1. A technique for controlling access to a shared computer resource by each of two or more computer processes requiring access to a shared computer resource which comprises: assigning an access value and a relative priority value to each of the computer processes; and thereafter for each access cycle permitting each computer process access to the shared computer resource in accordance with each process' access value and relative priority value such that for each access cycle; providing access to each computer processes having pending high priority requests is provided access to the shared computer resource until the access value of each such computer process is exhausted, and thereafter; providing access to each computer process having pending low priority requests access to the shared computer resource until the access value of each such computer process is exhausted whereupon; the access values of each computer process is reallocated by adding to any existing access value of each process the access value originally assigned prior to any access cycle, and thereafter; any remaining pending requests for access present in any computer process are provided access to the shared computer resource as a low priority request until all pending requests for access to the shared computer are satisfied.