Crowd Flow Modeling of Athletes in Mass Sports Events -- a Macroscopic Approach

We propose a macroscopic model in form of a dispersion-transport equation for non-congested flow of the athletes which is coupled to a kinematic-wave model for congested flow. The model takes into account the performance (i.e., free-flow speed distributions) of the athletes in the different starting groups. The model is calibrated and validated on data of the German $\textit{Rennsteig Half Marathon 2012}$ and the Swedish $\textit{Vasaloppet 2012}$ cross-country ski race. Simulations of the model allow the event managers to improve the organization by determining the optimum number of starting groups, the maximum size of each group, whether a wave start with a certain starting delay between the groups is necessary, or what will be the effects of changing the course. We apply the model to simulate a planned course change for the Rennsteig Half Marathon 2013, and determine whether critical congestions are likely to occur.