A computer determines free space of the thinly provisioned box and calculates a time of consumption of the free space. The computer increases a dispatch and a priority of a clean-up job based on determination that the time of consumption is below a threshold time of consumption value. The increase of the dispatch is performed by deletion of dirty extents from the thinly provisioned box. The priority of the clean-up job represents a priority for execution of a cleaning program on the thinly provisioned box, where the clean-up job deletes the dirty extents from the thinly provisioned box. The computer executes the clean-up job before allocation of a new extent in the free space of the thinly provisioned box based on determination that the free space is below a critical level value, where the new extent may reduce the free space of the thinly provisioned box.
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