The growth of internet trafï¬c forces telecom service providers to invest in new infrastructurernand/or expanding the network to achieve the desired Quality of Service (QoS) and copernup the network congestion. But several techniques available for granting QoS and networkrncongestion. The ï¬rst step is to understand the network performance. Network performancernneeds accurate trafï¬c modeling that has the potential to improve desired QoS, allocatingrnthe network resources (i.e. bandwidth). This thesis presents a statistical model of the internetrntrafï¬c applications by their random nature of flow-length and flow-size. Wiresharkrnnetwork monitoring and analysis tool is used to collect internet trafï¬c data from the ethiorntelecom core switch and generating experimental internet trafï¬c data in controlled environment.rnThe experimental data are used to train and test the machine learning model thatrnhelps to identify the internet applications. Firstly, identifying internet trafï¬c applicationsrnusing machine learning classiï¬cation techniques. Secondly, statistical methods are used tornï¬t the Cumulative Distribution Function (CDF) and select the parameters that best ï¬tted inrnboth flow-length and flow-size for identiï¬ed applications. Finally, deliver statistical modelrnto each applications and corresponding parameters. Recently internet trafï¬c modeling isrnapplicable in capacity planning for trafï¬c engineering, anomaly detection and performancernanalysis are some of them. Based on the result found the Log-normal distribution is bestrnï¬tted to flow-length and flow size for three applications and Weibull distribution is for SSHrnapplication in both flow length and flow size.