Journal of Engineering Mathematics

, Volume 101, Issue 1, pp 153–173 | Cite as

From individual behaviour to an evaluation of the collective evolution of crowds along footbridges

  • Luca Bruno
  • Alessandro Corbetta
  • Andrea Tosin


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.


Collective evolution Continuous crowd models Footbridges Individual behaviour 

Mathematics Subject Classification

35L65 35Q70 90B20 



The work of A. Corbetta was supported by a Lagrange Foundation PhD scholarship.


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of Architecture and DesignPolitecnico di TorinoTurinItaly
  2. 2.Department of Structural and Geotechnical EngineeringPolitecnico di TorinoTurinItaly
  3. 3.Department of Mathematics and Computer Science, CASA - Centre for Analysis, Scientific Computing and ApplicationsEindhoven University of TechnologyEindhovenThe Netherlands
  4. 4.Istituto per le Applicazioni del Calcolo “M. Picone”Consiglio Nazionale delle RicercheRomeItaly

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