Any performance evaluation of broadband networks requires statistical analysis and modeling of the actual network traffic. Since multimedia services and especially MPEG coded video streams are expected to be a major traffic component over these networks, modeling of such services and accurate estimation of the network resources are crucial for the reliable operation of the future telecommunication networks.In this paper, modeling and statistical analysis of video traffic, generated by long duration real world MPEG-1 encoders, are performed. Particularly, the MPEG video traffic is approximated by a stochastic model, consisting of two Markov chains, based on statistical properties of MPEG-1 sources. The chains are responsible for approximation of packet size and the respective arrival intervals of the traffic respectively. Experimental results are presented using two real-life MPEG-1 coded video sources at two different bit rates, which indicate the good performance of the proposed model as far as the estimation of the network resources is concerned at different buffer sizes and utilization degree.