Non-memoryless Pedestrian Flow in a Crowded Environment with Target Sets

This work deals with the problem of managing the excursionist flow in historic 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 func- tion 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. The problem is analized in the framework of Hamilton-Jacobi/transport equations, as it is standard in mean field games theory. In addition, to provide a starting datum for iterative solution algorithms, we introduce a second model in the framework of mathematical programming. For this second approach we present some numerical experiments.