Network traffic plays a critical role in network planning and control. The researchers assume that traffic from Ethernet and other IP-related networks have a self-similar nature: high-variability and long-term correlations. Many studies try to model these characteristics for simulation and further optimization. One of the most straightforward approaches to model these characteristics is to consider ON/OFF sources (packet-train), where ON- and OFF-periods are i.i.d., generated with random heavy-tailed distributions. Using information theory quantifiers, in particular the Causality Complexity-Entropy Plane, we show that heavy-tailed distributions do not capture most of the network traffic dynamics. They only reproduce the stochastic dynamics of traffic, which accounts for one of the smallest parts of it. We conduct this study by observing the Abilene dataset, fitting the LogNormal and LogLogistic distributions, and evaluating them onto Causality Complexity-Entropy Plane in comparison with $1/f$-noise, which is one of the most observed long-term correlated noises in nature stochastic processes. Also, to enhance our illustrated results, we use the k-nearest-neighbors (kNN) to classify the real and generated traffic according to the results obtained.