Probabilistic Modeling of Car Traffic Accidents
Uložené v:
| Názov: | Probabilistic Modeling of Car Traffic Accidents |
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| Autori: | Simone Göttlich, Thomas Schillinger, Andrea Tosin |
| Zdroj: | SIAM Journal on Applied Mathematics. 85:1099-1120 |
| Publication Status: | Preprint |
| Informácie o vydavateľovi: | Society for Industrial & Applied Mathematics (SIAM), 2025. |
| Rok vydania: | 2025 |
| Predmety: | Physics - Physics and Society, 65C20, 76A30, Probability (math.PR), FOS: Mathematics, FOS: Physical sciences, Traffic flow, random accidents, stochastic process, numerical simulations, Physics and Society (physics.soc-ph), Mathematics - Probability |
| Popis: | We introduce a counting process to model the random occurrence in time of car traffic accidents, taking into account some aspects of the self-excitation typical of this phenomenon. By combining methods from probability and differential equations, we study this stochastic process in terms of its statistical moments and large-time trend. Moreover, we derive analytically the probability density functions of the times of occurrence of traffic accidents and of the time elapsing between two consecutive accidents. Finally, we demonstrate the suitability of our modelling approach by means of numerical simulations, which address also a comparison with real data of weekly trends of traffic accidents. |
| Druh dokumentu: | Article |
| Popis súboru: | application/pdf |
| Jazyk: | English |
| ISSN: | 1095-712X 0036-1399 |
| DOI: | 10.1137/24m1698262 |
| DOI: | 10.48550/arxiv.2410.00446 |
| DOI: | 10.13140/rg.2.2.30080.85769/1 |
| DOI: | 10.13140/rg.2.2.30080.85769 |
| Prístupová URL adresa: | http://arxiv.org/abs/2410.00446 https://hdl.handle.net/11583/3000213 https://epubs.siam.org/doi/10.1137/24M1698262 https://doi.org/10.1137/24M1698262 |
| Rights: | arXiv Non-Exclusive Distribution |
| Prístupové číslo: | edsair.doi.dedup.....39e102835eadc4d62f280b0cb95fa9a5 |
| Databáza: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstrakt: | We introduce a counting process to model the random occurrence in time of car traffic accidents, taking into account some aspects of the self-excitation typical of this phenomenon. By combining methods from probability and differential equations, we study this stochastic process in terms of its statistical moments and large-time trend. Moreover, we derive analytically the probability density functions of the times of occurrence of traffic accidents and of the time elapsing between two consecutive accidents. Finally, we demonstrate the suitability of our modelling approach by means of numerical simulations, which address also a comparison with real data of weekly trends of traffic accidents. |
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| ISSN: | 1095712X 00361399 |
| DOI: | 10.1137/24m1698262 |