In a computing storage environment having multiple processor devices, lists of Task Control Blocks (TCBs) are maintained in a processor-specific manner, such that each of the multiple processor devices is assigned a local TCB list. The local TCB list of each of the multiple processor devices is populated with a respective number of TCBs from a global TCB list. The local TCB list of each of the multiple processor devices exchanges TCBs with the global TCB list during processes to maintain the local TCB list of each of the multiple processor devices at the respective number.