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WUSTL CSE 567M - Workload Characterization Techniques

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6-1©2006 Raj JainCSE567MWashington University in St. LouisWorkload Workload Characterization Characterization TechniquesTechniquesRaj Jain Washington University in Saint LouisSaint Louis, MO [email protected] slides are available on-line at:http://www.cse.wustl.edu/~jain/cse567-06/6-2©2006 Raj JainCSE567MWashington University in St. LouisOverviewOverview! Terminology! Components and Parameter Selection! Workload Characterization Techniques: Averaging, Single Parameter Histograms, Multi-parameter Histograms, Principal Component Analysis, Markov Models, Clustering! Clustering Method: Minimum Spanning Tree, Nearest Centroid! Problems with Clustering6-3©2006 Raj JainCSE567MWashington University in St. LouisTerminologyTerminology! User = Entity that makes the service request= Workload Unit or Workload component! Workload components:" Applications" Sites" User Sessions! Workload parameters or Workload features: Measured quantities, service requests, or resource demands.For example: transaction types, instructions, packet sizes, source-destinations of a packet, and page reference pattern.6-4©2006 Raj JainCSE567MWashington University in St. LouisComponents and Parameter SelectionComponents and Parameter Selection! The workload component should be be at the SUT interface.! Each component should represent as homogeneous a group as possible. Combining very different users into a site workload may not be meaningful.! Domain of the control affects the component: Example: mail system designer are more interested in determining a typical mail session than a typical user session.! Do not use parameters that depend upon the system, e.g., the elapsed time, CPU time.6-5©2006 Raj JainCSE567MWashington University in St. LouisComponents (Cont)Components (Cont)! Characteristics of service requests:" Arrival Time" Type of request or the resource demanded" Duration of the request" Quantity of the resource demanded, for example, pages of memory! Exclude those parameters that have little impact.6-6©2006 Raj JainCSE567MWashington University in St. LouisWorkload Characterization TechniquesWorkload Characterization Techniques1. Averaging2. Single-Parameter Histograms3. Multi-parameter Histograms4. Principal Component Analysis5. Markov Models6. Clustering6-7©2006 Raj JainCSE567MWashington University in St. LouisAveragingAveraging! Mean! Standard deviation:! Coefficient Of Variation:! Mode (for categorical variables): Most frequent value! Median: 50-percentiles/x6-8©2006 Raj JainCSE567MWashington University in St. LouisCase Study: Program Usage Case Study: Program Usage in Educational Environmentsin Educational Environments! High Coefficient of Variation6-9©2006 Raj JainCSE567MWashington University in St. LouisCharacteristics of an Average Editing SessionCharacteristics of an Average Editing Session! Reasonable variation6-10©2006 Raj JainCSE567MWashington University in St. LouisSingle Parameter HistogramsSingle Parameter Histograms! n buckets × m parameters × k components values.! Use only if the variance is high.! Ignores correlation among parameters.6-11©2006 Raj JainCSE567MWashington University in St. LouisMultiMulti--parameter Histogramsparameter Histograms! Difficult to plot joint histograms for more than two parameters.6-12©2006 Raj JainCSE567MWashington University in St. LouisPrincipal Component AnalysisPrincipal Component Analysis! Key Idea: Use a weighted sum of parameters to classify the components.! Let xijdenote the ith parameter for jth component.yj= ∑i=1nwixij! Principal component analysis assigns weights wi's such that yj's provide the maximum discrimination among the components.! The quantity yjis called the principal factor.! The factors are ordered. First factor explains the highest percentage of the variance.6-13©2006 Raj JainCSE567MWashington University in St. LouisPrincipal Component Analysis (Cont)Principal Component Analysis (Cont)! Statistically: " The y's are linear combinations of x's:yi= ∑j=1naijxjHere, aijis called the loading of variable xjon factor yi." The y's form an orthogonal set, that is, their inner product is zero:<yi, yj> = ∑kaikakj= 0This is equivalent to stating that yi's are uncorrelated to each other." The y's form an ordered set such that y1explains the highest percentage of the variance in resource demands.6-14©2006 Raj JainCSE567MWashington University in St. LouisFinding Principal FactorsFinding Principal Factors! Find the correlation matrix.! Find the eigen values of the matrix and sort them in the order of decreasing magnitude.! Find corresponding eigen vectors. These give the required loadings.6-15©2006 Raj JainCSE567MWashington University in St. LouisPrincipal Component ExamplePrincipal Component Example6-16©2006 Raj JainCSE567MWashington University in St. LouisPrincipal Component ExamplePrincipal Component Example! Compute the mean and standard deviations of the variables:6-17©2006 Raj JainCSE567MWashington University in St. LouisPrincipal Component (Cont)Principal Component (Cont)! Similarly:6-18©2006 Raj JainCSE567MWashington University in St. LouisPrincipal Component (Cont)Principal Component (Cont)! Normalize the variables to zero mean and unit standard deviation. The normalized values xs0and xr0are given by:6-19©2006 Raj JainCSE567MWashington University in St. LouisPrincipal Component (Cont)Principal Component (Cont)! Compute the correlation among the variables:! Prepare the correlation matrix:6-20©2006 Raj JainCSE567MWashington University in St. LouisPrincipal Component (Cont)Principal Component (Cont)! Compute the eigen values of the correlation matrix: By solving the characteristic equation:! The eigen values are 1.916 and 0.084.6-21©2006 Raj JainCSE567MWashington University in St. LouisPrincipal Component (Cont)Principal Component (Cont)! Compute the eigen vectors of the correlation matrix. The eigen vectors q1corresponding to λ1=1.916 are defined by the following relationship:{ C}{ q}1= λ1{q}1or:or:q11=q216-22©2006 Raj JainCSE567MWashington University in St. LouisPrincipal Component (Cont)Principal Component (Cont)! Restricting the length of the eigen vectors to one:! Obtain principal factors by multiplying the eigen vectors by thenormalized vectors:! Compute the values of the principal factors.! Compute the sum and sum of squares of the principal factors.6-23©2006 Raj JainCSE567MWashington University in St. LouisPrincipal Component (Cont)Principal Component (Cont)! The sum must be zero.! The sum of


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