A traffic model aware of real time data

Nowadays, traffic monitoring systems have access to real time data, e.g. through GPS devices. We propose a new traffic model able to take into account these data and, hence, able to describe the effects of unpredictable accidents. The well-posedness of this model is proved and numerical integrations show qualitative features of the resulting solutions. As a further motivation for the use of real time data, we show that the inverse problem for the Lighthill–Whitham and Richards (LWR) model is ill-posed.

[1]  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.

[2]  Huijiang Zhao.  FIRST ORDER QUASILINEAR EQUATIONS IN SEVERAL INDEPENDENT VARIABLES WITH SINGULAR INITIAL DATA Lp(p , 1996 .

[3]  M J Lighthill,et al.  ON KINEMATIC WAVES.. , 1955 .

[4]  R. Colombo,et al.  On general balance laws with boundary , 2008, 0810.5246.

[5]  Benedetto Piccoli,et al.  Vehicular Traffic: A Review of Continuum Mathematical Models , 2009, Encyclopedia of Complexity and Systems Science.

[6]  A. Bressan.  Hyperbolic systems of conservation laws : the one-dimensional Cauchy problem , 2000 .

[7]  E. Panov.  Erratum to: Existence and Strong Pre-compactness Properties for Entropy Solutions of a First-Order Quasilinear Equation with Discontinuous Flux , 2010 .

[8]  Bin Ran,et al.  Particle filter based traffic state estimation using cell phone network data , 2006, 2006 IEEE Intelligent Transportation Systems Conference.

[9]  F. Marcellini.  Free-congested and micro-macro descriptions of traffic flow , 2014 .

[10]  N. Risebro,et al.  On the uniqueness and stability of entropy solutions of nonlinear degenerate parabolic equations with rough coefficients , 2003 .

[11]  Angelo Alessandri,et al.  Estimation of freeway traffic variables using information from mobile phones , 2003, Proceedings of the 2003 American Control Conference, 2003..

[12]  A. Bressan.  Hyperbolic Systems of Conservation Laws , 1999 .

[13]  R. Colombo,et al.  A mixed ODE–PDE model for vehicular traffic , 2014, 1402.5097.

[14]  B. Piccoli,et al.  COUPLING OF MICROSCOPIC AND MACROSCOPIC TRAFFIC MODELS AT BOUNDARIES , 2010 .

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

[16]  R. LeVeque.  Numerical methods for conservation laws , 1990 .

[17]  A. Bayen,et al.  A traffic model for velocity data assimilation , 2010 .

[18]  Alexandre M. Bayen,et al.  Optimal Sensor Placement for Freeway Travel Time Estimation , 2009 .

[19]  N. Bellomo,et al.  On the multiscale modeling of vehicular traffic: From kinetic to hydrodynamics , 2014 .

[20]  Mauro Garavello,et al.  Flows on networks: recent results and perspectives , 2014 .

[21]  L1-Theory of Scalar Conservation Law with Continuous Flux Function☆ , 2000 .

[22]  E. Panov.  Existence and Strong Pre-compactness Properties for Entropy Solutions of a First-Order Quasilinear Equation with Discontinuous Flux , 2010 .

[23]  Axel Klar,et al.  Traffic flow: models and numerics , 2004 .

[24]  Nicola Bellomo,et al.  On the Modeling of Traffic and Crowds: A Survey of Models, Speculations, and Perspectives , 2011, SIAM Rev..