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Mathematical Problems in Engineering
Volume 2013, Article ID 852082, 18 pages
Research Article

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

Poznan University of Technology, Polanka 3, 60-965 Poznan, Poland

Received 10 March 2013; Accepted 7 May 2013

Academic Editor: Jun Jiang

Copyright © 2013 Mariusz Głąbowski et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.