This thesis provides results on trace data collecting and modeling of the Internet traffic over a Wide Area Network. The study is based on extensive data, gathered by tracing the actual packet exchange at the interfaces of devices on the WAN of BCCLS (Bergen County Cooperative Library System). A powerful network monitoring system WhatsUp Gold was employed to monitor the WAN, and logged the byte rates and packet rates sent and received at the interfaces. Different statistical distributions were employed to model the data traces. In comparison with some other statistical models - normal, lognormal, Weibull, and Pareto, which are widely used in network analysis, the one-dimensional hyperbolic distribution can achieve very small Kolmogorov-Smirnov (K-S) distance and large associated probability. The fining results for the data traces indicated that the one-dimensional hyperbolic distribution is an effective statistical model of the large, multiple network traffic activities.