A control system facilitates active management of a streaming data system. Given historical data traffic for each data stream processed by a streaming data system, the control system uses a machine learning model to predict future data traffic for each data stream. The control system selects a matching between data streams and servers for a future time that minimizes a cost comprising a switching cost and a server imbalance cost based on the predicted data traffic for the future time. In some configurations, the matching is selected using a planning window comprising a number of future time steps dynamically selected based on uncertainty associated with the predicted data traffic. Given the selected matching, the control system may manage the streaming data system by causing data streams to be moved between servers based on the matching.