Sid,
Start up times in sleeping risk premises are probably one of the most difficult things to predict. There are two things you can say for certain, firstly that they are very variable (when unmanaged) and secondly that they are likely to be very long (again, when unmanaged). Typically, 30 minutes.
I, of course, have no knowledge of the circumstances in which you are immersed and which led to this query but I can say that if you are trying to assess required escape times (RSET) against available safe times (ASET) then a good approach for coming up with a reliable estimation of this element of the required escape time is, rather than relying on people to rouse themselves in order to evacuate, to instigate a management regime that knocks each occupant up (so to speak) - someone going round the bedrooms banging on doors, to put it crudely. People will respond to this whereas they will bury their heads in pillows in response to alarms. Doing this, it is possible to come up with a reasonably accurate period of time that is required to get everyone moving.
This is not suitable for all premises, of course, but it may offer you or others a reliable way towards a solution.
Stu