Approximation Results for Preemptive Stochastic Online Scheduling

We present first constant performance guarantees for preemptive stochastic scheduling to minimize the sum of weighted completion times. For scheduling jobs with release dates on identical parallel machines we derive policies with a guaranteed performance ratio of 2 which matches the currently best known result for the corresponding deterministic online problem. Our policies apply to the recently introduced stochastic online scheduling model inwhich jobs arrive online over time. In contrast to the previously considered nonpreemptivesetting, our preemptive policies extensively utilize information on processing time distributions other than the first (and second) moments. In order to derive our results we introduce a new nontrivial lower bound on the expected value of an unknown optimal policy that we derive from an optimal policy for the basic problem on a single machine without release dates. This problem is known to be solved optimally by a Gittins index priority rule. This priority index also inspires the design of our policies.computer science applications;

Greed Works -- Online Algorithms For Unrelated Machine Stochastic Scheduling

This paper establishes performance guarantees for online algorithms that schedule stochastic, nonpreemptive jobs on unrelated machines to minimize the expected total weighted completion time. Prior work on unrelated machine scheduling with stochastic jobs was restricted to the offline case, and required linear or convex programming relaxations for the assignment of jobs to machines. The algorithms introduced in this paper are purely combinatorial. The performance bounds are of the same order of magnitude as those of earlier work, and depend linearly on an upper bound on the squared coefficient of variation of the jobs' processing times. Specifically for deterministic processing times, without and with release times, the competitive ratios are 4 and 7.216, respectively. As to the technical contribution, the paper shows how dual fitting techniques can be used for stochastic and nonpreemptive scheduling problems.Comment: Preliminary version appeared in IPCO 201