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 Rennsteig Half Marathon 2012 and the Swedish 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.