And a light-tailed distribution is better, because you are less likely to have these long periods with no drops at all. But there is nothing special about the uniform distribution other than its light tails, I think. Any number of other light-tailed distributions might do just as well. Lots of simulations. But nothing published.
C can be a function of avg-minth.
I think that anything periodic could lend itself to deterministic patterns of bias in certain scenarios. But roughly periodic with a little dollop of randomness should do just fine. Kluwer Boston, pp.