Recent studies in modern telecommunication networks have convincingly revealed that IP traffic exhibits a perceptible self-similar behavior over a wide range of time scales. Adapting the traditional Poisson model can therefore lead to erroneous conclusions regarding network performance dynamics. On the other hand, with growing demand for greater bandwidth, several optical paradigms have been proposed as substitutes for the next-generation Internet backbone. Among all these approaches, Optical Burst Switching (OBS) has been widely recognized as a suitable alternative to Optical Packet Switching (OPS) due to its support for bursty traffic and high bandwidth granularity. Thus, devising suitable buffers so as to accurately capture the fractal behavior of multimedia traffic in such optical core switches has become a major scientific endeavor. For the first time, in this paper, we propose an analytical model with Quality of Service (QoS) provision at a complete OBS network level. We then study the performance of the presented model in terms of blocking probability. Using this model, we also study the impact of burst aggregation time on the total loss probability and validate its correctness through simulation results.