Multiclass first-order traffic model using stochastic fundamental diagrams

The first-order continuum traffic model has been extensively studied in the state-of-the-art of traffic flow theory due to its simplicity and capability to represent many real traffic problems, such as a shock-wave formation. Furthermore, recent extension of the first-order model to multiclass traffic dynamics has revealed some interesting non-linear traffic phenomena such as hysteresis and capacity drop. However, most of the existing first-order continuum models do not display the widely scattered flow–density relationship. We argue in this article that the widely scattered flow–density relationship might be caused by the random variations in driving behaviour. It is shown that both of the hysteresis transitions and the wide scattering can be reproduced by a multiclass first-order model with a stochastic setting in the model parameters. The simulation results support our findings and are in good agreement with the real data.

[1]  Rinaldo M. Colombo,et al.  An $n$-populations model for traffic flow , 2003, European Journal of Applied Mathematics.

[2]  D. Durran.  Numerical Methods for Fluid Dynamics , 2010 .

[3]  Shing Chung Josh Wong,et al.  A multi-class traffic flow model: an extension of LWR model with heterogeneous drivers , 2002 .

[4]  Shing Chung Josh Wong,et al.  A hybrid scheme for solving a multi-class traffic flow model with complex wave breaking , 2008 .

[5]  Chi-Wang Shu,et al.  A weighted essentially non-oscillatory numerical scheme for a multi-class Lighthill-Whitham-Richards traffic flow model , 2003 .

[6]  Lily Elefteriadou,et al.  Probabilistic nature of breakdown at freeway merge junctions , 1995 .

[7]  S. Wong,et al.  A conserved higher-order anisotropic traffic flow model: Description of equilibrium and non-equilibrium flows , 2009 .

[8]  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.

[9]  Hein Botma,et al.  Assessment of Roadway Capacity Estimation Methods , 1996 .

[10]  Nakayama,et al.  Dynamical model of traffic congestion and numerical simulation. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[11]  S. Wong,et al.  Hyperbolicity and kinematic waves of a class of multi-population partial differential equations , 2006, European Journal of Applied Mathematics.

[12]  Dirk Helbing,et al.  Understanding widely scattered traffic flows, the capacity drop, and platoons as effects of variance-driven time gaps. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Daiheng Ni,et al.  Investigation of LWR Model with Flux Function Driven by Random Free Flow Speed , 2008 .

[14]  Werner Brilon,et al.  Reliability of Freeway Traffic Flow: A Stochastic Concept of Capacity , 2005 .

[15]  Dirk Helbing,et al.  Interpreting the wide scattering of synchronized traffic data by time gap statistics. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  D. Helbing,et al.  LETTER TO THE EDITOR: Macroscopic simulation of widely scattered synchronized traffic states , 1999, cond-mat/9901119.

[17]  Ihor Lubashevsky,et al.  Long-lived states in synchronized traffic flow: empirical prompt and dynamical trap model. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Dong Ngoduy,et al.  Multiclass first-order simulation model to explain non-linear traffic phenomena , 2007 .

[19]  R. Sollacher,et al.  Multi-anticipative car-following model , 1999 .

[20]  Dong Ngoduy.  Multiclass first-order modelling of traffic networks using discontinuous flow-density relationships , 2010 .

[21]  Dirk Helbing,et al.  Memory effects in microscopic traffic models and wide scattering in flow-density data. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  A. Soyster,et al.  A STOCHASTIC MODEL OF FLOW VERSUS CONCENTRATION APPLIED TO TRAFFIC ON HILLS , 1973 .

[23]  P. Wagner,et al.  Metastable states in a microscopic model of traffic flow , 1997 .

[24]  Nelson.  Synchronized traffic flow from a modified lighthill-whitman model , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[26]  James H Banks.  Investigation of Some Characteristics of Congested Flow , 1999 .

[27]  Dong Ngoduy.  OPERATIONAL EFFECTS OF ACCELERATION LANE ON MAIN TRAFFIC FLOW AT DISCONTINUITIES , 2008 .