Showing papers by "Micha Hofri published in 1989"

Scheduling Stochastic Jobs with a Two-Point Distribution on Two Parallel Machines

Abstract: We analyze the optimal preemptive sequencing of n jobs on two machines to minimize expected total flow time. The running times of the jobs are independent samples from the distribution Pr(X = 1) = p, Pr(X = κ + 1) = 1 − p. We verify that the shortest-expected-remaining-processing-time (SERPT) policy, which is optimal for independent and identically distributed (i.i.d.) running times with a monotone hazard-rate distribution, is not optimal for this distribution. However, we prove that if p ≥ 1/κ, then the number of decisions where SERPT and an optimal policy disagree is bounded by a constant independent of n. For p < 1/k, we prove that the expected number of such decisions has a similar bound. In addition, bounds on the expected increase in flow times under SERPT are derived; these bounds are also independent of n.

The Coupon-Collector Problem Revisited

Abstract: A standard combinatorial problem calls to cstlmate the expected number of purchases of coupons needed LO complete Ute collection of all possible m different types. Generalizing this problem. by letting lhe coupons be obtained with an arbitrary probability distribution. and considering other related processes, the problem has been found to model many practical siwations. The usefulness of lhis model has been seriously hampered by !.he computational difficulties in obtaining any numerical results concerning moments or distributions. We show, following Flajolet et al. [15], !hat Ute calculus of generating functions over regular languages may be applied La the problem, answer numerous questions about the sampling process and demonstrate their numerical efficiency. We also present a proof of a long-standing folk-theorem. concerning lhe extremalily of uniform reference probabilities. The paper concludes with a discussion of estimation problems related lo the engineering applications of lhis problem.