This was a really lovely piece of work; a pleasure to read.  If not
already known it would definitely be publishable, and the writeup is in
near-publishable form already.  Unfortunately, I've checked with some
colleagues and it looks like you were "scooped" a few years back.  I
recommend that you take a look at the paper, as there may be interesting
follow on questions you could tackle: http://www.sciencedirect.com/s
cience/article/pii/S0899825606001229

Almost all the writing was very clear.  The only piece I worried about a
bit was the truthfulness of the nonpreemptive "rounding" of the preemptive
schedule.  I agree that the preemptive version is truthful.  But, I worried
that perhaps the rounding procedure might introduce certain dependencies on
your job length that might lead you not to be truthful.  Even if so the
remainder of the paper is strong.

There's a simple inversion of your random variable formulation that would
allow you to rely on quite a bit more "standard" well known material.
Instead of setting Pr[X < c] = e^{-tc}, set Pr[X>c=e^{-tc}, and schedule in
the reverse order based on the *minimum* of a set of jobs.  Now your random
variables are exponential random variables and your ordering process is a
"Poisson Process". These are studied to death and many of the things you
rely on are well known for Poisson processes.

Grade: A