Software generators in the GPSS World environment for distributions-probability mixtures with quality assessment results

This article presents quality assessment results for the software generators of pseudo-random sequences (PRS) presented in [1; 2] for QS simulation, including second-order hyper-Erlang and hyper-exponential distributions of the second order, that flows organically from these works. These distribution laws are in demand in queuing theory as it provides a big range of changes in the variation coefficient which plays an important role in the average queue delay calculating. There is no data on such generators neither in scientific literature, no in the GPSS WORLD library. Software generator quality evaluation, regardless of the programming language, is usually made according to statistical tests. In this case, chi-squared and Kolmogorov-Smirnov's tests are used. In addition, the comparison between theoretical and statistical aspects of the corresponding order is provided. Unlike simple distribution laws, for which the use of the above mentioned statistical tests is provided for in well-known software products and does not cause any difficulties, in our case automatic testing is impossible. The well-known packages STATISTICA, STATGAPHICS, Matlab/Simulink, etc. do not provide for the use of the hyper-Erlang and hyper-exponential distribution laws we consider. Therefore, the Pearson statistical test is calculated and checked manually. The presented results should be useful for professionals of discrete event modeling in the GPSS WORLD environment.