Limitations of a Mapping Algorithm with Fragmentation Mimics (MAFM) when modeling statistical data sources based on measured packet network traffic

The MAFM algorithm allows the estimation of a theoretical packet-size histogram for different distributions of the data-length process. In this paper describes in detail the limitations of a developed algorithm, which are correlates with the long-range dependence of data-length distribution. It is shown that a developed MAFM algorithm has limited usability for distribution types which do not posses the finite value of an expected value. In order to improve the robustness for such types of distribution, the new parameter ULS (Upper Limit of Summa) is involved in the original MAFM algorithm. The ULS parameter limits the tail of the distribution. By assuming a finite ULS value, the MAFM algorithm can now be used for all distributions of the data-length process, as well as for distributions without a defined expected value, such as Pareto. The presented analytical results have been confirmed by experiments through the use of the simulation tool.