We consider a multiprocessor operating system in which each current
job is guaranteed a given proportion over time of the total processor
capacity. A scheduling algorithm allocates units of processor time to
appropriate jobs at each time step. We measure the goodness of such a
scheduler by the maximum amount by which the cumulative processor time
for any job ever falls below the “fair” proportion
guaranteed in the long term.
In particular we focus our attention on very simple schedulers which
impose minimal computational overheads on the operating system. For
several such schedulers we obtain upper and lower bounds on their
deviations from fairness. The scheduling quality which is achieved
depends quite considerably on the relative processor proportions
required by each job.

We will outline the proofs of some of the upper and lower bounds, both
for the unrestricted problem and for restricted versions where
constraints are imposed on the processor proportions. Many problems
remain to be investigated and we will give the results of some
exploratory simulations.

This is joint research with Micah Adler, Petra Berenbrink, Tom
Friedetzky, Leslie Ann Goldberg and Paul Goldberg.