The queue model P/M/1/K with the Hurst parameter (self-similarity parameter) estimator in the Simulink environment is described in the present paper using wavelet transformation. The estimation error of the parameter is analyzed depending on the parameter’s value, as well as the number of measurements based on which the parameter is estimated. This is an experimental paper aimed at accumulating knowledge on the practicability of estimating the Hurst parameter and on the estimation accuracy in the case of using wavelet analysis.