Simulation Of A Composite Queuing Model Of The Entrance And Exit Of Pilgrims From Al-Masjid Al-Haram
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Date
2012
Authors
Mahmoud, Roweda Mohammed Ali
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Publisher
Universiti Sains Malaysia
Abstract
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. Consequently, the movement of people in the vicinity of Ka'aba becomes very slow and at times comes to a halt. Furthermore the empirical data concerning the Hajj is manifold. Thus, it is very challenging to study the real system. This study proposed to model the arrival and departure of pilgrims by simulation composite queuing model to build a new model to systemize the entrance and exit of pilgrims from AlMasjid Al-Haram during the Hajj season. The Data of the new model proposed in the current study is collected from video of Tawaf. The video is made into a series of captured shots and thus an image processing of the photos is made. The simulation language used in this study is Arena which is currently one of the most popular simulation languages. Arena is a graphical simulation language for discreet and continuous events simulation which has been used to build a model. From the simulation results of the five main gates of Al-Masjid Al-Haram, it was found that the peak hours of entrance from highest density to lowest were at 5 am, 12 pm, 11 am and 5 pm. On the other hand, the peak hours of exit from Al-Masjid Al-Haram from highest density to lowest were at 7 am, 8 am, and 10 pm. This study concluds that using simulation of a composite queuing model is an encouraging step for studying the pedestrians’ congestion in large events.
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Keywords
Mathematics to suggest solutions to the problem , of overcrowd during ‘Tawaf’ ritual of Hajj