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

Mariusz Głąbowski,Maciej Stasiak,Damian Kmiecik

doi:10.3390/electronics10040508

Mariusz Głąbowski, Maciej Stasiak + Show 1 more

Open Access

https://doi.org/10.3390/electronics10040508

Copy DOI

Journal: Electronics	Publication Date: Feb 22, 2021
Citations: 6	License type: CC BY 4.0

Affiliation: Poznań University of Technology

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.

Highlights

Traffic overflow is one of the oldest techniques for the optimization of traffic stream distributions in telecommunications and computer networks
The overflow mechanism is initiated in time intervals that correspond to the states of total occupancies of resources termed primary resources, historically primary group or direct group
The initial assumption is that the primary resources of the system are offered mixtures of Erlang, Engset, and Pascal multi-service traffic streams

Summary

Introduction

Traffic overflow is one of the oldest techniques for the optimization of traffic stream distributions in telecommunications and computer networks. To describe the resources of present-day telecommunications networks, the term “network resources” is used, expressed in allocation units, for example, links, channels or basic bandwidth units [1]). In such states, new calls that cannot be serviced by the primary resources will be directed (will overflow) to other available resources that can service a given call at the time. Traffic overflow was primarily used in single-service hierarchical telecommunications networks with traffic redirection through alternative routes [2,3,4,5]. The use of alternative resources guaranteed easy adaptability of a network to changeable load conditions resulting from both changes in the intensity and structure of offered traffic and from damages to certain elements of the network (link groups, exchanges), without the costly necessity to develop and expand switching exchanges [6]

Objectives

Methods

Results

Conclusion