  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.
