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Requires two estimates if certainty is to be quantified Estimate the (1-X) quantile for the distribution of availability => Qx Estimate the lower X% confidence bound on the statistic Qx => Q(x,lb) If the estimates are unbiased, and the distribution is stationary, future availability duration will be larger than Q(x,lb) X% of the time, guaranteed ~8GnF  8 )       =            =  =t= = > '7The Brevik MethodJohn Brevik s invention based on Binomial distribution Probability that exactly j values are below qth quantile is 7" <   , TSee it In ActionJob Categories are defined by The machine on which the job will be submitted The queue (specified by name) into which the job will be submitted The requested processor count The requested run time (coming soon) Report three times: The 0.5 Quantile (50-50 chance) -- blue The 0.75 Quantile -- green The 0.95 Quantile -- purple Time format is hh:mm:ss Data updated every 60 seconds http://pompone.cs.ucsb.edu/~nurmi/batchq/nindex.html_k(H =%  5   k|Predicting Things Upside downDeadline scheduling: My job needs to start in the next X seconds for the results to be meaningful. 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Amitava Mujumdar, Tharaka Devaditha, Adam Birnbaum (SDSC) Need to run a 4 minute image reconstruction that completes in the next 8 minutes Given a Machine Queue Processor count Run time Deadline What is the probability that a job will meet the deadline? http://pompone.cs.ucsb.edu/~rgarver/invbqueue.php c:Q0mL:Q  0  mNc 1laInteresting Possibility@Internally, we build the following table for a specific deadlineA Little StatisticsIf they are independent Probability of failure by the deadline is the product of the failure probabilities We are computing success probabilities, but P(failure) = 1 - P(success) So Pall(failure) = (1-Psdsc(success))*(1-Puc(success))*(1-Pncsa(success)) Thus Pall(success) = 1 - Pall(failure) From the table, the probability that a job will get 64 nodes on some TG cluster is 1 - (0.78 * 0.63 * 0.81) = 0.61 Notice that adding fwgrid, boosts the probability to 0.95G" S"  " :"     @>!!Virtual Grid Resource ReservationVGiven a request for a specific set of nodes at a specific time Compute a set of job launch requests that has 95% chance of success before the deadline Launch requests in parallel When one or more requests acquire the processors, repeat Until there is no set that has 95% chance of success Hold the final set until the deadline Fits the  Find and Bind model in a curious way Keep Finding until the probability that no future Find will work is too high, then Bind Improves with scale Catch: Won t be able to say which processors will ultimately be selected?0X]?.90GCThe Virtual ClusterSpecify Number of processors in a processor metric Minimum point-to-point bw between any two processors Maximum point-to-point latency between any two clusters Minimum non-paged memory in any processor A deadline for when the Virtual Cluster is needed And the system returns a dedicated processor set fitting these constraints at (or before) the deadline If the computation is functional, can include automatic replication/checkpointing to ensure probability of success exceeds a specified threshold Could all be built into vgES66JZWFrom Here to Virtual ThereWe currently have The quantile and reverse quantile prediction software working and undergoing extensive testing Will demo EMAN using quantile parameterization at SC Working on a GridSAT version that uses Virtual Reservations Confidence bounds on BW Confidence bounds on resource availability What we would need Confidence bounds on latency and memory (hard, medium) Identification of independence sets (just starting) Resource selector (find best set of resources) Fault tolerance (replication and/or checkpointing) vgES implementation _qC_  4 ' -t  R $;   Near TermnDevelop scheduling models for EMAN based on quantile predictions Full distribution of quantiles can be used to guide scheduling Enhance the batch queue quantile predictors to take requested execution time into account Back filling makes estimates very conservative for short jobs Start work on a test implementation of Virtual Resource Reservations Looks entertaining on paper, be we don t believe it either GridSAT as a target applicationtA?Z>E[A?Z>E[  P, ! 8 P0`Lyonl1< 08  .,=>5/2347:-  p(  l  C 7O%   l  C ?P+I  H  0޽h ? lb   $(  $l $ C &O%   l $ C &  H $ 0޽h ? lbr !9;(   n|khhttp://pompone.cs.ucsb.edu/~nurmi/batchq/nindex.htmlvlbhttp://pompone.cs.ucsb.edu/~rgarver/invbqueue.php/ 0DTimesngbatsenPsd ackDCLB Helvetica Condensed Black DComic Sans MSCondensed BlackB0DZapf DingbatsCondensed Black@DArialingbatsCondensed Black"PDGenevangbatsCondensed Black a .  @n?" dd@  @@``   `, `  !; QQRS{C Q Qk ;+ ; +&%<M2    hb$?Rv$ ޜ7$R$ P߶\\y*4|D7$$$$$$$$$B$S&w;_牞m|B$ s΋adٞۻ d# lAA8c? % f@@! .R ʚ;fv3ʚ;g4KdKdsi0C/m Hpp+<4!d!dP`gʚ;<4ddddP`gʚ;<4ddddP`gʚ;0___PPT10 ___PPT9klJh___PPT2001D<4X? %^'g9Predicting Queue Waiting Time in Batch Controlled SystemsRich Wolski, Dan Nurmi, John Brevik, Graziano Obertelli Computer Science Department University of California, Santa Barbara VGrADS Workshop September 12, 2005 PEPFor Scheduling: It s all about the big QPredictions of the form  What is the maximum time my job will wait with X% certainty?  What is the minimum time my job will wait with X% certainty? Requires two estimates if certainty is to be quantified Estimate the (1-X) quantile for the distribution of availability => Qx Estimate the upper or lower X% confidence bound on the statistic Qx => Q(x,lb) If the estimates are unbiased, and the distribution is stationary, future availability duration will be larger than Q(x,lb) X% of the time, guaranteed ~8GnO  8 )       =            =  =t= = > '@The Brevik MethodJohn Brevik s invention based on Binomial distribution Probability that exactly j values are below qth quantile is 7" <   , TSee it In ActionJob Categories are defined by The machine on which the job will be submitted The queue (specified by name) into which the job will be submitted The requested processor count The requested run time (coming soon) Report three times: The 0.5 Quantile (50-50 chance) -- blue The 0.75 Quantile -- green The 0.95 Quantile -- purple Time format is hh:mm:ss Data updated every 60 seconds http://pompone.cs.ucsb.edu/~nurmi/batchq/nindex.html_k(H =%  5   k|Predicting Things Upside DownDeadline scheduling: My job needs to start in the next X seconds for the results to be meaningful. Amitava Mujumdar, Tharaka Devaditha, Adam Birnbaum (SDSC) Need to run a 4 minute image reconstruction that completes in the next 8 minutes Given a Machine Queue Processor count Run time Deadline What is the probability that a job will meet the deadline? http://pompone.cs.ucsb.edu/~rgarver/invbqueue.php c:Q0mL:Q  0  mNc 1laInteresting Possibility@Internally, we build the following table for a specific deadlineA Little StatisticsIf they are independent Probability of failure by the deadline is the product of the failure probabilities We are computing success probabilities, but P(failure) = 1 - P(success) So Pall(failure) = (1-Psdsc(success))*(1-Puc(success))*(1-Pncsa(success)) Thus Pall(success) = 1 - Pall(failure) From the table, the probability that a job will get 64 nodes on some TG cluster is 1 - (0.78 * 0.63 * 0.81) = 0.61 Notice that adding fwgrid, boosts the probability to 0.95G" S"  " :"     @>!!Virtual Grid Resource ReservationVGiven a request for a specific set of nodes at a specific time Compute a set of job launch requests that has 95% chance of success before the deadline Launch requests in parallel When one or more requests acquire the processors, repeat Until there is no set that has 95% chance of success Hold the final set until the deadline Fits the  Find and Bind model in a curious way Keep Finding until the probability that no future Find will work is too high, then Bind Improves with scale Catch: Won t be able to say which processors will ultimately be selected?0X]?.90GCThe Virtual ClusterSpecify Number of processors in a processor metric Minimum point-to-point bw between any two processors Maximum point-to-point latency between any two clusters Minimum non-paged memory in any processor A deadline for when the Virtual Cluster is needed And the system returns a dedicated processor set fitting these constraints at (or before) the deadline If the computation is functional, can include automatic replication/checkpointing to ensure probability of success exceeds a specified threshold Could all be built into vgES66JZWFrom Here to Virtual ThereWe currently have The quantile and reverse quantile prediction software working and undergoing extensive testing Will demo EMAN using quantile parameterization at SC Working on a GridSAT version that uses Virtual Reservations Confidence bounds on BW Confidence bounds on resource availability What we would need Confidence bounds on latency and memory (hard, medium) Identification of independence sets (just starting) Resource selector (find best set of resources) Fault tolerance (replication and/or checkpointing) vgES implementation _qC_  4 ' -t  R $;   Near TermnDevelop scheduling models for EMAN based on quantile predictions Full distribution of quantiles can be used to guide scheduling Enhance the batch queue quantile predictors to take requested execution time into account Back filling makes estimates very conservative for short jobs Start work on a test implementation of Virtual Resource Reservations Looks entertaining on paper, be we don t believe it either GridSAT as a target applicationtA?Z>E[A?Z>E[  P, ! 8 P0`Lyonl1< 08  .,=>5/2347:-  @ (   l   C 9O%   l   C `9  H   0޽h ? lb  tlP(  l  C  7O%   l  C @;  ^  6A 8c?@`  Z=xaxa1 ?' 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