Stochastic higher order macroscopic transportation modeling on road networks: managerial Implications[Modélisation stochastique macroscopique d'ordre supérieur du trafic sur les réseaux routiers : implications managériales]

Transport systems place a key role in the development of the economic growth of countries. However, the appearance of autonomous and electric vehicles and the restrictions put in place to limit the diffusion and impacts of Covid-19ain public transport have had particularly a widespread impaction transport problems in particular at junctions. The present research helps to address these problems. This paper is concerned with stochastic traffic flow modeling on road networks, thanks to macroscopic models that belong to the so-called generic class of second order models: the GSOM family. It has been shown that such higher order models can be solved in a Lagrangian framework whose coordinates move with the traffic. The difficulty to use this resolution trick on a network is to deal with Eulerian– fixed –discontinuities such as junctions. The aim of this work is two-fold: first, to propose adapted junction models for stochastic second order macroscopic traffic flow models and second, to solve the resulting model in a moving framework. Some numerical examples are provided to show the efficiency of the approach.