Verification of Kolmogorov Equation Usability for Reproduction and Death Processes

Abstract

A simulation is widely used as a basis for decision support systems. Many production systems may be considered as queuing systems if a time of processes more valuable than their physical meaning. Program models realized queuing systems are used in a planning and in optimization targets. But results of program simulation are not suitable for scientific qualification works according to traditions. Analytical conclusions are made using Kolvogorovs’ equations and some models derived from the one usually. But a question about possibility of using them with widespread statistical distributions is not quite explored. In this article we investigate a possibility of using the Kolmogorov's equations on a simple reproduction and death queuing system with some distributions. Numerical data is obtained from program models realized in GPSS and AnyLogic. Theoretical results in comparison with numerical data lead us to a conclusion. The possibility is present only when all statistical distributions in the model are exponential or very close to exponential. Else average error between the theory and the model is above 60%. So far as a small experimental data typical for observations in production systems does not allow to determine own statistical distribution surely, an uniform distribution is accepted as default, and Kolmogorov’s equations could not be used.