usl {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'.

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 main coefficients as result: alpha models the contention and beta the coherency delay of the system. The third coefficient gamma estimates the value of the dependent variable (e.g. throughput) for the single user/process/thread case. It therefore corresponds to the scale factor calculated in previous versions of the usl package.

The function coef extracts the coefficients from the model object.

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

• "nls" for a nonlinear regression model. This method estimates all coefficients alpha, beta and gamma. The R base function 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 all three coefficients. It is expected to be more robust than the nls method.

• "default" for the default method using a transformation into a 2nd degree polynom has been removed with the implementation of the model using three coefficients in the usl package 2.0.0. Calling the "default" method will internally dispatch to the "nlxb" solver instead.

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{\gamma N}{1 + \alpha (N - 1) + \beta N (N - 1)}

Value

An object of class USL.

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, optimal.scalability,USL-method, limit.scalability,USL-method, summary,USL-method, sigma,USL-method predict,USL-method, overhead,USL-method, confint,USL-method, coef, fitted, residuals, df.residual

Examples

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)