Congestions and Spectral Transition in Time-Lagged Correlations of Motorway Traffic
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
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| _version_ | 1866909274705231872 |
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| author | Hollbeck, Gabor B. Pilarczyk, René Wang, Shanshan Schreckenberg, Michael Guhr, Thomas |
| author_facet | Hollbeck, Gabor B. Pilarczyk, René Wang, Shanshan Schreckenberg, Michael Guhr, Thomas |
| contents | The congestion of a motorway section is propagated to its neighbouring sections, leading to correlations. The resulting correlation matrix encodes the information on congestion. Here, we study symmetrized time-lagged correlations and show how their spectral properties reveal congestion durations. We carry out an empirical analysis and find a transition behavior for the dominant eigenvalue as function of the time lag. Furthermore, we set up a numerical simulation model for indicator time series of traffic phases as well as a simplified model that we treat analytically. We consider various scenarios. Our results reveal a nonlinear relation between the spectral transition and the congestion duration. In our simplified model, we derive this relation analytically. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_12051 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Congestions and Spectral Transition in Time-Lagged Correlations of Motorway Traffic Hollbeck, Gabor B. Pilarczyk, René Wang, Shanshan Schreckenberg, Michael Guhr, Thomas Physics and Society Data Analysis, Statistics and Probability The congestion of a motorway section is propagated to its neighbouring sections, leading to correlations. The resulting correlation matrix encodes the information on congestion. Here, we study symmetrized time-lagged correlations and show how their spectral properties reveal congestion durations. We carry out an empirical analysis and find a transition behavior for the dominant eigenvalue as function of the time lag. Furthermore, we set up a numerical simulation model for indicator time series of traffic phases as well as a simplified model that we treat analytically. We consider various scenarios. Our results reveal a nonlinear relation between the spectral transition and the congestion duration. In our simplified model, we derive this relation analytically. |
| title | Congestions and Spectral Transition in Time-Lagged Correlations of Motorway Traffic |
| topic | Physics and Society Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2312.12051 |