Sounds simple enough when you are dealing with civilized people, but that's not the case here. Various groups of Muslims consider themselves superior to other such groups.
If you look up the history of these Hajj stampedes, you will find remarkable similarity on various factions refusing to yield. One of the bigger death tolls had to do with one group walking too slowly through an air-conditioned tunnel built specifically to handle these large crowds. One or more of the groups behind them took umbrage at the pace and created a stampede walking over them.
Put too many MS-13 gangster types in the same area and this type of mayhem is unavoidable.
They would probably be inclined to obey direct orders from armed Saudi policemen. You just have to adjust the crowd-control enforcement to the type of crowds you expect.