Modeling of Traffic Systems

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

The course is devoted to traffic systems modeling and statistics used for microscopic and macroscopic analysis of traffic sample. Selected models are analyzed with respect to random matrix theory.

Requirements:

Basic course of Equation of Mathematical Physics (in the extent of the courses 01RMF held at the FNSPE CTU in Prague).

Syllabus of lectures:

Introduction to the random matrix theory - random matrices, eigenvalue density, level spacing, spectral unfolding, spectral rigidity. Dysons? gases - thermal essence of Dysons? gases, connection to random matrix theory, short-range and long-range potential, Dyson?s Coulomb gas, traffic potentials, microscopic structure of thermal equilibrium, Fokker-Planck traffic equation. Traffic system - definitions, macroscopic characteristics, macroscopic characteristics, fundamentals of traffic theory, alternatives in traffic system description. Traffic data processing - elementary statistical analysis of traffic sample, principles of traffic data measurements.

Traffic models - IDM (Intelligent Driver Model), cellular modeling (Nagel-Schreckenberg model, ASEP model and its alternatives), nonlinear modeling, traffic flow modeled by granular fluid, thermodynamic model. Detailed microscopic structure analysis of chosen models - headway distribution and spectral rigidity for NaSch, TASEP and thermodynamic traffic gas models, analytic derivations, comparison with real data. Psychological aspects of traffic - distance perception, row effect, driver?s psychic condition analysis, direct and indirect detection of driver?s vigilance.

Systems related to traffic systems - pedestrian model, crowd model, panic modeling, selected economic systems, transport systems, EEG signal analysis using random matrix theory.

Syllabus of tutorials:

Fundamental terms from traffic modeling 2. Definitions of microscopic and macroscopic statistics used for traffic analyses 3. Using selected models for traffic flow modeling 4. Representation of driver?s psychological condition in traffic models.

Study Objective:

Knowledge: different types of traffic models, traffic flow modeling principles and fundamental statistics and distributions. Skills: Traffic sample diagnostic using selected models including calculation of microscopic and macroscopic statistics.

Study materials:

Key references:

[1] D.Helbing: Traffic and related self-driven many-particle systems, Rev. Mod. Phys. 73 (2001), 1064 - 1141,

[2] D. Chowdhury, L. Santen, A. Schadschneider, Statistical Physics of Vehicular Traffic and Some Related Systems, Physics Reports 329, (2000) 119

Recommended references:

[1] M. Tabor, Chaos and Integrability in Nonlinear Dynamics: An Introduction, Wiley-Interscience, 1989

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: