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As a ubiquitous phenomenon in communication networks, the self-similar nature of network traffic has recently received great interests and been extensively studied. In this paper, assuming the buffering capability of the source node, through combining the traffic properties and channel characteristics, we analyze the queuing behaviors of self-similar traffic which is characterized by Fractional Brownian Motion (FBM) model, and derive the asymptotic closed-form expressions for the tail distribution of the stable queue length, traffic characteristics and transmission rate in three-node cooperative relay wireless networks. We further analyze the effects of different degrees of self-similarity for long-range dependence (LRD) traffic on the queue length, and compare the queuing performance by adopting different relay cooperative strategies including amply-and-forward (AF) protocol and decode-and-forward (DF) protocol. Finally, simulation results validate the accuracy of the theoretical analysis, and further, some useful conclusions are obtained, such as, effects of long-range dependent traffic on network performance are different under small and large buffer sizes and there exists a buffer turning point; queuing behaviors for AF and DF cooperative transmission protocols also perform opposite trends at low signal-to-noise ratios and high signal-to-noise ratios, etc.