Syed Farooq Ahmed Zaidi
December 12, 2011


“With believe in God comes believe in devil” – Source Unknown.

Every year approximately 2.5 million Muslim during Hajj (Muslims pilgrimage to Mecca) performs the ritual of ‘Rammy-al-Jamarat’ to signify their defiance of the devil. To do this they walk the pedestrian Jamarat Bridge and throw 7 small pebbles at 3 pillars (now changed to 3 long walls). Jamarat Bridge was reconstructed in 2006 to avoid crowd stampedes and death incidents in to a 5 level bridge with several points of entry and exit.

Concepts Demonstrated

  • A Markov Decision Process are used to compute optimal path for each group..


Markov Decision Process(MDP) was not used as it is. The value iteration of the MDP was time dependent. So if at a particular time a level of the bridge is supposed to be full, the values for that level of the bridge will drop below negative so that the pilgrim group is re-routed to another level.

Evaluation of Results

Machine learning could have proved to be a better solution. Using a crowd behavior simulations if the system is allowed to learn it will give a more realistic solution. However, this can only be proven if a solution is developed based on Machine learning and compared with this solution.

Additional Comments

The current model does not takes care of the following problems:-

  • The pilgrim groups are not allowed to turn back. The routes are all one way.
  • If the pilgrim group is told to wait it may find a shorter path because eventually the traffic at bridge is bound to reduce.