A computer system allocates processor time to multiple users. A systems operator or other administrator specifies to the computer a share of processor time for each user. A particular user's CPU usage is limited to an absolute value in a `dispatch driven` multiprocessing system through the use of a monitor built into an active wait routine. The mechanism used is a list of users whose CPU resource must be limited so that their consumption does not exceed the limit value. The limit list is active wait monitored to determine when a user should be removed from the list in a low load situation and thus deliver the maximum CPU usage to the user if it is available.