The paper makes models the Internet traffic demand by applying statistical techniques on data collected between two nodes of Pakistan's Internet backbone over a period of two years. The traffic model is used to make predictions for future Internet usage which simplifies the task of capacity planning for the network management by helping them determine when and to what extent future provisioning is required in the backbone. This is not easy as quantified information is missing about the rate of increase and the pattern followed by the Internet traffic demand. We have used various statistical analysis methods on aggregate Internet demand between two nodes to isolate the long term trend from the noisy short term fluctuations in the overall traffic pattern, ensure its variance is within control limits and finally make a model out of it to make predictions for future. The accuracy of the traffic model developed is proven empirically by the comparative result showing that the future estimates deviated by only 7% from the actual values observed during that time interval.