Course description
The course was read for 6th year students of the PMF school of the FPMI MIPT.
Instructors
Alexander Gasnikov, Head of the MIPT MMO Laboratory
Course materials
Main book (Sections 1.1. 1.2, 2.1.2, 2.3)
Main Articles
Searching for equilibria in two-stage models of distribution of traffic flows over the network
An evolutionary view on equilibrium models of transport flows
Course video 2021
Course video 2022
Students in 2022 developed a number of projects:
The problem of the optimal distribution of buses along routes
Comparison of Bachmann models and stable dynamics on the example of Vladivostok
Estimation of the convergence time of the logit dynamics and dynamics of the best responses in the groping for balance models in the Bachmann Model (the results were included in the article)
Examples of projects from previous years. Among them:
Evgeny Nikitenko. Choosing the price of paid parking
Sergei Pavlov. Choosing the right parameters in the new correspondence settlement model
Artem Borzov. Determining the optimal price of a trip in a city with paid parking and car sharing (studying the splitting of movements into personal and various public transport)
You can also get acquainted with examples of projects on mathematical modeling of traffic flows
Exam program
1. The Bachmann Model
2. The Nesterov-de Palma stable dynamics model
3. Entropy model of correspondence matrix calculation
4. The method of conditional gradient of the equilibrium search in the Bachmann Model
5. Evolutionary derivation of the Bachmann Model
6. Equation of the state of the traffic flow (Tanaka formula, derivation of the dependence of the cost of travel of an edge on the flow on this edge).
7. Two-stage models of traffic flows and their reduction to the problem of convex optimization.
8. Numerical methods for finding equilibria in two-stage models of traffic flows.