On the modelling of crowd dynamics by generalized kinetic models

We introduce a new approach for modelling the behavior of pedestrians which borrows techniques from the kinetic theory of rarefied gazes. This approach is based on concepts from the kinetic theory for ‘active particles’. In our modelling of crowd movements, pedestrians are regarded as entities whose microscopic states include a geometric variable (to denote position), a mechanical variable (to denote speed), and a variable to describe the rate of development of individual strategies that influence the collective dynamics. Indeed, the third variable is introduced to account for the ability of individuals to modify their dynamics according to specific objectives and strategies. The equations eventually obtained are a set of nonlinear integro-differential equations of Vlasov or Boltzmann type.