A page fault equation for modeling the effect of memory size

Modeling the effect of memory size on page faults is very difficult, because they are the result of the interaction between process reference behavior and page replacement policy. Moreover, a change in memory size will alter the timing and pattern of references in a multiprogramming mix. This paper presents an equation to model how memory size affects page faults. The equation is derived with the help of a conjectured invariant on the interaction between reference behavior and replacement policy. The page fault equation is validated in several experiments with real applications and systems. The equation can be used for energy conservation and capacity planning, characterizing the memory requirement of software and managing memory allocation, modeling of processor cache misses and database buffer management.