Simulation model of a QS with hyperexponential distribution in the GPSS World environment

This article presents results obtained on the development of a pseudo-random sequence generator for simulation modeling of queueing system (QS) with second-order hyperexponential input distribution. In the scientific literature on GPSS WORLD, including web resources, the authors did not find any data in this subject area. The GPSS WORLD library includes many generators of various distribution laws, but there are no generators for such important composite distributions according to the queuing theory. It is known that the hyperexponential distribution concept provides a wide range of changes in the random variable variation coefficient from unity to an arbitrarily large value. Due to the fact that the variation coefficients of arrival and service intervals play an important role in estimating the delay of queue claims in queuing systems, thus this distribution concept plays a special role in modeling of QS. For ahyperexponential distribution of the second order, the authors previously obtained numerical-analytical results based on the Lindley integral equation spectral solution method. The article describes a developed algorythm and a program on GPSS WORLD to simulate the functioning of QS with hyperexponential input distribution incl. description of operation of logical switches. The difference between analytical and simulation modeling of the two-phase representation of a given distribution concept is explained on the example of the developed model. The adequacy of the obtained results was confirmed by comparing the simulation results with the results of numerical simulation in the Mathcad environment.