The Universal Scalability Law (Gunther 2007)
This is an R package to analyze system performance data with the Universal Scalability Law.
The Universal Scalability Law (USL) was developed by Dr. Neil J. Gunther. It can be used to analyze system performance data in order to learn more about the scalability limitations of the system.
Details are presented in the book Guerrilla Capacity Planning and on the authors website.
Here is an example for the scalability analysis of a Sun SPARCcenter 2000 in the SPEC SDM 91 benchmark. The data used is available for download from the SPEC website and also included as a demo dataset.
library(usl)# Load data from the SPEC SDM91 benchmarkdata(specsdm91)specsdm91# Analyze "throughput" by "load" for the "specsdm91" datausl.model <- usl(throughput ~ load, specsdm91)# Show a model summary including scalability coefficientssummary(usl.model)# Predict the location of the maximum in the scalability functionpeak.scalability(usl.model)# Plot original data and computed scalability functionplot(specsdm91, pch=16)plot(usl.model, col="red", add=TRUE)
summary command returns the following output:
Call: usl(formula = throughput ~ load, data = specsdm91) Scale Factor for normalization: 64.9 Efficiency: Min 1Q Median 3Q Max 0.1214 0.2254 0.3966 0.7799 1.0000 Residuals: Min 1Q Median 3Q Max -70.89 -23.59 19.39 86.14 274.88 Coefficients: Estimate Std. Error t value Pr(>|t|) sigma 1.705e-02 3.318e-03 5.137 0.00365 ** kappa 7.892e-05 2.492e-05 3.167 0.02489 * --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 140.6 on 5 degrees of freedom Multiple R-squared: 0.9624, Adjusted R-squared: 0.9549
The following image shows the plotted output:
The package is available from CRAN. Use the following command to install the package from the repository:
In addition to the package documentation there is also a package vignette available. Install the package and use the following command to open the vignette:
The vignette is also available from CRAN: https://CRAN.R-project.org/package=usl/vignettes/usl.pdf
CHANGES in `usl' VERSION 1.8.0 (2017-08-07)
nlsrpackage will replace the older
nlmrtpackage. The package has been updated accordingly.
CHANGES in `usl' VERSION 1.7.0 (2016-10-13)
CHANGES in `usl' VERSION 1.6.0 (2016-06-17)
Remove unused parameter
R' from the signature of theconfint()' function.
Add additional section about multivalued data to vignette.
CHANGES in `usl' VERSION 1.5.0 (2016-02-25)
nlxb' as fallback if the value for the scale factor is missing in the data and thedefault' method is used. A warning message is printed
in this case. This is more user-friendly than the error message given
Remove unused parameter
R' from the signature of theusl()' function.
CHANGES in `usl' VERSION 1.4.1 (2014-12-29)
methods' package instead of importing it. This fixes a problem with callingusl()' from Rscript.
Minor fixes concerning coding style and typos.
CHANGES in `usl' VERSION 1.4.0 (2014-11-04)
CHANGES in `usl' VERSION 1.3.1 (2014-06-20)
CHANGES in `usl' VERSION 1.3.0 (2014-06-02)
The estimation of standard errors for the coefficients has been rewritten.
Bootstrapping is no longer used for the calculation. Therefore the argument
R' for theusl()' function and the argument
type' for theconfint()'
function have been deprecated. The arguments will be removed in the next
Added coefficient standard errors and residual standard error to the summary output.
Added implementation for the df.residual() function to get the degrees of freedom for the model.
Removed misleading calculation of deviance.
Used roxygen2 4.0.1 to generate the documentation.
Added a new demo data set `oracledb'.
CHANGES in `usl' VERSION 1.2.2 (2014-04-03)
Use roxygen2 3.1 to generate documentation.
Fix handling of unsorted input data frame for method="default".
CHANGES in `usl' VERSION 1.2.1 (2013-08-12)
CHANGES in `usl' VERSION 1.2.0 (2013-04-29)
CHANGES in `usl' VERSION 1.1.0 (2013-02-26)
Added a package vignette.
Import' instead ofDepend' for the used packages.
efficiency()' now returns a named vector. The names are the values of the independent variable, cf.fitted()' or `residuals()'.
CHANGES in `usl' VERSION 1.0.0 (2013-02-10)