Abstract
Two models for the motion in the Mataf of the Holy Mosque of Makkah that are applicable to any so-called social force or agent-based model are presented. The first model assigns a desired distance to the Kaaba to each pilgrim. The second model assumes that pilgrims desire to get as close as possible to the Kaaba until a tolerable density is reached. Both models are realistic: image data shows behaviours of both types. The models are very simple to incorporate into any computational crowd dynamics code, and yield results that correlate surprisingly well with observed data.
Highlights
One of the obligatory rites of Muslim pilgrims visiting Makkah is the sevenfold circumambulation of the Kaaba at the center of the Holy Mosque - the so-called Mataf
Video footage shows that even when there are very few pilgrims, some pilgrims do not venture close to the Kaaba, implying that this model is not unrealistic
The second model assumes that pilgrims want to get as close as possible to the Kaaba when performing the Tawaf but have a limited tolerance for high density
Summary
The motion of pedestrians in the Mataf has been the focus of much modeling effort over the last years. At this point there does not exist a reliable predictive model for this motion. The second model assumes that pilgrims want to get as close as possible to the Kaaba when performing the Tawaf but have a limited tolerance for high density. This implies that they will stop trying to get closer to the Kaaba if the density is above a certain threshold. Video footage shows that even when there are very many pilgrims, some pilgrims keep trying to get to the Kaaba or very close to it, i.e. are not afraid of high densities
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