In an embodiment, a method comprises processing an input data stream as the data stream is streamed and producing a derived stream therefrom; storing the input data stream in an input archive; suspending processing of the input data stream; subsequent to suspending processing, resuming processing of the input data stream, wherein resuming comprises: storing newly received data in the input data stream in a buffer, as the input data stream is streamed; determining a first timestamp; determining a second timestamp; searching the input archive to find a data item that matches the first timestamp of the last processed data item; processing data in the input archive having timestamps that are greater than the first timestamp until arriving at data with a third timestamp that is greater than the second timestamp; processing the input data stream from the buffer; continuing processing the input data stream as the input stream is streamed.