Jin,et al.  Kinematic Wave Traffic Flow Model for Mixed Traffic , 2002 .

[38]  C. Daganzo,et al.  The bottleneck mechanism of a freeway diverge , 2002 .

[39]  Wen-Long Jin,et al.  The Inhomogeneous Kinematic Wave Traffic Flow Model as a Resonant Nonlinear System , 2003, Transp. Sci..

[40]  H. M. Zhang,et al.  On the distribution schemes for determining flows through a merge , 2003 .

[41]  S. Sherwin,et al.  One-dimensional modelling of a vascular network in space-time variables , 2003 .

[42]  Axel Klar,et al.  Modeling, Simulation, and Optimization of Traffic Flow Networks , 2003, SIAM J. Sci. Comput..

[43]  A. Quarteroni,et al.  One-dimensional models for blood flow in arteries , 2003 .

[44]  Wen-Long Jin,et al.  Multicommodity Kinematic Wave Simulation Model for Network Traffic Flow , 2004 .

[45]  Soyoung Ahn,et al.  Driver Turn-Taking Behavior in Congested Freeway Merges , 2004 .

[46]  Meide Zhao,et al.  A Hyperbolic System of Equations of Blood Flow in an Arterial Network , 2004, SIAM J. Appl. Math..

[47]  Peter Hidas,et al.  Modelling vehicle interactions in microscopic simulation of merging and weaving , 2005 .

[48]  M. Herty,et al.  Network models for supply chains , 2005 .

[49]  Mauro Garavello,et al.  Traffic Flow on a Road Network , 2005, SIAM J. Math. Anal..

[50]  J. Lebacque.  First-Order Macroscopic Traffic Flow Models: Intersection Modeling, Network Modeling , 2005 .

[51]  Mauro Garavello,et al.  Source-Destination Flow on a Road Network , 2005 .

[52]  Daiheng Ni,et al.  A simplified kinematic wave model at a merge bottleneck , 2005 .

[53]  J. P. Lebacque.  Intersection Modeling, Application to Macroscopic Network Traffic Flow Models and Traffic Management , 2005 .

[54]  Anna Nagurney,et al.  On a Paradox of Traffic Planning , 2005, Transp. Sci..

[55]  Wen-Long Jin.  A kinematic wave theory of lane-changing traffic flow , 2005 .

[56]  Axel Klar,et al.  Communications in Mathematical Sciences , 2005 .

[57]  CIRO D’APICE,et al.  Packet Flow on Telecommunication Networks , 2006, SIAM J. Math. Anal..

[58]  B. Piccoli,et al.  Traffic Flow on a Road Network Using the Aw–Rascle Model , 2006 .

[59]  Michael Herty,et al.  Optimization criteria for modelling intersections of vehicular traffic flow , 2006, Networks Heterog. Media.

[60]  Georges Bastin,et al.  A second order model of road junctions in fluid models of traffic networks , 2007, Networks Heterog. Media.

[61]  Michiel C.J. Bliemer,et al.  Dynamic Queuing and Spillback in Analytical Multiclass Dynamic Network Loading Model , 2007 .

[62]  Benedetto Piccoli,et al.  A Fluid Dynamic Model for Telecommunication Networks with Sources and Destinations , 2008, SIAM J. Appl. Math..

[63]  Wen-Long Jin,et al.  Continuous Kinematic Wave Models of Merging Traffic Flow , 2008, 0810.3952.

[64]  Michael Herty,et al.  Multicommodity flows on road networks , 2008 .

[65]  Thomas Durlin,et al.  Dynamic Network Loading Model with Explicit Traffic Wave Tracking , 2008 .

[66]  Liang Chen,et al.  An Urban Intersection Model Based on Multi-commodity Kinematic Wave Theories , 2008, 2008 11th International IEEE Conference on Intelligent Transportation Systems.

[67]  W. Jin,et al.  Supply-demand Diagrams and a New Framework for Analyzing the Inhomogeneous Lighthill-Whitham-Richards Model , 2010, 1005.4624.

[68]  Wen-Long Jin,et al.  Asymptotic traffic dynamics arising in diverge–merge networks with two intermediate links , 2009 .

[69]  Soyoung Ahn,et al.  Empirical macroscopic evaluation of freeway merge-ratios , 2010 .