4.5 Modeling page
replacement algorithms
Belady’s anomaly

Intuitively, the more page frames we have the
better (i.e., less page faults).

This is NOT always true for all page
replacement algorithms!

Ex. FIFO exhibits Belady’s anomaly; LRU
does not.
FIFO and Belady’s anomaly
Characterizing page replacement
algorithms
1.
2.
3.
4.
Reference string (ordered list of pages
referred to by a process as it executes)
Page replacement algorithm
m=number of page frames available in
memory
M=set of pages currently in memory
Ex. LRU
{
{
M
not in
memory
Stack algorithms
Algorithms which exhibit:
M m,r  M m1,r
where M is the set of pages currently in memory, m is the number
of page frames, and r is the rth memory reference in the
reference string.


LRU has this property; FIFO does not.
Stacking algorithms do NOT suffer from Belady’s anomaly.
Distance string

distance from top of stack
top
not present
Distance string
More normal distribution (left) satisfied w/ k
page frames than uniform (right).
Predicting page fault rates
20
18
17
13
11
9
8
 n

Fm    Ck   C
 k m1 