Empirical analysis on the runners’ velocity distribution in city marathons

Polarised crowd in motion: Insights into statistical and dynamical behavior

“…As we increase time, the nature of density vs. velocity plot remains the same, but slowly crowd disperse and both density and velocity shifts towards the smaller values. This non-monotonic nature is intrinsic to the collective behaviour of participants moving in different races as found in previous experiments 29 . The presence of band of high density is responsible for such non-monotonic behaviour.…”

“…Another prominent event is the marathon race, which demands special attention when addressing crowd control measures. Indeed, there are numerous studies focused on city marathons [29][30][31][32][33][34][35] , which aim to capture and analyze crowd dynamics during the races where these studies utilize various methods, including video analysis, data tracking, and participant surveys to understand how the crowd behave and interact during marathon events. The computer-simulated numerical models [36][37][38][39] for marathon attempt to replicate the real events.…”

“…Based on the experiments on the real races 29,34,37,44 , various observable such as velocity and density waves, speed and velocity distribution of the participants, distribution of density in the system as well as density and velocity auto-correlation can be examined to explore the dynamics and characteristics of the moving crowd. These observable are valuable tools for characterizing the dynamic behavior of participants during the races.…”

Modelling dynamics of marathons – A mixture model approach

“…Due to the central limit theorem, many human variables such as height can be approximated by the Gaussian distribution; however, this assumption may not hold for running velocity. As presented in Lin and Meng (2018), average velocities were found switching between Gaussian and log-normal distributions at different stage of a marathon. The cause of this phenomenon has not been studied; in view of this, we believe a study on marathon dynamics would lead to a better understanding of this phenomenon.…”