Dealing with "past" events

Given:
N = "now"
R = task release time
D = task's deadline time
E = event time
The only real invariant is that R < N as code executing in a
task can't execute until the task has been released.
Specifically, there are no guaranteed relationship between
*most* of these times; N > E, N > D, D < R, etc. are all
possible in a generic system.
Though, in a nominal setting, R < N < E < D when the code tries
to initiate an event at a particular (future) time (E).
But, what happens when E < N -- i.e., when you try to schedule
an action (event) at a time that has already passed?  And, does
E << N lead to a different interpretation/handling?
I've argued that the OS shouldn't special-case such activities.
If you request something to happen in the past, then the OS
should just act as if it has *just* happened, regardless as to
whether you were a microsecond "late" in issuing your request
or *years*!  In particular, the OS shouldn't dismiss such request
unilaterally -- or, throw an error to alert the issuer to the
*apparent* inconsistency.