A study on multi-resolution scheme of macroscopic-microscopic traffic simulation model

Multi-Resolution traffic flow schemes, coupling a microscopic (vehicle based), mesoscopic (cell based) and macroscopic (flow based) representations of traffic flow may be a useful tool to better understand and utilize the relationships between the various types of representation. The paper proposes a new classification of traffic model which is according to the representation scale and the behavioural law firstly. In addition, it shows that the LWR model which is a macroscopic continuum model can be numerically solved in Weighted Essentially Non-Oscillatory (WENO) scheme. Furthermore, the paper mainly studies the hybrid scheme which can couple a macroscopic model (LWR) and a microscopic model (Wiedemann). Simple transformation methods are analyzed to translate the variables parameters between both models. Finally, simulation results show that two shock waves (stopping-starting wave) can propagate along two models differently described. The hybrid scheme can keep the result consistency between the both models.

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

[2]  Haris N. Koutsopoulos,et al.  Hybrid Mesoscopic-Microscopic Traffic Simulation , 2004 .

[3]  Ludovic Leclercq,et al.  Hybridization of a class of "second order" models of traffic flow , 2007, Simul. Model. Pract. Theory.

[4]  Axel Klar,et al.  Derivation of Continuum Traffic Flow Models from Microscopic Follow-the-Leader Models , 2002, SIAM J. Appl. Math..

[5]  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.

[6]  J.-B. Lesort,et al.  Various Scales for Traffic Flow Representation: Some Reflections , 2005 .

[7]  Carlos F. Daganzo,et al.  On the Numerical Treatment of Moving Bottlenecks , 2003 .

[8]  Jean-François Gabard,et al.  Towards an hybrid macro-micro traffic flow simulation model , 2000 .

[9]  W Leutzbach,et al.  DEVELOPMENT AND APPLICATIONS OF TRAFFIC SIMULATION MODELS AT THE KARLSRUHE INSTITUT FUR VERKEHRWESEN , 1986 .

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

[11]  Sze Chun Wong,et al.  A weighted essentially non-oscillatory numerical scheme for a multi-class traffic flow model on an inhomogeneous highway , 2006, J. Comput. Phys..

[12]  Dirk Helbing,et al.  Macroscopic Simulation of Open Systems and Micro-Macro Link , 2000 .

[13]  Jean-Baptiste Lesort,et al.  Mixing Microscopic and Macroscopic Representations of Traffic Flow: Hybrid Model Based on Lighthill–Whitham–Richards Theory , 2003 .

[14]  M. Lighthill,et al.  On kinematic waves I. Flood movement in long rivers , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[15]  Ludovic Leclercq,et al.  Hybrid approaches to the solutions of the "Lighthill-Whitham-Richards" model , 2007 .

[16]  Jiang Zhang,et al.  Hybrid Mesoscopic-Microscopic Traffic Simulation Model: Design, Implementation, and Computational Analysis , 2006 .

[17]  Elsevier Sdol.  Transportation Research Part B: Methodological , 2009 .

[18]  Sun Jian,et al.  A Multiple Representation Entity-Based Approach to Hybrid Traffic Simulation Model , 2008, 2008 International Conference on Information Management, Innovation Management and Industrial Engineering.