On the distribution schemes for determining flows through a merge

In this paper, we study various distribution schemes for determining flows through a merge in the supply-demand framework. Upon a thorough analysis of existing schemes, we propose a simple distribution scheme that satisfies the "fairness" condition, in which the flow from an upstream link is proportional to its traffic demand. We demonstrate that this scheme can capture major characteristics of a merge, such as differences in link capacities and the control of an on-ramp link. Moreover, this scheme leads to a merge model that is computationally efficient and easy to calibrate. Wave solutions of a general Riemann problem will be of interest in future studies.

[1]  H. Lo.  A DYNAMIC TRAFFIC ASSIGNMENT FORMULATION THAT ENCAPSULATES THE CELL-TRANSMISSION MODEL , 1999 .

[2]  Markos Papageorgiou,et al.  ALINEA Local Ramp Metering: Summary of Field Results , 1997 .

[3]  Moshe Ben-Akiva,et al.  DEVELOPMENT AND EVALUATION OF A DYNAMIC RAMP METERING CONTROL MODEL , 1997 .

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

[5]  Gordon F. Newell,et al.  A SIMPLIFIED THEORY OF KINEMATIC WAVES , 1991 .

[6]  Hideyuki Kita,et al.  A merging–giveway interaction model of cars in a merging section: a game theoretic analysis , 1999 .

[7]  Carlos F. Daganzo,et al.  Remarks on Traffic Flow Modeling and Its Applications , 1999 .

[8]  G. F. Newell.  A simplified theory of kinematic waves in highway traffic, part II: Queueing at freeway bottlenecks , 1993 .

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

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

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

[12]  E. Isaacson,et al.  Nonlinear resonance in systems of conservation laws , 1992 .

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

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

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

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

[17]  Kerner,et al.  Structure and parameters of clusters in traffic flow. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[19]  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.