For thresholding task control blocks (TCBs) for staging and destaging, a first tier of TCBs are reserved for guaranteeing a minimum number of TCBs for staging and destaging for storage ranks. An additional number of requested TCBs are apportioned from a second tier of TCBs to each of the storage ranks based on a scaling factor that is calculated at predefined time intervals. At least one of the TCBs is freed by those storage ranks executing a number of the TCBs above a maximum number of the TCBs in order to execute only the maximum number of the TCBs.