The eruption of the World Wide Web as a medium for information dissemination, movies, music and entertainment, has made it extremely important to understand the characteristics of its traffic. Bit-Torrent (BT), communication protocol for peer-to-peer (P2P) file sharing, continues to still remain a dominant source of upstream traffic worldwide. This wide spread popularity of BT has attracted exponentially increasing attention of the researchers in the networking domain. Existing studies on BT systems have reported analytical performance modeling, which includes Markov chain model, Deterministic model, Queuing network model and Fluid flow model. This research study presents exhaustive survey of BT protocol and various mathematical modeling reported for its performance evaluation under transient and steady condition. Precise and apt comparison of the performance parameters in terms of complexity, precision and flexibility is initially summarized in this research. This study further incorporates rigorous experimentation on a huge dataset (BT-data packet traffic) explicitly created for this research to evaluate and analyze other significant parameters like heavy tailedness, self-similarity, autocorrelation, power spectral density and burstiness ( packet inter-arrival time and packet size), which conform the self-similar behavior of BT traffic . Analysis of such parameters is crucial and inevitable during the simulation of the data traces, designing accurate models and is also required by the network provider to design and manage internet traffic efficiently, in order to avoid unnecessary deterioration of quality of service caused by heavy-tailedness. However, such rigorous and wide-ranging analysis of BT traffic, has received meager attention in the reported literature, and is the key contribution of this research study.