Dynamic Traffic Models in Transportation Science

Summary

Traffic assignment models play an important role for traffic planners to predict traffic distributions, especially, in light of possible changes of the infrastructure, e.g., road constructions, traffic light controls, speed limits, tolls, 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. On the other hand, dynamic models 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, link tolls, or traffic light controls) 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; not to speak of the resulting optimization problem for the first level.

On the other hand, 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 ignores 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.

The seminar brought together leading researchers from three different communities - Simulations (SIM), Dynamic Traffic Assignment (DTA) and Algorithmic Game Theory (AGT). This years seminar was centered around three topics:

• Horizontal queueing models. Most of the static traffic assignment models assume that queues can occur, but do not take up any physical space. In order to make the current models more realistic one should assume that queues might effect traffic on other nearby road segments, thus, include possible spill-back effects.
• Oligopolistic competition. With the rise of autonomous vehicles new routing decisions need to be made. As a novel aspect, individual vehicles might to be interested in selfishly optimizing their routes, but cooperate with other vehicles using the same software in order to decrease the average journey time.
• Risk-averse travelers. Current static traffic models often assume that each player is rational, and has the sole purpose of minimizing travel time or distance. However, the exact travel time of many routes might be uncertain at the moment of departure. Hence, travelers might stick to a more predictable route and might be unwilling to explore possibly better alternatives.

Again, the seminar was a big success both in terms of stimulating new and very fruitful collaborations. We got enthusiastic feedback from many participants which is also reflected in the survey conducted by Dagstuhl.