Two-Dimensional Convolution Algorithm for Modelling Multiservice Networks with Overflow Traffic

Abstract

The present paper proposes a new method for analytical modelling multiservice networks with implemented traffic overflow mechanisms. The basis for the proposed method is a special two-dimensional convolution algorithm that enables determination of the occupancy distribution and the blocking probability in network systems in which traffic streams of individual classes can be serviced by both primary and alternative resources. The algorithm worked out by the authors makes it possible to model systems with any type of traffic offered to primary resources. In order to estimate the accuracy of the proposed method, the analytical results of blocking probabilities in selected networks with traffic overflow have been compared with simulation data.

Optimized two dimensional convolution algorithm for modelling systems with overflow traffic

“…1 is composed of many primary groups. [10] proposes a division of such a system into smaller subsystems, called basic subsystems. A basic system is a system that is composed of a primary group and an alternative group.…”

“…The proposed division of the system with traffic overflow into subsystems provides an opportunity to develop a method for the analysis of such systems on the basis of an appropriately devised convolution algorithm, the so-called twodimensional convolution [10]. Unlike in modelling methods that use Hayward's approach [8], [9], [13], in the convolution algorithm the capacities of both groups remain the same and are not modified, and the same applies to the number of demanded BBUs by a single call.…”

“…for individual subsystems j (j ∈ K) make it possible to determine, according to [10], the occupancy distribution in the whole of the multiservice system with traffic overflow, and then to determine traffic characteristics of such a system. This article proposes a method, simplified as compared to [10], for a determination of the two-dimensional occupancy distribution for basic subsystems.…”

“…The variety of offered network services currently available makes the formerly adopted assumptions, however, insufficient for a precise description of call streams generated in packet networks. In order to make analytical modelling of the network with any distribution of call streams offered to primary resources possible, [10] proposes a new method for modelling multi-service packet networks with implemented traffic overflow mechanisms. The basis of the proposed method is the so-called two dimensional convolution algorithm.…”

“…The basis of the proposed method is the so-called two dimensional convolution algorithm. The method for a determination of twodimensional occupancies presented in [10] is characterized by high accuracy, though at the expense of its high computational complexity. The present article aims to develop a method that would allow the computational complexity of the twodimensional convolution method to be decreased [10] retaining at the same time its high accuracy of calculations, so that it would be still applicable in engineering practice.…”