Maximizing job benefits on-line

We consider a benefit model for on-line preemptive scheduling. In this model jobs arrive at the on-line scheduler at their release time. Each job arrives with its own execution time and benefit function. The flow time of a job is the time that passes from its release to its completion. The benefit function specifies the benefit gained for any given flow time. A scheduler's goal is to maximize the total benefit gained. We present a constant competitive ratio algorithm for that model in the uniprocessor case for benefit functions that do not decrease too rapidly. We also extend the algorithm to the multiprocessor case while maintaining constant competitiveness. The multiprocessor algorithm does not use migration, i.e. preempted jobs continue their execution on the same processor on which they were originally processed.