TU Dresden » ... » Professur für Ökonometrie und Statistik, insbes. im Verkehrswesen » Studium » Master Course Traffic Flow Dynamics and Simulation

Dr. Treiber



Simulating traffic flow interactively at traffic-simulation.de

Corona Simulation (Ger)

3D-Simulation movies
Movie1 Movie2

alte Klausuren (German)

Master Course Traffic Flow Dynamics and Simulation SS 2020

(Vorlesung Verkehrsdynamik und -simulation, SS ≤2019)

(2020-07-17) Important organisatorial details for the aural exams: The aural exam takes 20 minutes, one at a time, on July 28, 2020. The times for the candidates are as follows:

MatrikelnummerTime on July 28, 2020
4646656 09:00
4508630 09:30
4603453 10:00
4906280 10:30
4865911 11:00
4529677 11:30


(07.07.2020) Informations on this year's examinations are now online.

(22.06.2020) Final English lecture slides. The full curriculum for this year is now online.

(07.06.2020) Further English lecture slides

(07.06.2020) New English lecture slides

(07.06.2020) All tutorials and solution suggestions are now online (German)

(29.05.2020) New lecture slides

(05.04.2020) Correction regarding check your examination of the past Econometrics Master's course (Klausureinsicht). I have been informed that, these days, a lot of red tape has been implemented regarding organizing consultations/checking events. It is not possible to communicate face-to-face, not even for a single student! Furthermore, Skype & Co is also off-limits! . A dedicated institutional secure mail service will be set up for this purpose. However, if there are only general questions, e.g., the detailled point distribution for the three tasks, you can write me a mail .

(2020-04-17) A good example of a math model describing societal things is the hot topic of simulating the Corona infection spread dynamics. For this, I have set up an interactive simulator (German) and also a series of videos
While only marginally traffic related, these videos of my Econometrics course give a good example of mathematical models and what you can do with them

(2020-03-24) Until further notice, the lecture will be held as a virtual lecture this summer semester.

About half of the curriculum has already been recorded in my lectures (and later in a film studio) during my scientific visit in India.

However, it may take some time to bring the data (and myself) out of India. While the material for the German students is already fully available, I will upload in the next days the first English lecture notes.

The full curriculum is also included in the textbook Traffic flow dynamics (Springer, 2013, also available as an e-book). Otherwise, the material to be provided on this site soon will also be enough for the whole course

(2019-08-22) Starting with the summer semester 2020, this master course will be delivered in English. The German script will still be available


Due to the special circumstances, the examination will take place as a 20-minute oral test in person at our chair of Econometrics and Statistics, esp. in the Transport Sector at the Würzburger Str. 35, Room 123 (two floors up from the entrance!) on July 28, 2020 individually at the times given here.. Notice: depending on the student's choice, the language at the aural exam may be English or German


