An analysis system receives data streams generated by instances of instrumented software executing on external systems. The analysis system evaluates an expression using data values of the data streams over a plurality of time intervals. For example, the analysis system may aggregate data values of data streams for each time interval. The analysis system determines whether or not a data stream is considered for a time interval based on when the data value arrives during the time interval. The analysis system determines a maximum expected delay value for each data stream being processed. The analysis system evaluates the expression using data values that arrive before their maximum expected delay values. The analysis system also determines a failure threshold value for a data stream. If a data value of a data stream fails to arrive before the failure threshold value, the analysis system marks the data stream as dead.