Response Surface Analysis of Crowd Dynamics during Tawaf

A refined cellular automata model is applied to simulate the crowd movement of Muslim pilgrims performing the Tawaf ritual within the Al-Haram Mosque in Mecca. The results from the simulation are obtained and the influence of the predictor variables of the evacuation process (pedestrian flow and Tawaf duration) on the responses (pedestrian density, average walking speed, and cumulative evacuee) is investigated using response surface methodology (RSM). The average results from the experiments with an rms error less than 0.5 are obtained from the RSM. Its performance indicates that the RSM possesses excellent predictive ability for the model evacuation study, because both the experimental and the predicted values agree well with the results obtained in this study.