Abstract: A tunable operating system in a multiprogrammed data processing system prevents lockout of I/O bound tasks of low priority by CPU bound tasks of high priority. A range signal in the master control block and a range divider signal in each task control block together define a queue subset for each task. The queue subsets for different tasks are overlapped by at least one queue, and preferably by at least three queues. A plurality of time-slice values, preferably two, are assigned when tasks are dispatched; the time-slice values are assigned with respect to the task range divider signal and therefore are not fixed with respect to each queue. The invention permits the weight given to the user-set task priority and to the priority based on recent task behavior to be varied as desired. The range value, the divider values, and the time-slice values are variable to permit tuning of the operating system.