Synchronization is a promising approach to solve the consistency problems in replicated distributed file systems. The synchronization can be repeated periodically, with fixed time interval or a time interval which can be adjusted adaptively. In this paper, we propose a policy-based performance efficient distributed file synchronization approach, in which synchronization processes occur in varying time intervals and adjusted adaptively. The study is based on tracing network idle times by means of measuring and clustering Round Trip Time (RTT) values. K-means clustering is used to cluster RTT values as idle, normal, and busy. To estimate the most suitable synchronization time intervals, the measured RTT values are included into these classes with an algorithm similar to Transmission Control Protocol (TCP) Additive-Increase/Multiplicative-Decrease (AIMD) feedback control. The efficiency and feasibility of the proposed technique is examined on a distributed file synchronization application within the scope of Fatih project, which is one of the most important educational projects in Turkey.