Funny thing is that when you call Housekeeping (the only reason why I mentioned the Call Center filtering to Housekeeping is because not everyone sees or uses the Housekeeping button, they just automatically hit that Front Desk button), you don't go to the Call Center at all... you get connected to the Housekeeping dispatcher. Walk all the way to the Front Desk and guess who they call? The Housekeeping dispatcher.
However, they are asking the Front Desk to refrain from calling the Housekeeping dispatcher directly and instead put in a work order (so there is a record of the request and it is automatically dispatched to the Housekeeper assigned to your area via their radio) though the system. This is also the same system that the Housekeeping dispatcher uses to add and maintain the work orders currently in the system... and yes, it's done on a first-come, first-served basis and if there's a lot of work orders in the system, the response/resolution might not be immediate.