The goal of the letter is to highlight the impact of the inactive period distribution of an ON-OFF source On the autocorrelation structure of the model. In particular, two discrete-time ON-OFF models, both with geometric distribution of the active period, are considered: the GeoGeo Model (GGM) and the ParetoGeo Model (PGM), characterized by a geometric and Pareto-like distribution of the OFF periods length, respectively. The two models are compared in terms of their main statistical features as well as queueing impact. The asymptotic behavior of the autocorrelation function for the proposed PGM has been analytically evaluated. It is shown it has a hyperbolic decay related to the tail behavior of the OFF periods distribution.