The latest information technologies have revealed new properties of application flows and their service procedures, which are generally reflected in the property of self-similarity of traffic. The problem is the insufficient attention of developers to the methods of calculating the parameters of queuing systems (QS) taking into account the properties of self-similarity. In modern studies of new-generation information systems, an attempt is made to analyze the parameters of QS associated with ensuring quality of service (QoS). This provides more accurate QoS values in comparison with the analysis of parameters for the simplest flow of events. The objective of this study is to analytically and quantitatively assess the discrepancies in the assessment of the performance indicators of QS with self-similarity features compared to the results of their calculations using traditional mathematical models with Poisson flows. The main attention in the study is paid to the advantages of using the Weibull distribution over the Pareto distribution in describing phenomena in QS with self-similarity features. The article presents the results of modeling QS using the tools of Weibull and Pareto distributions, emphasizing the preference of the Weibull distribution. The article discusses through quantitative indicators the importance and features of the influence of the self-similarity property on the quantitative parameters of QoS in queuing systems.