In the article, two models of instability of quantum frequency standards (QFS) are considered. This is a generally accepted stochastic model that describes the effect of noise with different frequencies on the stability of the clock and the simulation model proposed by the authors of this article, based on the Monte Carlo method and a software random number generator. Based on simulation results, a comparative analysis of advantages and disadvantages of the proposed QFS model in comparison with the classical model was carried out. The results of modeling, which showed good convergence with the accepted theoretical assumptions, are presented. The rationale for the feasibility of using the proposed model in the processing of navigation measurements is given. The possibilities of increasing the accuracy of synchronization of remote sets of reference time are shown.