Calculation of the Self-similar Traffic Characteristics Which Is an Approximation to the Pareto Distribution

: pp. 63 - 67
О.S. Popov Odessa national academy of telecommunications
О.S. Popov Odessa national academy of telecommunications

The model of self-similar traffic is widely used, but some tasks of assessing the quality of service in the packet network are unresolved. It is known that in the presence of self-similarity properties in the incoming stream of requirements with increasing load intensity ρ, the quality of service characteristics deteriorate, but not as much as is assumed by the Norros method. The discrepancy between the results of modeling and estimates obtained by the Norros method is hundreds of percent. It is obvious that the estimate of Norros formula is significantly overestimated, which requires finding a more accurate solution. A method is proposed for increasing the accuracy of calculating the quality characteristics of servicing self-similar traffic due to a more accurate determination of the Hurst coefficient as a function of the parameter of the Pareto distribution form. For the self-similar traffic described by the Pareto distribution, a new formula for calculating the Hurst coefficient is obtained. In this case, the calculation of the quality of service characteristics can be performed on the basis of the Norros formula. The proposed method allows us to calculate the quality of service characteristics of self-similar traffic described by the Pareto distribution in a single-channel system with discrete time of packets service is much simpler. This simplicity is explained by the fact that in order to calculate the self-similarity coefficient of Hurst, you only need to know the parameter a of the Pareto distribution form and you do not have to calculate for this traffic in a very complicated way, for example, using absolute least-squares methods or R/S-statistics.

1. Lozhkovskyi A. G., 2008, Сравнительный анализ методов расчета характеристик качества обслуживания при самоподобных потоках в сети [Comparative analysis of methods for calculating the quality of service characteristics with self-similar flows in the network], Modeling and Information Technologies: Coll. Science. pr. IPM NAS of Ukraine., 47, 187–193. 2. Lozhkovskyj A. G., Verbanov O. V. & Kolchar V. M., 2011, Математическая модель пакетного трафика [Mathematical model of packet traffic], Bulletin of the National Polytechnic University “HPI”, 9, 113–119. 3. Lozhkovskyj A. G. & Verbanov O. V., 2014, Моделирование трафика мультисервисных пакетных сетей с оценкой его коэффициента самоподобности [Modeling the traffic of multiservice packet networks with an estimate of its self-similarity coefficient], Collection of scientific works O. S. Popov ONAT, 1, P. 70–76. 4. Krylov V. V. & Samohvalova S. S., 2005, Teletraffic theory and its applications, SPb.: BHV-Peterburg, 288 p. 5. Norros Ilkka, 1994. A storage model with self-similar input. Queuing Systems, 16. 6. Mandelbrot B., 2002, Fractal Geometry of Nature // Computing in mathematics, physics, biology. transl., M.: Publishing house of the Institute of Computer Research. 7. Lozhkovskyi A. G., Salmanov N. S. & Verbanov O. V., 2007, Моделирование многоканальной системы обслуживания с организацией очереди [Simulation of multi-channel queuing system with queuing’, Eastern European journal of advanced technologies], 3/6(27), 72–76.