This paper studies a new attention-based recurrent architecture, lighter and less computationally expensive than a global attention network. This type of architecture achieves better performance than commonly used recurrent networks for time series regression. An application to congestion control is considered, where the history of round trip times (RTT) evolution history is used to monitor congestion control. The performance of the proposed new congestion control strategy is evaluated with both synthetic and real traces, showing that it can be efficiently used to estimate the congestion state of a network.