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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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2016/6902086 |
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| _version_ | 1832562898641092608 |
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| author | Alessandro Corbetta Andrea Tosin |
| author_facet | Alessandro Corbetta Andrea Tosin |
| author_sort | Alessandro Corbetta |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-ac0b5955be5a40c89798d53f7b0661f9 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-ac0b5955be5a40c89798d53f7b0661f92025-02-03T01:21:28ZengWileyAdvances 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 |
| spellingShingle | Alessandro Corbetta Andrea Tosin Comparing First-Order Microscopic and Macroscopic Crowd Models for an Increasing Number of Massive Agents Advances in Mathematical Physics |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2016/6902086 |
| work_keys_str_mv | AT alessandrocorbetta comparingfirstordermicroscopicandmacroscopiccrowdmodelsforanincreasingnumberofmassiveagents AT andreatosin comparingfirstordermicroscopicandmacroscopiccrowdmodelsforanincreasingnumberofmassiveagents |