Dynamic Traffic Network Model and Time-Dependent Braess’ Paradox
We propose a dynamic traffic network model and give the equilibrium condition and the equivalent variational inequality of the network. In this model, instead of the influence of inflow rate and output rate on the link congestion, the influence of the adjacent links at the same paths is considered;...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2014/802129 |
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| _version_ | 1832566418035441664 |
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| author | Chunxue Zhao |
| author_facet | Chunxue Zhao |
| author_sort | Chunxue Zhao |
| collection | DOAJ |
| description | We propose a dynamic traffic network model and give the equilibrium condition and the equivalent variational inequality of the network. In this model, instead of the influence of inflow rate and output rate on the link congestion, the influence of the adjacent links at the same paths is considered; in this case, the equivalence between the equilibrium condition and the variational inequality is proved. Then we take an example about the paradox using the variational inequality and find that the probability and the severity that Braess’ paradox occurs change with the influence of other links changing. Subsequently, we discuss the influence of other links on whether the adding link works under the dynamic system optimal. At last, we give the relationship between the total congestion under dynamic user equilibrium and that under dynamic system optimal. The results imply that we should take some methods and adjust the interaction between links rationally with the dynamic change of traffic situations. |
| format | Article |
| id | doaj-art-89100b5a47024bf48581c86ede279d3a |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-89100b5a47024bf48581c86ede279d3a2025-02-03T01:04:18ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2014-01-01201410.1155/2014/802129802129Dynamic Traffic Network Model and Time-Dependent Braess’ ParadoxChunxue Zhao0School of Mathematics and Statistics, Anyang Normal University, Anyang 455000, ChinaWe propose a dynamic traffic network model and give the equilibrium condition and the equivalent variational inequality of the network. In this model, instead of the influence of inflow rate and output rate on the link congestion, the influence of the adjacent links at the same paths is considered; in this case, the equivalence between the equilibrium condition and the variational inequality is proved. Then we take an example about the paradox using the variational inequality and find that the probability and the severity that Braess’ paradox occurs change with the influence of other links changing. Subsequently, we discuss the influence of other links on whether the adding link works under the dynamic system optimal. At last, we give the relationship between the total congestion under dynamic user equilibrium and that under dynamic system optimal. The results imply that we should take some methods and adjust the interaction between links rationally with the dynamic change of traffic situations.http://dx.doi.org/10.1155/2014/802129 |
| spellingShingle | Chunxue Zhao Dynamic Traffic Network Model and Time-Dependent Braess’ Paradox Discrete Dynamics in Nature and Society |
| title | Dynamic Traffic Network Model and Time-Dependent Braess’ Paradox |
| title_full | Dynamic Traffic Network Model and Time-Dependent Braess’ Paradox |
| title_fullStr | Dynamic Traffic Network Model and Time-Dependent Braess’ Paradox |
| title_full_unstemmed | Dynamic Traffic Network Model and Time-Dependent Braess’ Paradox |
| title_short | Dynamic Traffic Network Model and Time-Dependent Braess’ Paradox |
| title_sort | dynamic traffic network model and time dependent braess paradox |
| url | http://dx.doi.org/10.1155/2014/802129 |
| work_keys_str_mv | AT chunxuezhao dynamictrafficnetworkmodelandtimedependentbraessparadox |