Delayed Traffic Models in Multiple Scales: New Macroscopic Models And Their Numerics
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This thesis shows the derivation of novel macroscopic traffic models with an explicit time delay. For this models of the delayed PDE type, numerical methods are shown and investigated. Furthermore, the models are tested with real data and compared to classical traffic models.
Traffic becomes an ever more important topic in modern days, as it plays a vital role in economics, environmental issues and the daily life of most people. The simulation of traffic with mathematical models dates back to at least the 1950s. In that, microscopic models with explicit time delays, modeling the reaction times of both the driver and the car, are well known.
Starting from them, we derive new macroscopic traffic models, which keep this explicit time delay. This leaves us with partial differential equations with explicit time delay, a hardly investigated type of differential equations.
In this thesis we take a closer look at the analysis and especially the numerics for this models, show some properties of the equations and the numerical discretizations, and compare them to well-known, undelayed models.
Finally, we will fit these models to real data and run simulations, comparing the behavior to undelayed models. Also, we compare the results to real measurements, showing that the simulations are often closer to real world traffic than undelayed simulations.
Traffic becomes an ever more important topic in modern days, as it plays a vital role in economics, environmental issues and the daily life of most people. The simulation of traffic with mathematical models dates back to at least the 1950s. In that, microscopic models with explicit time delays, modeling the reaction times of both the driver and the car, are well known.
Starting from them, we derive new macroscopic traffic models, which keep this explicit time delay. This leaves us with partial differential equations with explicit time delay, a hardly investigated type of differential equations.
In this thesis we take a closer look at the analysis and especially the numerics for this models, show some properties of the equations and the numerical discretizations, and compare them to well-known, undelayed models.
Finally, we will fit these models to real data and run simulations, comparing the behavior to undelayed models. Also, we compare the results to real measurements, showing that the simulations are often closer to real world traffic than undelayed simulations.
| Erscheinungsdatum | 09.04.2021 |
|---|---|
| Zusatzinfo | num., mostly col. illus. and tab. |
| Verlagsort | Stuttgart |
| Sprache | englisch |
| Maße | 148 x 210 mm |
| Themenwelt | Mathematik / Informatik ► Informatik |
| Mathematik / Informatik ► Mathematik ► Analysis | |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Schlagworte | B • Data Fitting • Delayed PDEs • differential calculus & equation • Fraunhofer ITWM • Mathematical Modelling • Mathematiker • Numerical analysis • Numerical Methods • Physiker • Stadtplaner • Traffic Simulation • Verkehrsingenieur • Verkehrsingenieure |
| ISBN-10 | 3-8396-1708-1 / 3839617081 |
| ISBN-13 | 978-3-8396-1708-3 / 9783839617083 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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Buch | Hardcover (2025)
De Gruyter Oldenbourg (Verlag)
CHF 125,90
