As the Internet role changes from the experimental environment to the social infrastructure, end-to-end quality for data transfer of various types of traffic has been required as well as its connectivity. So we should precisely measure some performance such as packet loss probability and delay at routers on some source-destination path. By using so-called passive measurement technique, we can get the queue length distribution from some routers individually and estimate the end-to-end transmission delay. However, there may be some correlation between queue lengths of two or more routers packets go through in sequence, which would lead to inaccurate estimation of end-to-end delay performance. Thus in this paper, we model two tandem routers as queueing system, and analyze the queue length distributions and their correlation. Through some numerical results, we will investigate the impact of traffic parameters on the degree of correlation and how it affects the estimation of delay performance.