By assuming network traffic to be independent from each other, the analysis of network pevformance can be simplified. However, the real traffic sources may have some correlation which makes their behavior tends to converge or diverge. This phenomenon has tremendous influence on the congestion control. In this paper, we explain the possible reasons of the correlated behavior, namely, top-down and client-server correlation, and analyze their impacts. We also use the rapid matrix-geometric solution to investigate the cost to pay when applying the Leaky Bucket input control scheme on the independent, such as Poisson, traffic sources and the correlated, such as ON-OFF and HAP (Hierarchical Arrival Process), traffic sources.