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Analysis of the parameters of the functioning of software-defined networks is very relevant. There are many approaches using the methods of queuing theory to evaluate the processing quality parameters in the G/G/1 system. At this stage of development of infocommunication networks, it is required to develop analytical models that allow assessing the parameters of the quality of service for traffic in software-defined networks. In the paper, analytical expressions are obtained that allow estimating the average waiting time for a request in the SDN switch using the mathematical apparatus of the queuing theory based on the analysis of the drive. In this case, random time intervals between incoming requests have a hyperexponential distribution. A queuing system of the H2/G/1/∞ type was used as a model. A mixture of exponential distributions makes it possible to take into account the fractal properties of the sequence of random time intervals between incoming requests, the “heavy tail” of the initial simulated distribution, and the correlation properties of the considered time intervals. The paper compares the results of calculating the waiting time of a claim in the storage for the H2/G/1/∞ system with the result for the G/G/1/∞ system, which is approximated by a queue model of the P/W/1/∞ type, where the average waiting time is estimated applications in the queue were carried out on the basis of solving the Lindley equation by the spectral method. It is shown that the obtained results are consistent.