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Mathematics for traffic flow modelling


ContextTraining course at Gustave Eiffel University
Organisation9 * 2 hours of lecture and exercise with NetLogo
MaterialSlides + NetLogo script


The course covers the mathematical basics of the theory of pedestrian dynamics and road traffic flow. This includes main variables and statistics, measurement in experiments or field trials, modelling and its application in computer simulations of traffic. The operational modelling part range from microscopic models describing individual agent trajectories to macroscopic approaches for aggregated quantities such as density and flow rate. Further modelling consist in intersection models and optimisation of traffic networks. Particular attention is paid to the calibration and validation of the models. Theoretical emphases rely on stability analysis, collective phenomena and self-organisation.  The different modelling approaches are illustrated with real time simulation using NetLogo platform.


  1. Introduction to the traffic flow theory
  2. Variables and mesureament methods
  3. Empirical characteristic of traffic flow and pedestrian dynamics
  4. Microscopic, mesosocopic and macroscopic modelling approaches
  5. Collective stability analysis
  6. Model calibration and validation
  7. Traffic simulation softwares
  8. Application to autonomous and connected driving
  9. Application to optimisation of traffic networks


M. Treiber und A. Kesting. Traffic Flow Dynamics, Springer, 2013.
B. S. Kerner. The Physics of Traffic, Springer, 2004


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