Second-Order Fluid Dynamics Models for Travel Times in Dynamic Transportation Networks
In recent years, traffic congestion in transportation networks has grown rapidly and has become an acute problem. The impetus for studying this problem has been further strengthened due to the fast growing field of Intelligent Vehicle Highway Systems (IVHS). Therefore, it is critical to investigat...
| Main Authors: | , |
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| Format: | Article |
| Language: | en_US |
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2003
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| Online Access: | http://hdl.handle.net/1721.1/4011 |
| _version_ | 1811082637055361024 |
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| author | Kachani, Soulaymane Perakis, Georgia |
| author_facet | Kachani, Soulaymane Perakis, Georgia |
| author_sort | Kachani, Soulaymane |
| collection | MIT |
| description | In recent years, traffic congestion in transportation networks has grown rapidly and has become an acute problem. The impetus for studying this problem has been further strengthened due to the fast growing field of Intelligent Vehicle Highway Systems (IVHS). Therefore, it is critical to investigate and understand its nature and address questions of the type: how are traffic patterns formed? and how can traffic congestion be alleviated? Understanding drivers' travel times is key behind this problem. In this paper, we present macroscopic models for determining analytical forms for travel times. We take a fluid dynamics approach by noticing that traffic macroscopically behaves like a fluid. Our contributions in this work are the following: (i) We propose two second-order non-separable macroscopic models for analytically estimating travel time functions: the Polynomial Travel Time (PTT) Model and the Exponential Travel Time (ETT) Model. These models generalize the models proposed by Kachani and Perakis as they incorporate second-order effects such as reaction of drivers to upstream and downstream congestion as well as second-order link interaction effects. (ii) Based on piecewise linear and piecewise quadratic approximations of the departure flow rates, we propose different classes of travel time functions for the first-order separable PTT and ETT models, and present the relationship between these functions. (iii) We show how the analysis of the first-order separable PTT Model extends to the second-order model with non-separable velocity functions for acyclic networks. (iv) Finally, we analyze the second-order separable ETT model where the queue propagation term - corresponding to the reaction of drivers to upstream congestion or decongestion - is not neglected. We are able to reduce the analysis to a Burgers equation and then to the more tractable heat equation. |
| first_indexed | 2024-09-23T12:06:13Z |
| format | Article |
| id | mit-1721.1/4011 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:06:13Z |
| publishDate | 2003 |
| record_format | dspace |
| spelling | mit-1721.1/40112019-04-12T08:07:56Z Second-Order Fluid Dynamics Models for Travel Times in Dynamic Transportation Networks Kachani, Soulaymane Perakis, Georgia dynamic traffic flow dynamic travel time fluid models In recent years, traffic congestion in transportation networks has grown rapidly and has become an acute problem. The impetus for studying this problem has been further strengthened due to the fast growing field of Intelligent Vehicle Highway Systems (IVHS). Therefore, it is critical to investigate and understand its nature and address questions of the type: how are traffic patterns formed? and how can traffic congestion be alleviated? Understanding drivers' travel times is key behind this problem. In this paper, we present macroscopic models for determining analytical forms for travel times. We take a fluid dynamics approach by noticing that traffic macroscopically behaves like a fluid. Our contributions in this work are the following: (i) We propose two second-order non-separable macroscopic models for analytically estimating travel time functions: the Polynomial Travel Time (PTT) Model and the Exponential Travel Time (ETT) Model. These models generalize the models proposed by Kachani and Perakis as they incorporate second-order effects such as reaction of drivers to upstream and downstream congestion as well as second-order link interaction effects. (ii) Based on piecewise linear and piecewise quadratic approximations of the departure flow rates, we propose different classes of travel time functions for the first-order separable PTT and ETT models, and present the relationship between these functions. (iii) We show how the analysis of the first-order separable PTT Model extends to the second-order model with non-separable velocity functions for acyclic networks. (iv) Finally, we analyze the second-order separable ETT model where the queue propagation term - corresponding to the reaction of drivers to upstream congestion or decongestion - is not neglected. We are able to reduce the analysis to a Burgers equation and then to the more tractable heat equation. Singapore-MIT Alliance (SMA) 2003-12-23T02:58:52Z 2003-12-23T02:58:52Z 2002-01 Article http://hdl.handle.net/1721.1/4011 en_US High Performance Computation for Engineered Systems (HPCES); 571373 bytes application/pdf application/pdf |
| spellingShingle | dynamic traffic flow dynamic travel time fluid models Kachani, Soulaymane Perakis, Georgia Second-Order Fluid Dynamics Models for Travel Times in Dynamic Transportation Networks |
| title | Second-Order Fluid Dynamics Models for Travel Times in Dynamic Transportation Networks |
| title_full | Second-Order Fluid Dynamics Models for Travel Times in Dynamic Transportation Networks |
| title_fullStr | Second-Order Fluid Dynamics Models for Travel Times in Dynamic Transportation Networks |
| title_full_unstemmed | Second-Order Fluid Dynamics Models for Travel Times in Dynamic Transportation Networks |
| title_short | Second-Order Fluid Dynamics Models for Travel Times in Dynamic Transportation Networks |
| title_sort | second order fluid dynamics models for travel times in dynamic transportation networks |
| topic | dynamic traffic flow dynamic travel time fluid models |
| url | http://hdl.handle.net/1721.1/4011 |
| work_keys_str_mv | AT kachanisoulaymane secondorderfluiddynamicsmodelsfortraveltimesindynamictransportationnetworks AT perakisgeorgia secondorderfluiddynamicsmodelsfortraveltimesindynamictransportationnetworks |