Eliminating migration in multi-processor scheduling

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 / r(i), pmtn / Sigma w(i)(1 - U-i) and special cases thereof, the ability of the scheduler to migrate jobs is of only limited advantage. Our proof is constructivt, 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 /r(i), pmtn / Sigmaw(i)(1 - U-i) to the problem 1 / r(i), pmtn / Sigma w(i)(1 - U-i). The proof of correctness of this reduction critically uses the fact that there is a nonmigratory schedule that closely approximates the optimal migratory schedule. (C) 2001 Academic Press.