Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2012, Article ID 547909, 17 pages doi:10.1155/2012/547909 Research Article Properties of Recurrent Equations for the Full-Availability Group with BPP Traffic Mariusz Gla ¸bowski, Maciej Stasiak, and Joanna Weissenberg Communication and Computer Networks, Faculty of Electronics and Telecommunications, Poznan University of Technology, ul. Polanka 3, 60-965 Poznan, Poland Correspondence should be addressed to Mariusz Gła ¸bowski, mariusz.glabowski@put.poznan.pl Received 27 April 2011; Accepted 1 August 2011 Academic Editor: Yun-Gang Liu Copyright q 2012 Mariusz Gła ¸bowski 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 paper proposes a formal derivation of recurrent equations describing the occupancy distribution in the full-availability group with multirate Binomial-Poisson-Pascal BPP traffic. The paper presents an effective algorithm for determining the occupancy distribution on the basis of derived recurrent equations and for the determination of the blocking probability as well as the loss probability of calls of particular classes of trafficoffered to the system. A proof of the convergence of the iterative process of estimating the average number of busy traffic sources of particular classes is also given in the paper. 1. Introduction Dimensioning and optimization of integrated networks, that is, Integrated Services Digital Networks ISDN and Broadband ISDN B-ISDN as well as wireless multiservice networks e.g., UMTS, have recently developed an interest in multirate models 1–5. These models are discrete models in which it is assumed that the resources required by calls of particular traffic classes are expressed as the multiple of the so-called Basic Bandwidth Units BBUs. The BBU is defined as the greatest common divisor of the resources demanded by all call streams offered to the system 6, 7. Multirate systems can be analysed on the basis of statistical equilibrium equations resulting from the multidimensional Markov process that describe the service process in the considered systems 8–13. Such an approach, however, is not effective because of the quickly increasing—along with the system’s capacity—number of states in which a multidimensional Markov process occurring within the system can take place 14. Consequently, for an analysis of multirate systems, there are used methods based on the convolution algorithm