Thing is, the message has to be passed along either by an intercom or by the person moving to the next room passing it on... Either way or travels at fastest at the speed of light, so you'll have people in the corridors moving to the next room for an infinite amount of time purely from the time it takes to propagate.

Given you're therefore committing to (at least on average) at least one person being without a room for the rest of time, why not just tell the chap in the first room to keep walking until he finds an available room? In terms of overall inconvenience (overall time spent without a room per person), it's the same as the original as both are infinite, but for the average person it goes from the time to walk from one room to the next to 0