1 / 22

Pick up the Pieces Average White Band

Pick up the Pieces Average White Band. Modeling Resource Availability in Federated, Globally Distributed Computing Environments Rich Wolski Dan Nurmi University of California, Santa Barbara John Brevik Wheaton College. Virtualization.

yitro
Télécharger la présentation

Pick up the Pieces Average White Band

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Pick up the Pieces Average White Band

  2. Modeling Resource Availability in Federated, Globally Distributed Computing Environments Rich Wolski Dan Nurmi UniversityofCalifornia,SantaBarbara John Brevik Wheaton College

  3. Virtualization • Characterize resource performance in terms of predicted • Performance level (CPU fraction, BW, latency, available memory) • Availability duration • Classify resources in terms of • Equivalence • Statistical independence • From these, we can build “virtual machines” with provable performance and availability characteristics • Compute machines • Storage machines

  4. Sample Based Techniques • Each measurement is modeled as a “sample” from a random variable • Time invariant • IID (independent, identically distributed) • Stationary (IID forever) • Well studied in the literature • Exponential distributions • Compose well • Memoryless • Popular in database and fault-tolerance communities • Pareto distributions • Potentially related to self-similarity • “heavy-tailed” implying non-predictability • Popular in networking, Internet, and Dist. System communities

  5. Why not Weibull? • Proposed originally by Waloddi Weibull in 1939 • PDF: f(x) = (a/b) * ( ((x - c)/b)^(a-1) ) * e^-(((x-c)/b)^a) • a is scale parameter > 0 • b is shape parameter > 0 • c is location parameter, (-inf,inf) • Used extensively in reliability engineering • Modeling lifetime distributions • Modeling extreme values in bounded cases • Not memoryless • F(x)x+k | k <> F(x) • Maximum Likelihood Estimation (MLE) of parameters is “hard” • Requires solution to non-linear system of equations or optimization problem • Sensitive to numerical stability of numerical algorithms

  6. Our Initial Investigation • Measure availability as “lifetime” in a variety of settings • Student lab at UCSB, Condor pool • New NWS availability sensors • Data used in fault-tolerance communityfor checkpointing research • Predicting optimal checkpoint • Develop robust software for MLE parameter estimation • Automatically Fit Exponential, Pareto, and Weibull distributions • Compare the fits • Visually • Goodness of fit tests • Goal is to provide an automated mechanism for the NWS • Let the best distribution win

  7. UCSB Student Computing Labs • Approximately 85 machines running Red Hat Linux located in three separate buildings • Open to all Computer Science graduate and undergraduates • Only graduates have building keys • Power-switch is not protected • Anyone with physical access to the machine can reboot it by power cycling it • Students routinely “clean off” competing users or intrusive processes to gain better performance response • NWS deployed and monitoring duration between restarts • Can we model the time-to-reboot?

  8. UCSB Empirical CDF

  9. MLE Weibull Fit to UCSB Data

  10. Comparing Fits at UCSB

  11. Goodness of Fit • Kolmogorov-Smirnov (K-S) Goodness-of-Fit Test • P-values averaged over 1000 subsamples, each size 100 • Weibull: 0.36 • Exponential: 2 x 10^-5 • Pareto: 5 x 10^-4 • Anderson-Darling (A-D) Goodness-of-Fit Test • P-values averaged over 1000 subsamples, each size 100 • Weibull: 0.07 • Exponential: 0 • Pareto: 0 • At .95 significance level, reject null hypothesis for both Exponential and Pareto.

  12. Can do Better with a few Statistical Tricks

  13. Condor • Cycle harvesting system (M. Livny, U. Wisconsin) • Workstations in a “pool” run the (trusted) Condor daemons • Each machine agrees to contribute a machine by installing and running Condor • Condor users submit job-control scripts to a batch queue • When a machine becomes “idle,” Condor schedules a waiting job • Machine owners specify what “idle” and “busy” mean • When a machine running a Condor job becomes “busy” • Job is checkpointed and requeued (standard universe) • Job is terminated (vanilla universe) • NWS sensor uses vanilla universe and records process lifetime • Unknown and constantly changing number of workstations in UWisc Condor Pool (> 1500) • 210 machines used by Condor for NWS sensor

  14. Condor Weibull Fit

  15. Comparing Condor Fits

  16. Long, Muir, Golding Internet Survey (1995) • 1170 Hosts “across” the Internet in 1995 • Use response to rpc.statd (NFS daemon) as heartbeat • Long, Muir, Golding (UCSC, HP-labs) investigated exponentials as models for • Availability time • Downtime • Plank and Elwasif (UTK,1998) and Plank and Thomason (UTK, 2000) use data and exponentials as basis for checkpoint interval determination • All researchers conclude that data is not-well modeled by exponentials • No plausible distribution determined

  17. Weibull Again

  18. If the Weibull Fits, Wear It • Three different availability surveys under three different sets of circumstances • UCSB Student Labs • Adversarial chaos • U. Wisc Condor Pool • Background cycle harvesting • Internet host survey • Convolution of host and network availability circa 1995 • In all three cases an MLE-fit Weibull is, by far, the best model • Visual and GOF evidence • Uncharacteristically, the assumptions for the model seem to hold • Stationarity and Independence

  19. What Does This Mean for VGrADS? • If a continuous, closed form distribution is needed to model machine availability in federated distributed systems, a Weibull is probably the best choice • Empirical evidence from different scenarios makes bias unlikely • Weibulls were invented to model lifetimes • Why Should we Care? • Grid simulators • Probably useful to uGrid • Optimal Checkpoint scheduling • Paper in progress • Replication systems • Independence allows us to set the joint failure probability • It does not mean, that Weibulls are best for predicting availability • We can beat the distributional approach using a non-parametric method

  20. Optimal Checkpoint Interval • Goal: minimize the expected execution time given checkpoint overhead cost C for each checkpoint • Old formula (Vaidya’s approximation) • eL(T+ C) (1 - LT) • L is failure rate (exponential) and T is optimal checkpoint interval • Our new formula based on Weibulls • (b + C + (b + C/b)a * a * b) / ((b + C/b)a * a • Two parameter Weibull with shape a and scale b • Conservative value • Optimal unconditional value • Conditional value may be possible • Requires application to recalculate interval at each checkpoint • Pie in the sky for now

  21. Where we are and What’s Next • We have automatic fitting software prototyped for availability • Uses mathematica and/or matlab for solver quality • New NWS sensors going up on VGrADS testbed • We have non--parametric failure prediction software prototyped for individual machines • We need to • Integrate with NWS infrastructure • Develop VGrADS presentation layer • Develop classification software (independence and equivalence) • Translate results to time-series realm • Study time-to-availability problem • Develop optimal checkpoint interval determination service • Dan Nurmi, John Brevik

  22. Thanks • Miron Livny and the Condor group at the University of Wisconsin • Darrell Long (UCSC) and James Plank (UTK) • UCSB Facilities Staff • NSF and DOE • nurmi@cs.ucsb.edu, jbrevik@wheatonma.edu, rich@cs.ucsb.edu

More Related