Engineering Approach to Calculating QoS of Server with Self-Similar Incoming Traffic Based on Recursive Scalable Poisson Model

Abstract

Abstract:To date the prospects for using the accumulated over many years mathematical and software for the modeling of telecommunications with the Poisson input flow are under a big question. The matter is that a new fractal queuing theory is already on the threshhold. This article formulates and solves the problem of application of a queuing system model with a Poisson incoming flow for the purposes of server modeling described by QS with self-similar incoming traffic of the "fractal Brownian motion" type (according to Norros). Based on the results of the morphological analysis, the Norros model was decomposed into Poisson components connected by a scalable recurrence scheme. The variance of the number of packets in the server, raised to the power determined by the Hurst parameter acts as the similarity coefficient of fractal and Poisson QSs. The method for rescaling Poisson solutions into fractal solutions was constructed on the basis of the similarity coefficient. According to this method in order to find the fractal delay of access, the Poisson delay should be multiplied by the similarity coefficient, and to estimate the probability of packet loss, it is necessary to extract a root of degree equal to the similarity coefficient from classical exponential losses. The scope of the re-scaling method focuses on the pre-project stages of creating telecommunications, where there is no need for high accuracy of simulation results.