Eliminating Migration in Multi-processor Scheduling

Abstract

We investigate the power of migration in real-time multi-processor scheduling with preemption. We show that every collection of jobs that can be completed by some schedule S on m processors can also be completed by a nonmigratory schedule S′ on 6m−5 processors. We can conclude from this result that, for many scheduling problems, such as P∣ri,pmtn∣∑wi(1−Ui) and special cases thereof, the ability of the scheduler to migrate jobs is of only limited advantage. Our proof is constructive, and can be implemented to run in pseudo-polynomial time (or in polynomial time at the cost of raising the bound from 6m−5 to 12m−5). As an example of the usefulness of this result, we give a polynomial-time 6-approximation reduction from the problem P∣ri,pmtn∣∑wi(1−Ui) to the problem 1∣ri,pmtn∣∑wi(1−Ui). The proof of correctness of this reduction critically uses the fact that there is a nonmigratory schedule that closely approximates the optimal migratory schedule.