Laura Vargas Koch: Competitive variants of discrete and continuous flows over time
Urban population is rapidly growing worldwide and so is the number of vehicles in metropolitan areas. To get control of this rising traffic volume intelligent traffic planning is of central importance. In particular it is essential to solve many of the major traffic problems in today’s cities, e.g., air and noise pollution and long travel times. In other words, a well-planned traffic does not only increase the quality of life for traffic users but also benefits the economy and environment. Improved navigation systems and the availability of massive amounts of traveling data give a huge opportunity to optimize the infrastructure for the growing demand. This draws the attention to more realistic mathematical traffic models and algorithmic approaches for the interplay of individual road users. Unfortunately, on the one hand, realistic models used in simulations are mathematically poorly understood and, on the other hand, theoretically precise models that are mathematically well- analyzed are very simplified. This is where I want to contribute to with my research.
In detail: in the traffic simulation programs MATSim, traffic is simulated as flow driving through a network over the time. Given the choices of all travelers, a fraction of the travelers is allowed to reroute. After some time, this converges to an equilibrium state and this is seen as the traffic situation we would get in a city.
Since neither the uniqueness of such an equilibria is proven theoretically, nor the convergence of the algorithm, there are a lot of interesting open questions.
In my work I try to answer some of them. We investigate this questions in discrete (competitive packet routing) and continuous (Nash flows over time) models that take the deterministic queueing model which is used in MATSim as a basis. In these models we try to understand the structure and the quality of equilibria. Further we are also interested in network design questions which is for instance choosing good priority rules.
I work closely together with the UnRAVeL member Björn Tauer.