In this paper, we present a model of the data exchange process between users in P2P live streaming network with buffering mechanism - buffer occupancy model. The model is developed in terms of discrete Markov chain. We study the probability measures of the model - buffer position occupancy probability and probability of playback continuity. The model is very tractable and compacted formulas were obtained. While considering user churn in the model we examine how user departure affects buffer occupancy and playback continuity. For our numerical experiment we develop a simulation tool for the considered model. © Springer-Verlag Berlin Heidelberg 2011.