Response time bounds for parallel processor allocation policies (1993) [5 citations — 3 self]
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Abstract:
ABSTRACT. The first result of this paper is a lower bound on mean response time, under a very general workload model, per class of multiprogrammed parallel processor allocation policies. This bound is derived from the mean response time of the optimal uniprocessor scheduling policy that uses the same workload information as the class of parallel processor allocation policies. The derivation of the bound also suggests how tighter bounds can be obtained on a per policy basis in some cases. Key features of the workload model include general job demands, available parallelisms, execution rates, and inter-arrival times, with arbitrary dependencies among these workload variables. The second result is that for linear execution rates (i.e., perfect speedups) and for i.i.d. exponential job demands that are independent of everything else, the Preemptive Smallest Available Parallelism First policy is optimal among policies that use no explicit information about job demand. Likewise, among all processor conserving policies the Preemptive Largest Available Parallelism First policy is pessimal. For the same assumptions it is also shown that the performance of a processor conserving policy is best when every job can make use of all processors and is worst when all jobs are fully sequential. This third result leads to easily computable bounds on mean response time. The second and third results are shown to be sensitive to the assumption of exponential job demands. Finally, some quantitative results are given that illustrate the use and tightness of the derived bounds.
