While there exists an extensive body of prior work on Internet traffic characterization, there has been very little attempt to study the impact of aggregation on Internet traffic. The existed work focus on characterization of the Internet traffic by the single granularity. By zooming the granularity of the observation from two different points of view, we analyze in depth the properties of several real traces collected from two big sites. These traces can be divided into two groups. One is from China and the other is from Japan. By the method of non-parametric test, we find that the Gamma distribution can fit the Internet traffic well when the granularity zoomed is greater than a special value regardless of the observation types. Furthermore, we demonstrate that TCP traffic shows the same behavior with the total traffic and it also has the Gamma distribution characterization, but none of the typical distributions can fit the UDP traffic well in any granularity from any perpective. In particular, our results stay fairly consistent over time and different traces from different sites. Our finding will be helpful to the research on the traffic modelling and future Internet protocols and architectures.