Simulation Using GPSS
Application of GPSS Five to Discrete System Simulation
Application of GPSS Five to Discrete System Simulation
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This paper presents a technique for sampling from the three-parameter Weibull distribution within the context of GPSS, and briefly discusses the routine extension of this technique to the case of sampling from the gamma distribution. The several alternative algorithms which appear in the literature for sampling from these important distributions cannot be implemented directly in GPSS, because they involve such things as evaluation of logarithms and exponentiation, capabilities which GPSS does not currently have. The Weibull sampling technique developed and illustrated here in detail consequently involves creating generalized tables of pertinent functions, then performing lookups in these tables to support the sampling process. Kolmogorov-Smirnov and Chi-square testing of a large variety of samples drawn via this technique support the hypothesis at the 0.05 significance level that the samples were drawn from Weibull populations. The Weibull and gamma distributions are important in describing the behavior of a variety of random phenomena which occur in the fields of inventory theory, queuing theory, reliability studies, and maintenance scheduling. Because of the wide variety of shapes which these distributions can assume, they are also of interest in fitting empirical data which, consistent with the Weibull and gamma distributions, are typically non-negative, skewed, and unimodal. The methodology presented here, although straightforward, has not previously appeared in the literature, and is thought to be of potential interest and utility to a large number of GPSS users.