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.