Teorie a numerické řešení dopravních modelů
| Název práce v češtině: | Teorie a numerické řešení dopravních modelů |
|---|---|
| Název v anglickém jazyce: | Theory and numerical solution of traffic models |
| Klíčová slova anglicky: | Traffic flow models, conservation laws, traffic networks |
| Akademický rok vypsání: | 2018/2019 |
| Typ práce: | disertační práce |
| Jazyk práce: | |
| Ústav: | Katedra numerické matematiky (32-KNM) |
| Vedoucí / školitel: | doc. RNDr. Václav Kučera, Ph.D. |
| Řešitel: | skrytý - zadáno a potvrzeno stud. odd. |
| Datum přihlášení: | 27.09.2018 |
| Datum zadání: | 27.09.2018 |
| Datum potvrzení stud. oddělením: | 29.10.2018 |
| Zásady pro vypracování |
| Traffic flows describe the movement of vehicles on individual roads or their networks. Traffic flows can be described on the microscopic level, where individual vehicles are traced, kinetic (mesoscopic) level, where the flow is described by a density distribution function and finally the macroscopic description, where the flow is described by quantities such as density or velocity. Mathematically, the corresponding descriptions are systems of ordinary equations, kinetic Boltzmann-type equations and partial differential equations - usually first order hyperbolic systems. However other descriptions exist, e.g. using cellular automata.
The goal of the work is to study various traffic flow models in various descriptions, devise efficient and robust numerical methods for the corresponding equations and compare the outcomes between various models, their levels of description and compare to real data on single roads and networks. |
| Seznam odborné literatury |
| M. Garavello, B. Piccoli: Traffic Flow on Networks, American Institute of Mathematical Sciences, 2006.
P. Kachroo, S. Sastry: Traffic Flow Theory - Mathematical Framework, University of California Berkeley. B. S. Kerner: Introduction to Modern Traffic Flow Theory and Control, Springer, 2009. M. Treiber, A. Kesting: Traffic Flow Dynamics - Data, Models and Simulation, Springer, 2012. R. J. LeVeque: Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, 2002. |