With the introduction of the new generation high speed routers, it becomes possible to improve the Quality of Service, the Quality of Experience for users and the network efficiency for ISPs with the help of "flow-aware" traffic management. An example of the "flow-aware" traffic management is the Alcatel-Lucent framework "Semantic Networking," where short-lived and long-lived TCP flows are treated differently. Short-lived flows are processed with high priority and long-lived flows are controlled in a "flow-aware" fashion. To control efficiently the long-lived flows, one needs to know an estimation of the Round Trip Time (RTT). In the present work, we provide an online RTT estimation algorithm which is passive and can deal with a one-way traffic. The one-way traffic requirement is essential for the application of the algorithm for "flow-aware" traffic management inside the network. To the best of our knowledge, there was no online one-way traffic RTT estimators. Tests on the Internet demonstrate high accuracy of the proposed estimator. The results show that, 75% (resp. 99%) of the time, the RTT estimation is within 10% (resp. 20%) of the RTT at the source.