Use of a Levy Distribution for Modeling Best Case Execution Time Variation
Minor variations in execution time can lead to out-sized effects on the behavior of an application as a whole. There are many sources of such variation within modern multi-core computer systems. For an otherwise deterministic application, we would expect the execution time variation to be non-existent (effectively zero). Unfortunately, this expectation is in error. For instance, variance in the realized execution time tends to increase as the number of processes per compute core increases. Recognizing that characterizing the exact variation or the maximal variation might be a futile task, we take a different approach, focusing instead on the best case variation. We propose a modified (truncated) Levy distribution to characterize this variation. Using empirical sampling we also derive a model to parametrize this distribution that doesn’t require expensive distribution fitting, relying only on known parameters of the system. The distributional assumptions and parametrization model are evaluated on multi-core systems with the common Linux completely fair scheduler.
KeywordsExecution Time Gumbel Distribution Markovian Arrival Process Processor Sharing NUMA Node
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