Choosing preemption points to minimize typical running times

The problem of selecting "effective preemption points" in a program --- points in the code at which to permit preemption --- in order to minimize overall running time is considered. Prior solutions that have been proposed for this problem are based on workload models in which worst-case known upper bounds are assumed for the duration needed to perform preemptions at particular points in the code, and of the time needed to non-preemptively execute the code between preemption points. Since these solutions are based on worst-case assumptions, they tend to select effective preemption points in a conservative manner; consequently the overall execution time of the program may be needlessly large under most typical run-time circumstances. We consider a more general workload model in which "typical" values, as well as upper bounds, are assumed to be known for the preemption durations and the non-preemptive code-execution durations; given such information, we derive algorithms for the optimal placement of preemption points in a manner that minimizes the typical overall running time (while continuing to guarantee, if needed, upper bounds on the worst-case over-all running time). Both off-line solutions (in which all preemption points are selected prior to run-time) and on-line solutions (where the selection of some of the preemption points is made during run-time and therefore can exploit knowledge of the actual durations of prior preemptions and of the executions of already executed pieces of code) are presented and proved optimal.