Virtual memory formulas

Weighted average of a hit-path access (time m) and a faulting access (total time S).

Use this form when the question gives S as a delay added on top of the normal memory access, so a faulting access costs m + S.

d is the fraction of faults whose victim is dirty; S_clean and S_dirty are the service times for a clean and a dirty victim.

Keeps EAT at most (1+ε)·m, i.e. a slowdown of at most 100ε percent, with S the total time of a faulting access. Follows from (1-p)m + pS ≤ (1+ε)m.

s_i is the size (in pages) of process i and m the number of available frames. If a share is not whole, use the rounding the question states (for example, round down and keep the leftover frames free), keeping each share at or above the minimum.

If D is greater than the number of available frames m, thrashing is likely; the OS should suspend a process (freeing its frames). If D is at most m, the OS may start another process.