Quantification of the level of crowdedness for pedestrian movements

• Comprehensive review of measures to estimate the level of crowdedness in a crowd.
• Quantitative comparison of the measures w.r.t. pedestrian movement behaviours.
• Most of the studied measures introduce large errors in the ‘fundamental relations’.
• The Voronoi Diagram measure and the X-T measure are ‘best’ estimating crowdedness.

Within the realm of pedestrian research numerous measures have been proposed to estimate the level of crowdedness experienced by pedestrians. However, within the field of pedestrian traffic flow modelling there does not seem to be consensus on the question which of these measures performs best. This paper shows that the shape and scatter within the resulting fundamental diagrams differs a lot depending on the measure of crowdedness used. The main aim of the paper is to establish the advantages and disadvantages of the currently existing measures to quantify crowdedness in order to evaluate which measures provide both accurate and consistent results. The assessment is not only based on the theoretical differences, but also on the qualitative and quantitative differences between the resulting fundamental diagrams computed using the crowdedness measures on one and the same data set. The qualitative and quantitative functioning of the classical Grid-based measure is compared to with the X-T measure, an Exponentially Weighted Distance measure, and a Voronoi-Diagram measure. The consistency of relating these measures for crowdedness to the two macroscopic flow variables velocity and flow, the computational efficiency and the amount of scatter present within the fundamental diagrams produced by the implementation of the different measures are reviewed. It is found that the Voronoi-Diagram and X-T measure are the most efficient and consistent measures for crowdedness.