Empirical relationship for queue length estimation in a system with fractal shot input

Traffic in modern data networks and information systems are most adequately described by different classes of fractal models. This kind of models takes into account the following key characteristics of traffic as high variability events grouping and explicit correlation structure on different time scales. Fractal shot process FSNDP, referring to the fractal point process is sufficiently accurate approximation of the network load at individual workstations or small workgroups, is defined with five numerical parameters, with known estimating algorithms on available samples (based on actual traffic dumps). Studies based on queueing system simulation with input FSNDP stream managed to establish a stable relationship between the change in each of the input parameters and the average queue length in the system. Confirmed direct correlation queue length of the parameter characterizing the amplitude of the individual load bursts, found an inverse relationship of the index related to the Hurst parameter and master degree of fractal properties. Based on the identified dependencies, obtained empirical relations between parameters of FSNDP process and the average queue length in single-channel queueing system with unlimited queue and deterministic service discipline FSNDP/D/1. These relationships allow to estimate the average volume of buffer used and the average delay introduced by the network equipment in the load conditions expressed fractal properties from measurements of real traffic. The presence of the formulae increases the importance of traffic models based on FSNPD, since it makes possible to perform a full cycle analysis of queueing systems and queueing networks without involving the simulation methods.