It is known that given N random subintervals of [0, 1], one can find a disjoint subcollection that covers all of [0, 1] except a set of length about (log N)2/N. We investigate what happens when the distribution of the intervals is biased to favor shorter intervals or intervals close to the...

We give a short proof of the Jackknife Estimate of Variance of Efron-Stein using martingale difference techniques. The method could be used to get information on other moments than the second moment.

Let [phi] be a convex function defined on R+, with [phi](0) = 0 and limx--0[phi](x)/x=0. We show that there exists a uniformly bounded process (Xt) on [0,1] with continuous sample paths that satisfies the increment condition for every u t, E([phi]( Xt- Xu)) [less-than-or-equals, slant] t - u....

In most classical scheduling models, it is assumed that a job is dispatched to a customer immediately after its processing completes. In many practical situations, however, a set of delivery dates may be fixed before any jobs are processed. This is particularly relevant where delivery is an...