Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables. Courier Dover Publications (2012)
Anderson, T.W., Darling, D.A.: Asymptotic theory of certain “goodness of fit” criteria based on stochastic processes. The Annals of Mathematical Statistics, 193–212 (1952)
Bryant, R., O’Hallaron, D.R.: Computer Systems: A Programmer’s Perspective. Prentice Hall (2003)
Chakravarty, I., Roy, J., Laha, R.: Handbook of Methods of Applied Statistics. McGraw-Hill (1967)
Edgar, S., Burns, A.: Statistical analysis of WCET for scheduling. In: Proc. of 22nd IEEE Real-Time Systems Symposium, pp. 215–224 (2001)
Engblom, J., Ermedahl, A.: Pipeline timing analysis using a trace-driven simulator. In: Proc. of 6th Int’l Conf. on Real-Time Computing Systems and Applications, pp. 88–95 (1999)
Jain, R.: The Art of Computer Systems Performance Analysis. John Wiley & Sons (1991)
Kullback, S., Leibler, R.A.: On information and sufficiency. The Annals of Mathematical Statistics, 79–86 (1951)
Li, T., Baumberger, D., Hahn, S.: Efficient and scalable multiprocessor fair scheduling using distributed weighted round-robin. ACM SIGPLAN Notices 44(4), 65 (2009)
Mazouz, A., Touati, S.A.A., Barthou, D.: Study of variations of native program execution times on multi-core architectures. In: Proc. of Int’l Conf. on Complex, Intelligent and Software Intensive Systems, pp. 919–924 (2010)
Nolan, J.: Stable Distributions: Models for Heavy-tailed Data. Birkhauser (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Beard, J.C., Chamberlain, R.D. (2014). Use of a Levy Distribution for Modeling Best Case Execution Time Variation. In: Horváth, A., Wolter, K. (eds) Computer Performance Engineering. EPEW 2014. Lecture Notes in Computer Science, vol 8721. Springer, Cham. https://doi.org/10.1007/978-3-319-10885-8_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-10885-8_6
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-10884-1
Online ISBN: 978-3-319-10885-8
eBook Packages: Computer ScienceComputer Science (R0)