Bridging discrete and continuous differential models of crowd dynamics : a fundamental-diagram-aided comparative study

In this paper we exploit a recently introduced multiscale mathematical method, based on the measure theory, for bridging discrete and continuous dynamical systems modeling pedestrian traffic. The main goal is to establish a minimal common background allowing for qualitative and quantitative comparisons of models which are heterogeneous in their mathematical formalization. Specifically, such comparisons are driven by fundamental diagrams, which the proposed multiscale method can derive a posteriori, as a result of low scale interactions among pedestrians, in both discrete and continuous frameworks.