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

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

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...

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Main Authors: Alessandro Corbetta, Andrea Tosin
Format: Article
Language:English
Published: Hindawi Limited 2016-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2016/6902086
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spelling doaj-ac0b5955be5a40c89798d53f7b0661f92021-07-02T01:48:05ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392016-01-01201610.1155/2016/69020866902086Comparing First-Order Microscopic and Macroscopic Crowd Models for an Increasing Number of Massive AgentsAlessandro Corbetta0Andrea Tosin1Department of Structural and Geotechnical Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, ItalyIstituto per le Applicazioni del Calcolo “M. Picone”, Consiglio Nazionale delle Ricerche, Via dei Taurini 19, 00185 Roma, ItalyA 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.http://dx.doi.org/10.1155/2016/6902086
collection DOAJ
language English
format Article
sources DOAJ
author Alessandro Corbetta
Andrea Tosin
spellingShingle Alessandro Corbetta
Andrea Tosin
Comparing First-Order Microscopic and Macroscopic Crowd Models for an Increasing Number of Massive Agents
Advances in Mathematical Physics
author_facet Alessandro Corbetta
Andrea Tosin
author_sort Alessandro Corbetta
title Comparing First-Order Microscopic and Macroscopic Crowd Models for an Increasing Number of Massive Agents
title_short Comparing First-Order Microscopic and Macroscopic Crowd Models for an Increasing Number of Massive Agents
title_full Comparing First-Order Microscopic and Macroscopic Crowd Models for an Increasing Number of Massive Agents
title_fullStr Comparing First-Order Microscopic and Macroscopic Crowd Models for an Increasing Number of Massive Agents
title_full_unstemmed Comparing First-Order Microscopic and Macroscopic Crowd Models for an Increasing Number of Massive Agents
title_sort comparing first-order microscopic and macroscopic crowd models for an increasing number of massive agents
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2016-01-01
description 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.
url http://dx.doi.org/10.1155/2016/6902086
work_keys_str_mv AT alessandrocorbetta comparingfirstordermicroscopicandmacroscopiccrowdmodelsforanincreasingnumberofmassiveagents
AT andreatosin comparingfirstordermicroscopicandmacroscopiccrowdmodelsforanincreasingnumberofmassiveagents
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