Analysis of a Stochastic Switching Model of Freeway Traffic Incidents
This paper introduces a model for freeway traffic dynamics under stochastic capacity-reducing incidents, and provides insights for freeway incident management by analyzing long-time (stability) properties of the proposed model. Incidents on a multicell freeway are modeled by reduction in capacity at...
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| Format: | Article |
| Language: | English |
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Institute of Electrical and Electronics Engineers (IEEE)
2020
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| Online Access: | https://hdl.handle.net/1721.1/125657 |
| _version_ | 1811074695342063616 |
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| author | Jin, Li Amin, Saurabh |
| author2 | Massachusetts Institute of Technology. Department of Civil and Environmental Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Civil and Environmental Engineering Jin, Li Amin, Saurabh |
| author_sort | Jin, Li |
| collection | MIT |
| description | This paper introduces a model for freeway traffic dynamics under stochastic capacity-reducing incidents, and provides insights for freeway incident management by analyzing long-time (stability) properties of the proposed model. Incidents on a multicell freeway are modeled by reduction in capacity at the affected freeway sections, which occur and clear according to a Markov chain. We develop conditions under which the traffic queue induced by stochastic incidents is bounded. A necessary condition is that the demand must not exceed the time-average capacity adjusted for spillback. A sufficient condition, in the form of a set of bilinear inequalities, is also established by constructing a Lyapunov function and applying the classical Foster-Lyapunov drift condition. Both conditions can be easily verified for realistic instances of the stochastic incident model. Our analysis relies on the construction of a globally attracting invariant set, and exploits the properties of the traffic flow dynamics. We use our results to analyze the impact of stochastic capacity fluctuation (frequency, intensity, and spatial correlation) on the throughput of a freeway segment. |
| first_indexed | 2024-09-23T09:53:53Z |
| format | Article |
| id | mit-1721.1/125657 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T09:53:53Z |
| publishDate | 2020 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/1256572022-09-30T17:33:55Z Analysis of a Stochastic Switching Model of Freeway Traffic Incidents Jin, Li Amin, Saurabh Massachusetts Institute of Technology. Department of Civil and Environmental Engineering This paper introduces a model for freeway traffic dynamics under stochastic capacity-reducing incidents, and provides insights for freeway incident management by analyzing long-time (stability) properties of the proposed model. Incidents on a multicell freeway are modeled by reduction in capacity at the affected freeway sections, which occur and clear according to a Markov chain. We develop conditions under which the traffic queue induced by stochastic incidents is bounded. A necessary condition is that the demand must not exceed the time-average capacity adjusted for spillback. A sufficient condition, in the form of a set of bilinear inequalities, is also established by constructing a Lyapunov function and applying the classical Foster-Lyapunov drift condition. Both conditions can be easily verified for realistic instances of the stochastic incident model. Our analysis relies on the construction of a globally attracting invariant set, and exploits the properties of the traffic flow dynamics. We use our results to analyze the impact of stochastic capacity fluctuation (frequency, intensity, and spatial correlation) on the throughput of a freeway segment. National Science Foundation (U.S.) (Grant 1239054) National Science Foundation (U.S.) (CAREER Award CNS 1453126) 2020-06-03T18:51:49Z 2020-06-03T18:51:49Z 2019-04 2020-05-12T18:46:28Z Article http://purl.org/eprint/type/JournalArticle 0018-9286 1558-2523 https://hdl.handle.net/1721.1/125657 Jin, Li and Saurabh Amin. “Analysis of a Stochastic Switching Model of Freeway Traffic Incidents.” IEEE Transactions on Automatic Control 64 (2019): 1093-1108. en https://dx.doi.org/10.1109/TAC.2018.2822872 IEEE Transactions on Automatic Control Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Institute of Electrical and Electronics Engineers (IEEE) arXiv |
| spellingShingle | Jin, Li Amin, Saurabh Analysis of a Stochastic Switching Model of Freeway Traffic Incidents |
| title | Analysis of a Stochastic Switching Model of Freeway Traffic Incidents |
| title_full | Analysis of a Stochastic Switching Model of Freeway Traffic Incidents |
| title_fullStr | Analysis of a Stochastic Switching Model of Freeway Traffic Incidents |
| title_full_unstemmed | Analysis of a Stochastic Switching Model of Freeway Traffic Incidents |
| title_short | Analysis of a Stochastic Switching Model of Freeway Traffic Incidents |
| title_sort | analysis of a stochastic switching model of freeway traffic incidents |
| url | https://hdl.handle.net/1721.1/125657 |
| work_keys_str_mv | AT jinli analysisofastochasticswitchingmodeloffreewaytrafficincidents AT aminsaurabh analysisofastochasticswitchingmodeloffreewaytrafficincidents |