Abstract: In connection with an information processing network in which multiple processing devices have individual cache memories and also share a main storage memory, a process is disclosed for allocating multiple data operations or tasks for subsequent execution by the processing devices. A plurality of task dispatching elements (TDE) forming a task dispatching queue are scanned in an order of descending priority, for either a specific affinity to a selected one of the processing devices, or a general affinity to all of the processing devices. TDEs with specific affinity are assigned immediately if the selected processor is available, while TDEs of general affinity are reserved. TDEs with a specific affinity are bypassed if the selected processor is not available, or reserved if a predetermined bypass threshold has been reached. Following the primary scan a secondary scan, in an order of ascending priority, assigns any reserved tasks to the processing devices still available, without regard to processor affinity.