Modeling of Traffic Systems
Code  Completion  Credits  Range  Language 

01MDS  Z,ZK  3  2+1  Czech 
 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, shortrange and longrange potential, Dyson?s Coulomb gas, traffic potentials, microscopic structure of thermal equilibrium, FokkerPlanck 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 (NagelSchreckenberg 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 selfdriven manyparticle 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, WileyInterscience, 1989
 Note:
 Further information:
 No timetable has been prepared for this course
 The course is a part of the following study plans: