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COMMUN. STATIST. -SIMULA., 20(1), 375-390 (1991)


Kimmo E. E. Raatikainen

University of Helsinki, Department of Computer Science
Teollisuuskatu 23{25, SF-00510 Helsinki, Finland

Key Words and Phrases: modeling of simulation input data; nonlinear data transformation; robust regression.


Shapes of service-time distributions in queueing network models have a great impact on the distribution of system response-times. It is essential for the analysis of response-time distribution that the modeled service-time distributions have the correct shape. Tradionally modeling of service-time distributions is based on a parametric approach by assuming a specific distribution and estimating its parameters. We introduce an alternative approach based on the principles of exploratory data analysis and nonparametric data modeling. The proposed method applies nonlinear data transformation and resistant curve fitting. The method can be used in cases, where the available data is a complete sample, a histogram, or the mean and a set of 5-10 quantiles. The reported results indicate that the proposed method is able to approximate the distribution of measured service times so that accurate estimates for quantiles of the response-time distribution are obtained.


When queueing network models are simulated, the analyst must specify the service-time distributions and the branching probabilities. The traditional approach of modeling service-time distributions has been to assume that the distribution belongs to the Coxian family, and then to estimate the parameters. The Coxian family of distributions, introduced by Cox (1955), consists of all the distributions having a