CALCULATION ACCURACY OF THE HURST EXPONENT AND SERVICE WAITING PROBABILITY OF PACKETS SELF-SIMILAR TRAFFIC

Abstract

Estimation of the service quality (QoS) characteristics in a single-channel system with an infinite queue of the packet network often reduces to determining the Hurst exponent of self-similar traffic, after which on the Norros formula calculates the average number of packets in the system and all other characteristics. The Hurst exponent can be determined by R/S-statistics method based on actual measurements of traffic characteristics or from probability distribution functions describing this traffic. However, the well-known formulas for calculating the Hurst exponent, which show its dependence on the parameters of the probability distribution of traffic, are not accurate. A method is proposed for improving the accuracy of calculating QoS characteristics in a packet communication network by more accurately finding the traffic self-similarity coefficient or the Hurst exponent depending on the parameters of the probability distribution function of the time interval between packets. In case when, in traffic, the time interval between packets is described by Pareto or Weibull distributions, new formulas have been obtained for calculating the traffic self-similarity factor based on the shape parameter of these distributions. After a more accurate determination of the Hurst exponent in this way, the average number of packets in the system is then calculated using the Norros formula, and then from the proposed approximation of the system state distribution function, service waiting probability of packet to calculate. With an increase in the accuracy of calculating the Hurst exponent, the accuracy of calculating the service quality characteristics also increases. Simulation modeling confirmed the validity of these methods for calculating QoS characteristics in a system with self-similar traffic. In this case, the discrepancy between the results of modeling and calculation does not exceed 5% when the system load changes in the range of 0.3 < ρ < 1 and the value of the Hurst exponent is 0.5 < H < 0.9.