Modeling and Simulation of Tawaf and Sa'yee: A Survey of Recent Work in the Field

Between 2002 and 2012 the number of pilgrims taking part in the 5-day hajj (the annual pilgrimage to Mecca) rose dramatically from 1.9m to 3.2m, before stabilizing at around 2 million following the introduction of new quotas in 2013. The gathering together of so many people has obvious crowd-safety implications, ranging from stampedes and protests to pickpocketing and dis- ease control, and there is an obvious need for models and simulations of the relevant crowd behaviours. More- over, the regular occurrence of the event, the size and diversity of the crowds involved, and the amount of freely available information make this an excellent case study for the study of crowd behaviour. We survey recent at- tempts to model the key hajj rituals of tawaf (during which pilgrims collectively circumambulate the Ka’aba seven times) and sa’yee (running or walking seven times between two nearby hills), and highlight ways in which some of the limitations of these studies may be overcome in future work.