New utilization criteria for online scheduling

Abstract

In the classical scheduling problems, it has been assumed that complete knowledge of the problem was available when it was to be solved. However, scheduling problems in the real world face the possibility of the lack of the knowledge. Uncertainties frequently encountered in scheduling environments include the appearance of new jobs and unknown processing times. In this work, we take into account these realistic issues.

This thesis deals with the problem of non-preemptive scheduling independent jobs on m identical parallel machines. In our online model, the jobs are submitted over time non-clairvoyantly. Therefore, the processing times of the jobs are unknown until they complete. Further, we assume that the ratio of weight to processing time is equal for all jobs, that is, all jobs have the same priorities. The jobs are assigned to the machines in a nondelay fashion. Our main scheduling objective is to maximize the utilization of the system.

We show that the commonly used makespan criterion usually cannot reflect the true utilization of this kind of online scheduling problems. For this reason, it is very important to find another criterion capable of evaluating system utilization. Therefore, we introduce two new alternative criteria that more accurately capture the utilization of the machines. Moreover, we derive competitive factors for both criteria. Those competitive factors are tight for one criterion and almost tight for the other. Finally, we present an experimental investigation to evaluate the performance of the nondelay online algorithm with respect to our criteria. The experimental results show the confirmation of our theoretical results.