Accommodating a particular kind of out-of-order data; namely, when data arrives out-of-order because the data is generated in systems that may have different application timelines. As data arrives, it arrives with a particular partition key. For instance, the partition key might identify the source of the data. The data from each partition key is kept in-order with respect to all other data from that same partition key. That said, data from one key is permitted to have a different timeline as compared to data from any other key. Thus, the data may not be in-order when viewed globally across keys. Rather, data is tolerated to be out-of-order globally so long as the lag in the arrived data is within some tolerated lag. If the data arrives having a time that exceeds the maximum tolerated lag, then the system applies some policy to determine what to do with the delayed data.