usl (version 1.8.0)

usl: Create a model for the Universal Scalability Law

Description

usl is used to create a model for the Universal Scalability Law.

Usage

usl(formula, data, method = "default")

Arguments

formula

An object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be analyzed. The details of model specification are given under 'Details'.

data

A data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which usl is called.

method

Character value specifying the method to use. The possible values are described under 'Details'.

Value

An object of class USL.

Details

The Universal Scalability Law is used to forcast the scalability of either a hardware or a software system.

The USL model works with one independent variable (e.g. virtual users, processes, threads, ...) and one dependent variable (e.g. throughput, ...). Therefore the model formula must be in the simple "response ~ predictor" format.

The model produces two coefficients as result: sigma models the contention and kappa the coherency delay of the system. The function coef extracts the coefficients from the model object.

The argument method selects which solver is used to solve the model:

• "default" for the default method using a transformation into a 2nd degree polynom. It can only be used if the model frame contains a value for the normalization where the predictor equals "1" for one measurement. This is the algorithm introduced by Dr. Neil J. Gunther in the book Guerrilla Capacity Planning.

• "nls" for a nonlinear regression model. This method estimates not only the coefficients sigma and kappa but also the scale.factor for the normalization. nls with the "port" algorithm is used internally to solve the model. So all restrictions of the "port" algorithm apply.

• "nlxb" for a nonliner regression model using the function nlxb from the nlsr package. This method also estimates both coefficients and the normalization factor. It is expected to be more robust than the nls method.

The "nlxb" solver is used as fallback if the "default" method is selected and a predictor equal "1" is missing. A warning message will be printed in this case.

The Universal Scalability Law can be expressed with following formula. C(N) predicts the relative capacity of the system for a given load N:

$$C(N) = \frac{N}{1 + \sigma (N - 1) + \kappa N (N - 1)}$$

References

Neil J. Gunther. Guerrilla Capacity Planning: A Tactical Approach to Planning for Highly Scalable Applications and Services. Springer, Heidelberg, Germany, 1st edition, 2007.

John C. Nash. nlsr: Functions for nonlinear least squares solutions, 2017. R package version 2017.6.18.

See Also

efficiency,USL-method, scalability,USL-method, peak.scalability,USL-method, summary,USL-method, predict,USL-method, overhead,USL-method, confint,USL-method, coef, fitted, residuals, df.residual

Examples

# NOT RUN {
require(usl)

data(raytracer)

## Create USL model for "throughput" by "processors"
usl.model <- usl(throughput ~ processors, raytracer)

## Show summary of model parameters
summary(usl.model)

## Show complete list of efficiency parameters
efficiency(usl.model)

## Extract coefficients for model
coef(usl.model)

## Calculate point of peak scalability
peak.scalability(usl.model)

## Plot original data and scalability function
plot(raytracer)
plot(usl.model, add=TRUE)

# }