Processing streaming data in accordance with policies that group data by source, enforce a maximum permissible late arrival value for streaming data, a maximum permissible early arrival for data and/or a maximum degree to which data can be out of order and still be compliant with the out of order policy is described. The correct starting point for reading a data stream so as to produce correct output from a given output start time can be enabled using the early arrival policy. Using combinations of policies, output can be generated promptly (with low latency). When input from a given source is not disrupted, output can be generated with low latency. Output can be generated even when the input stops by applying a late arrival policy.