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Comparing First‐Order Microscopic and Macroscopic Crowd Models for an Increasing Number of Massive Agents

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  • Alessandro Corbetta
  • Andrea Tosin

Abstract

A comparison between first‐order microscopic and macroscopic differential models of crowd dynamics is established for an increasing number N of pedestrians. The novelty is the fact of considering massive agents, namely, particles whose individual mass does not become infinitesimal when N grows. This implies that the total mass of the system is not constant but grows with N. The main result is that the two types of models approach one another in the limit N → ∞, provided the strength and/or the domain of pedestrian interactions are properly modulated by N at either scale. This is consistent with the idea that pedestrians may adapt their interpersonal attitudes according to the overall level of congestion.

Suggested Citation

  • Alessandro Corbetta & Andrea Tosin, 2016. "Comparing First‐Order Microscopic and Macroscopic Crowd Models for an Increasing Number of Massive Agents," Advances in Mathematical Physics, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnlamp:v:2016:y:2016:i:1:n:6902086
    DOI: 10.1155/2016/6902086
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    References listed on IDEAS

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    1. Francesco Zanlungo & Tetsushi Ikeda & Takayuki Kanda, 2012. "A Microscopic “Social Norm” Model to Obtain Realistic Macroscopic Velocity and Density Pedestrian Distributions," PLOS ONE, Public Library of Science, vol. 7(12), pages 1-10, December.
    2. Hughes, Roger L., 2002. "A continuum theory for the flow of pedestrians," Transportation Research Part B: Methodological, Elsevier, vol. 36(6), pages 507-535, July.
    3. Anders Johansson & Dirk Helbing & Pradyumn K. Shukla, 2007. "Specification Of The Social Force Pedestrian Model By Evolutionary Adjustment To Video Tracking Data," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 10(supp0), pages 271-288.
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