Simulation Of A Composite Queuing Model Of The Entrance And Exit Of Pilgrims From Al-Masjid Al-Haram

Mathematics has always provided solutions for practical life problems. This study uses mathematics to suggest solutions to the problem of overcrowd during ‘Tawaf’ ritual of Hajj. One of the rituals during Hajj is the ‘Tawaf”, that is the circling seven times around Ka'aba. This ritual is among the ‘problems’ faced by pilgrims in the Hajj season due to the overcrowd occurring when individuals or groups of pilgrims arrive to perform the Tawaf in random order. All arrivals are allowed to perform the Tawaf at anytime. The density of pilgrims circulating close around Ka’aba reaches the maximum at certain times of the day