The CMPP (Circulant Modulated Poisson Process) modeling approach represents an appealing solution since it provides the integration of traffic measurement and modeling. At the same time, it maintains the Markovian hypothesis that permits analytical transient and steady-state analyses of queueing systems using efficient algorithms. These relevant features of CMPP approach has driven us to analyze in more details the fitting procedure when it is applied to actual broadband traffic. In the paper, investigating the estimation algorithm of model parameters, we emphasize the difficulty of CMPP in capturing the upper tail of marginal distribution of actual data, which leads to an optimistic evaluation of network performance. As shown in the paper, a simple relation exists between the number of significant eigenvalues obtained by the spectral decomposition and the peak rate that the CMPP structure is able to capture. The relation evidences the difficulties of CMPP to model actual traffic, characterized by long tailed distribution, as well as traffic data with the well accepted hypothesis of gaussian marginal.