All what is relevant are the ten sets of slides , particularly Lecture 01: Trajectories, Lecture 03: Analysis of Stationary Detector Data, The two lectures Lecture 06 and Lecture 07 on first-order macroscopic models, and Lecture 09 and Lecture 10 on microscopic models. Notice that questions in aural exams tend to be more focussed on the understanding rather than calculations (although, of course, some simple formulas will be there as well). Typical questions include the following:
  • Summarize the contents of traffic flow dynamics [as displayed on the ten sets of slides] in a few words
  • What is traffic flow dynamics good for? give some use cases
  • Determine macroscopic quantities such as traffic flow, density, average speed, propagation velocities of traffic waves from a sketch or plot of trajectories that will be handed out during the exam
  • What is the difference between trajectory data as extracted from fixed cameras, FC data, and stationary detector data (SDD)? Give the strenghts and weaknesses of each data category with respect to some use cases
  • A stationary detector detects six passages of a vehicle within a sampling period of one minute and records an average speed of 36 km/h. Give the estimated flow in vehiclesa/hour and density in veh/km. Why is the density estimate probably biased?
  • What is a flow-density scatter plot and a fundamental diagram (FD)? Draw a typical fundamental diagram and flow-density data containing both free and congested traffic
  • (advanced) Explain the Simpson effect when analyzing a day of traffic flow data
  • (advanced) [Given a sheet of paper with some data points of vehicle trajectories (FCD) and stationary detector data (SDD) in the x-t plane]. How data inconsistencies may arise when both SDD and FCD are available? How to resolve this issue?
  • Discuss the difference between microscopic and macroscopic traffic flow models
  • Discuss the differences between time-continuous models, iterated maps, and cellular automata. Is it possible to formulate a macroscopic model by a cellular automaton?
  • How to derive the hydrodynamic relation flow=speed times density?
  • Write down the simplest continuity equation (homogeneous road) on a sheet of paper. Now integrate both sides of this equation over space from x1 to x2. What do you get?
  • Discuss the Eulerian and Lagrangian point of view
  • Write the simplest LWR on a sheet of paper and discuss the terms and variables
  • Given a LWR model with a certain fundamental diagram on a sheet of paper and two points p1 and p2 on it.
    • How to determine local propagation velocities at a density corresponding to p1?
    • Given is a transition from p1 to p2 while traffic is in state p1 upstream and in state p2 downstream of the transition region, respectively: Under which condition a shockwave will form? If it forms, what will be its velocity?
  • Give examples of traffic-related bottlenecks (the more, the better)
  • A traffic jam with a sharp transition free to congested forms upstream of a bottleneck. How to determine if the jam area increases or shrinks based on a counting detector at the bottleneck and a detector in the free-flow region further upstream? (Notice: may also come as a numerical example)
  • Give to mechanisms leading to a resolution of an existing traffic jam (from the demand and supply side)
  • A partial road block caused by an accident and causing a congestion is removed. Give the spatiotemporal dynamics of the congested region
  • How to macroscopically model traffic lights?
  • (advanced) explain the idea behind the supply-demand method when numerically integrating LWR models
  • Give the difference between micro and macroscopic traffic flow models
  • Discuss in words the plausibility criteria for the acceleration function f(.) of a time-continuous car-following model
  • (advanced) [Given a simple time-continuous or iterated-map car-following model such as dv/dt=(v0-v)/tau - lambda1/s + lammbda2*(vl-v) with speed v, leading speed vl, gap s]
    • Discuss the meaning and typical values of the model parameters v0, tau, lambda1, lambda2
    • Determine the homogeneous steady state/the fundamental diagram
    • Check the plausibility criteria
  • Discuss the relation between a car-following model and the core of an adaptive-cruise control
  • Which human characteristics are not considered by the Intelligent-Driver Model? (primarily the finite reaction time but also many more)
  • Discuss the rough idea behind the derivation of the Gipps model and the IDM (no calculations!)
Notice I: It is probably a good idea to try understand all the in-slide questions ( orange "?" or text) and check the given answers ( green "!" or text)

Notice II: It is also a good idea to check the relevant tutorial questions including the given solutions (although, of course, many tutoral problems do not fit into the aural format)

Virtual Lectures on the Covid-19 Model and Simulation (German)

these and more can be found on my Youtube Kanal Ökonometrie.

Virtual Lectures on Traffic Flow Data

Coming soon

Virtual Lectures on Traffic Flow Data

These have already been recorded in India and will be presented as soon as the Covid19 turbulences in India allow

Lecture Notes


Slides (German)

(2020-03-24) English lecture slides coming soon

Other Links


The complete course (and more) is covered by each of the following textbooks:
M. Treiber and A. Kesting
Traffic Flow Dynamics
Springer, 2013, XII+503 pages, 194 illus. (54 in color), hardcover
ISBN: 978-3-642-32459-8

M. Treiber und A. Kesting
Verkehrsdynamik und -simulation: Daten, Modelle und Anwendungen der Verkehrsflussdynamik
Springer-Lehrbuch, 2010, XII, 368 S. 176 Abb., 56 in Farbe., Softcover ISBN: 978-3-642-05227-9

Hint: within the TU Dresden domain, you can buy your personal discounted softcover copy at link.springer.com It costs less than half the regular price. In contrast to the regular one, it ships with b/w figures, though.

Martin Treiber