The paper presents measurements and analysis of a LAN long-range dependence traffic collected in IITiS PAN (The Institute of Theoretical and Applied Informatics of the Polish Academy of Sciences). Several methods of Hurst parameter estimation were used, the results obtained by the methods differ substantially. The analysis was made for the whole traffic and traffics generated by particular types of protocols. We seek for a dependence of Hurst parameter on a protocol type. Then, a MMPP(Markov-Modulated Poisson Process) model was applied to mimic the traces. It allows us to consider Markovian queueing models with long-range dependent and self-similar traffic, an important factor as we dispose an efficient software tool to solve numerically very large continuous-time Markov chains.