Wireless telecommunication networks have become fundamental to daily activities. The mobile telecommunication market in Ethiopia is grown significantly in the past few years. Recently there are about 67.5 million mobile subscribers served by 7,353 base stations. Now a day’s optimizing the energy consumption of wireless telecommunications infrastructure has become a new challenge for the research community, governments and industries in order to reduce CO2 emission and operational energy cost. In view of the above problems, operators should have to have proper strategy to own energy efficient network. Studying the relationship between traffic load and power consumption at a Base Station (BS) could help to have proper strategy. The real time hourly data of the power consumption and traffic load have been obtained from servers where measurement is performed on a fully operated base stations. In this thesis, we analyze and model traffic load based on power consumption at a BS using MATLAB, R-studio and Excel. The analysis show a direct relationship is obtained between base station traffic load and power consumption. According to the relationship, we develop a piecewise linear model for base stations serving GUL (GSM, UMTS and LTE) and GU (GSM and UMTS) technologies. This result can be input for energy saving techniques. This thesis also analyzes the power consumption data has lognormal distribution and the traffic load data has Weibull distribution.