It is slightly surprising to me that you don't directly need those deadlines when computing S
Exactly.
Although come to think of it, a thought experiment makes it seem plausible that everything is abstracted into S (which is what you *really* want to know, at least for this application, you just can't believe the deadlines aren't important). Imagine A as a block of time allocated from SA with all the tasks running successively in order of deadline. In terms of combining A with other tasks it's just like one task with SA and LA. Does it make a difference if any of the deadlines are moved? If it's a tight deadline (ie. if you start at SA then the task is done exactly by the deadline) then moving it forward is reflected in SA moving forward. If it's the only tight deadline then moving it back is reflected in SA moving back. If not, then it doesn't make any difference to SA, but doesn't make any difference to S either, since you might as well do all the tasks as quickly as you can regardless if any of them have slack or not.
Imagine A as a block of time allocated from SA with all the tasks running successively in order of deadline. In terms of combining A with other tasks it's just like one task with SA and LA.
Ah yes, I think I believe that too. Nice reanalysis!
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Exactly.
Although come to think of it, a thought experiment makes it seem plausible that everything is abstracted into S (which is what you *really* want to know, at least for this application, you just can't believe the deadlines aren't important). Imagine A as a block of time allocated from SA with all the tasks running successively in order of deadline. In terms of combining A with other tasks it's just like one task with SA and LA. Does it make a difference if any of the deadlines are moved? If it's a tight deadline (ie. if you start at SA then the task is done exactly by the deadline) then moving it forward is reflected in SA moving forward. If it's the only tight deadline then moving it back is reflected in SA moving back. If not, then it doesn't make any difference to SA, but doesn't make any difference to S either, since you might as well do all the tasks as quickly as you can regardless if any of them have slack or not.
Ah yes, I think I believe that too. Nice reanalysis!