### 04.10.15 - 09.10.15, Seminar 15412

# Dynamic Traffic Models in Transportation Science

### Diese Seminarbeschreibung wurde vor dem Seminar auf unseren Webseiten veröffentlicht und bei der Einladung zum Seminar verwendet.

## Motivation

Traffic assignment models play an important role for traffic planers to predict traffic distributions, especially, in light of possible changes of the infrastructure, e.g., road constructions, traffic light controls, etc. The prevailing mathematical approaches used in the transportation science literature to predict such distributions can be roughly classified into static traffic assignment models based on aggregated static multi-commodity flow formulations and dynamic traffic assignment (DTA) models based on the methodology of flows over time. While static models have seen several decades of development and practical use, they abstract away too many important details and, thus, become less attractive. Dynamic models, on the other hand, are known to be notoriously hard to analyze in terms of existence, uniqueness and computability of dynamic equilibria. In light of the prevailing computational difficulties for realistic-sized networks, the systematic optimization of such networks (e.g., by designing the network infrastructure) becomes even more challenging as the resulting mathematical programs with equilibrium constraints contain already in the lower level presumably “hard” optimization-, complementarity- or variational inequality problems.

Complementary to mathematical approaches, there is a trend in the transportation science community to use large-scale computer-based microsimulations for predicting traffic distributions. The striking advantage of microscopic simulations over DTA models is that the latter usually ignore the feedback of changing network conditions on user behavior dimensions such as flexible departure time choice, mode choice, activity schedule choice, and such. Current simulation tools integrate all these dimensions and many more. The increasing model complexity, however, is by far not matched by the existing theory of dynamic traffic assignments. For many microscopic simulation models (and even DTA models) the following questions are especially pertinent:

- Under which conditions do the models admit an equilibrium?
- Is an equilibrium efficiently (polynomial time) computable or is the computation (PPAD)-hard?
- Are multiple equilibria possible and how can they be qualitatively as well as quantitatively distinguished?
- Which type of equilibrium is computed depending on the choice of the learning processes of agents?
- How do we efficiently compute optimal (or approximatively) network designs or traffic light controls subject to dynamic equilibrium constraints?
- How does stochasticity, for example in the behavioral models and/or in the network loading, affect the results and their mathematical interpretation?

In this seminar we want to bring together leading researchers from three different communities (Simulations, Dynamic Traffic Assignment and Algorithmic Game Theory) to discuss ways to narrow the existing gap between complex simulation based models and the existing theory.