In a data storage system in which a first storage array and a second storage array maintain first and second replicas of a production volume, the first storage array is responsive to a write command from a host to send a notification to the second storage array indicating that the replicated production volume will be updated. The notification has information that enables the second storage array to implement pre-processing steps to prepare for subsequent receipt of data associated with the write command. Both storage arrays implement the pre-processing steps at least partly concurrently. When the data associated with the write command is subsequently received, the first storage array writes the data to cache and then sends a copy of the data to the second storage array, i.e. in series. The second storage array then writes the data to cache. Elapsed time between receipt of the write command and returning an acknowledgment to the host may be improved by concurrent pre-processing.