Non-memoryless pedestrian flow in a crowded environment with target sets

This work deals with the problem of managing the excursionist flow in historical cities. Venice is considered as a case study. There, in high season, thousands of excursionists arrive by train in the morning, spend the day visiting different sites, reach again the train station in late afternoon, and leave. With the idea of avoiding congestion by directing excursionists along different routes, a mean field model is introduced. Network/switching is used to describe the excursionists costs as a function of their position taking into consideration whether they have already visited a site or not, i.e., allowing excursionists to have memory of the past when making decisions. In particular, we analyze the model in the framework of Hamilton-Jacobi/transport equations, as it is standard in mean field games theory. Finally, to provide a starting datum for iterative solution algorithms, a second model is introduced in the framework of mathematical programming. For this second approach, some numerical experiments are presented.