Abstract: Apparatus for controlling the division of working memory space among n competitive programs with different characteristics, running in a multiprogramming and virtual memory environment, in which the allocation of working space is optimized by adjusting the size of the working set for each competing program. Under this optimization scheme, "the value of a page frame" (the amount of reduction in the page fault rate if an additional page frame is allocated to that program) is sought to be equalized for all programs. Every memory access increments an access counter. When it reaches its maximum count of 1024, the reference register value stored in an associative memory for each page is incremented by one count, except that for the page accessed it is reset to zero. The stored numbers range from 0 to 31. Whenever a page fault occurs, the number of pages of that program having a reference register count equal to each of the numbers 0 to 31 is temporarily stored as a table of 32 Wd values.