Abstract
This paper proposes a critical analysis of the literature addressed to modelling and simulations of human crowds with the aim of selecting the most appropriate scale out of the microscopic (individual based), mesoscopic (kinetic), and macroscopic (hydrodynamical) approaches. The selection is made focusing on possible applications of the model. In particular, model validation and safety problems, where validation consists of studying the ability of models to depict empirical data and observed emerging behaviors. The contents of the paper look forward to computational applications related to the flow crowds on the Jamarat bridge.
Highlights
We look forward to computational applications related to the flow of crowds and safety problems on the Jamarat bridge to be treated in a forthcoming paper
The answers to the three key questions will pervade our paper consistently with the phenomenological interpretation of crowd dynamics which is delivered by the aforementioned answers and subsequent reasonings
This subsection expands the brief concepts on model validation introduced in Section 2 referring to the rationale developed in [16] with focus on the kinetic theory approach
Summary
Human crowds of very many individuals, as it is known, occur in venues characterized by several interconnected areas, each of them presenting different geometrical and qualitative features. The answers to the three key questions will pervade our paper consistently with the phenomenological interpretation of crowd dynamics which is delivered by the aforementioned answers and subsequent reasonings After these introductory reasonings, the rationale of a possible approach to modelling can be defined independently from the specific scale which is adopted towards the derivation of mathematical tools. Let us define the complexity features of crowds which have been object in [14] of sharp reasonings: Strategy: Individual walkers can develop strategies which take into account the geometry of the venue and the interactions with the surrounding walkers. All aforementioned features should be taken into account, as far as it is possible, in the selection of the representation and modelling scale and subsequently in the derivation of mathematical and computational tools.
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