A computing system includes nodes executing data processing programs that each process at least one stream of data units. A data storage system stores shared data accessible by at least two of the programs. Processing at least one stream using a first data processing program includes: processing a first stream of data units that includes multiple subsets of contiguous data units; initiating termination of processing within the first data processing program, between processing a first subset of contiguous data units and processing a second subset of contiguous data units adjacent to the first subset of contiguous data units within the first stream of data units; durably storing at least some changes to the shared data caused by processing the first subset of contiguous data units after determining that the termination of processing within the first data processing program has completed; and resuming processing within the first data processing program.