An introduction to the modeling of crowd dynamics

In this chapter we begin the discussion about crowd dynamics from an informal phenomenological point of view. In particular, we put in evidence how simple interaction rules adopted independently by pedestrians generate, at a collective level, complex group behaviors featuring various forms of self-organization. Bearing in mind the ultimate goal of the book, which is mathematical modeling, we promote the idea that understanding such basic behavioral rules contributes to the modeling at all scales, also those not directly focused on single individuals. In the light of these arguments, we critically analyze the main scales of observation and representation which are typically used in mathematical modeling, namely the microscopic, the macroscopic, and the mesoscopic (or kinetic) scale. For each of them we discuss the advantages/drawbacks in catching/losing specific features of crowd dynamics, with a view also to the interplay with the available experimental knowledge about crowds. Finally we elucidate the role of the book in this cultural framework and we give reading directions through the various chapters targeted to a few different kinds of readerships.