On Increasing the Accuracy of Modeling Multi-Service Overflow Systems with Erlang-Engset-Pascal Streams

Abstract

In this article, we present an analysis of the accuracy level of methods for modeling the multi-service overflow systems that service Erlang, Engset, and Pascal traffic. In systems with traffic overflow, new calls that cannot be serviced by the primary resources are overflown (directed) to other available resources that can service a given call, that is, to the secondary resources (alternative resources). In the article, we focus on studying the influence of methods for determining the parameters of traffic that overflows to the secondary resources on the accuracy of determining the traffic characteristics of overflow systems. Our analysis revealed that the main source of the inaccuracy of the existing methods is their approach to determining both the average value and the variance of multi-service Pascal traffic streams offered to the secondary resources. Therefore, we proposed a new method for determining the parameters of Pascal overflow traffic. The method is based on the decomposition of multi-service primary resources into single-service resources and the subsequent conversion of Engset and Pascal streams into equivalents of Erlang traffic. The results of the analytical calculations obtained on the basis of the new method are then compared with the results of simulation experiments for a number of selected structures of overflow systems that service Erlang, Engset, and Pascal traffic. The results of the study indicate that the proposed theoretical model has a significantly higher accuracy than the models proposed in the literature. The method can be used in the analysis, dimensioning, and optimization of multi-service telecommunication systems composed of separated resources, for example, mobile cellular systems.