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From individual behaviour to an evaluation of the collective evolution of crowds along footbridges. (English) Zbl 1360.76038

Summary: This paper proposes a crowd dynamic macroscopic model grounded on microscopic phenomenological observations which are upscaled by means of a formal mathematical procedure. The actual applicability of the model to real-world problems is tested by considering the pedestrian traffic along footbridges, of interest for Structural and Transportation Engineering. The genuinely macroscopic quantitative description of the crowd flow directly matches the engineering need of bulk results. However, three issues beyond the sole modelling are of primary importance: the pedestrian inflow conditions, the numerical approximation of the equations for non trivial footbridge geometries and the calibration of the free parameters of the model on the basis of in situ measurements currently available. These issues are discussed, and a solution strategy is proposed.

MSC:

76A99 Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena
35L65 Hyperbolic conservation laws
35Q70 PDEs in connection with mechanics of particles and systems of particles
90B20 Traffic problems in operations research
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