Being an ATC at one of the airports where ASDE-X is installed I believe its principals are what we the OP is looking for,.
The ASDE-X system is a prediction system. It alerts on the prediction of a colission within the bounds of a runway. An aircraft approaching an intersection that is slowing while an aircraft is landing is not enough to generate an alert. The 2 aircraft have to be predicted to be at the same place in time.
As an example:
An aircraft on a 1 mile final with an aircraft crossing down field already past the centerline and not slowing will not be in conflict with the landing A/C.
To even drive the prediction aspect firther. There was an incedent where a ramp vehical was crossing the runway(without ATC permission) 7000' down the runway as a 737 was crossing the threshold and the ASDE-X didn't alert. The software never predicted a colission.
So to the idea of an aircraft behind you not being a factor... This would depend on speed. This is a valid method to limit alerts and make the system more of an "OMG WTF!!!" system then the boy who cries wolf.
With that said... The math is going to be fun!!!
Thanks
Delta Echo