Abstract: 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. The share can be absolute or relative. The system executes users which are I/O bound with processor time less than their respective, specified share(s) by not using significant processor time on users which are waiting for an I/O operation to complete but expediting allocation of a processor to users after their respective I/O operations complete. The system executes users which are CPU bound with processor time greater than their respective, specified share(s) based on their respective shares in relation to a sum of shares of other CPU bound users but excluding shares of I/O bound users. For each user there is also a specified “soft limit”, “hard limit” or “no limit”. When any hard limit user reaches its hard limit, no further allocation is made.