Mogno, Caterina (2016) Modeling pedestrian dynamics by means of Discrete Thermostatted Kinetic Theory methods. [Magistrali biennali]
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A novel discrete thermostatted kinetic framework is derived for the modeling of complex adaptive systems subjected to external force field (non-equilibrium system). In order to model the non-equilibrium stationary states of the system, the external force field is coupled to a dissipative term (thermostat). The well-posedness of the new framework is mathematically investigated (local and global existence and uniqueness of solution of the related Cauchy problem) thus allowing the discrete thermostatted framework to be suitable for the derivation of specific models and the related computational analysis. This framework is employed for the modeling of the pedestrians dynamics at the entrance of a metro station. Specifically a model is proposed for analysing the time distribution of the pedestrians approaching at different gates (turnistiles) according to a choice dynamics which depends on the microscopic interactions among the pedestrians (internal dynamics). The microscopic interactions, assumed binary, depend on the local pedestrians density (nonlinear interactions) and follow a game theory approach based on the leader-follower dynamics. The external force field mimics different events that can affect significantly pedestrian internal dynamics (collective hurry, preferential gates recommended, periodic sound signals or evacuation alarms), and the thermostat term allows the conservation of the total number of pedestrians. Numerical simulations are addressed to analyse the system behaviour, and in particular a sensitivity analysis on the parameters and the initial conditions is performed. The results show that the model is able to reproduce qualitatively some known emerging behaviours in the metro station, e.g. flow imposed by leader dynamics, concentration of pedestrians at the central gates, and pedestrians tendency to choose progressively with time all the gates available. Moreover the simulations highlight the capability of the new model to capture non-equilibrium stationary states. Perspectives include the possibility to introduce the spatial and velocity dynamics for taking into account the geometry of the domain of interactions.
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