An archival data storage service dispatches a first robotic device of a data storage library to perform a first task that involves moving a first data storage tape from a tape drive to a slot of the data storage library. The service select a second task to be performed by a second robotic device, which can be performed without the first robotic device causing delay of the second task. While the first robotic device is performing the first task, the archival data storage service dispatches the second robotic device to perform the second task.