Mathematical modelling for AL-Hajj movement

Abstract

One of the rituals during pilgrimage is the ‘Tawaf’, that is circling around the Ka'aba seven times each and for a number of times. These are among the ‘problems’ faced by pilgrims in the Hajj season when individual or groups of pilgrims arrive to perform the Tawaf in a random order. All arrivals are allowed to perform the Tawaf at anytime. The density of pilgrims close to the Ka’aba reaches a maximum at times. Consequently, the movement of people in the vicinity of the Ka'aba becomes very slow and at times comes to a halt. In our work, Arena simulation program has been used to build a new model to systemize pilgrims movement around the Ka’aba during the hajj season. Several stages of observations and restrictions were done to study the random movement in order to reduce the incidents at the Ka’aba .