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Modelling of state-dependent multirate systems carrying BPP traffic

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Abstract

This paper presents a simple approximate calculation methodology of the occupancy distribution and the blocking probability in state-dependent systems with multirate Binomial–Poisson–Pascal traffic. The particular traffic streams are generated by an infinite, as well as by a finite, population of traffic sources. The proposed methodology is based on the generalized Kaufman–Roberts recursion. The model enables calculations to be carried out for the systems in which accepting a new call depends on an admission control algorithm (e.g., a model of a full-availability group with bandwidth reservation) as well as for those systems in which accepting a new call depends on the structure of a system (e.g., a model of a limited-availability group). The results of the analytical calculations have been compared with the simulation results of exemplary state-dependent systems.

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Notes

  1. In all of the models listed above, “state dependance” results from the specific features of the servicing system. Additionally, the term “state-dependent system” is also used for the systems in which state dependance results from the specific features of traffic sources, i.e., in the case of limited number of traffic sources.

  2. In the paper, it is assumed that the letter “i” denotes a Poisson (Erlang) traffic class, the letter “j” a Binomial (Engset) traffic class, the letter “k” a Pascal traffic class, and the letter “c” an arbitrary traffic class, (c = i|j|k).

  3. Full-availability group is a model of a single link with complete sharing policy. This is an example of state-independent system that can be modeled by GKRR with σ c (n) = 1 for c = 1, 2, ..., M 1 + M 2 + M 3.

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  1. Communication and Computer Networks, Poznań University of Technology, ul. Polanka 3, 60-965, Poznań, Poland

    Mariusz Głąbowski

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Głąbowski, M. Modelling of state-dependent multirate systems carrying BPP traffic. Ann. Telecommun. 63, 393–407 (2008). https://doi.org/10.1007/s12243-008-0034-5

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