CMPT 300
Introduction to Operating
Systems
Page Replacement Sample Questions
1
True or False I
 Q: Adding more RAM always reduces the
number of page faults that occur in a system.
 A: False - See Belady's Anomaly. This can
occur with FIFO replacement. One can come
up with an example of page accesses that
actually result in an increase in the amount of
page faults; however, most systems probably
use a better replacement policy and Belady's
Anomaly is probably not the common case so do not let that dissuade you from
purchasing additional RAM.
2
True or False II
 Q: Compulsory misses can be reduced by
prefetching data before they are used.
 A: True - If access pattern consists of
reading data sequentially, then by
prefetching large blocks of data in
advance, I can reduce the number of
cache misses/page faults as the next
piece of data I want to read will have
already been loaded ready for use.
3
True or False III
 Q: Compulsory misses can be reduced by
prefetching data before they are used.
 A: True - If access pattern consists of
reading data sequentially, then by
prefetching large blocks of data in
advance, I can reduce the number of
cache misses/page faults as the next
piece of data I want to read will have
already been loaded ready for use.
4
True or False IV
 Q: The LRU Algorithm always replaces
the oldest page on a page fault, where
age is defined by amount of time the page
has been in RAM.
 A: False. FIFO does that.
5
Degree of MultiProgramming
 Q: Consider a demand-paged computer system where the
degree of multiprogramming (# of concurrently running
processes) is currently fixed at four. The system was recently
measured to determine utilization of CPU and the paging
disk. The results are one of the following alternatives. For
each case, can the degree of multiprogramming be increased
to increase the CPU utilization?



a. CPU utilization 13 percent; disk utilization 97 percent
b. CPU utilization 87 percent; disk utilization 3 percent
c. CPU utilization 13 percent; disk utilization 3 percent
 A: a. Thrashing is occurring. Should decrease degree of
multiprogramming
 b. CPU utilization is sufficiently high to leave things alone.
 c. Can increase the degree of multiprogramming.
6
Bounds
 Assume a stream of page references with
length p, containing n distinct Physical Page
Numbers (PPNs) occurring in it. Assuming
the physical memory has m memory frames
(initially all empty). For any pagereplacement algorithm, what is the lower
bound & upper bound on the number of
page faults? (assuming m >= n).
 A: lower bound: n; upper bound: p
7
Page Replacement I

Q: Consider a two-dimensional array A: int A[][] = new int[100][100]; where
A[0][0] is at location 200 bytes, in a paged system with pages of size 200
bytes. (The page sizes are unrealistic; for illustration purposes only.) A small
process is in page 1 (locations 0 to 199) for manipulating the matrix; thus,
every instruction fetch will be from page 0. Assuming the matrix is stored in
row-major order, i.e., each row is stored one after another. For a physical
memory of 3 page frames, how many page faults are generated by the
following array initialization loops, using LRU replacement, and assuming
page frame 1 has the process in it, and the other two are initially empty
(assuming 16-bit integer):





A: for (int j = 0; j < 100; j++)
for (int i = 0; i < 100; i++) A[i][j] = 0;
B: for (int i = 0; i < 100; i++)
for (int j = 0; j < 100; j++) A[i][j] = 0;
Answer: An int is 2 bytes and each page has length 200 bytes. Then each row
of array A (100 ints) fits exactly in a page. Algorithm A processes one column
at a time, hence it generates a page fault at every inner loop iteration, with a
total of 100*100=10,000 page faults. Algorithm B processes one row at a time,
hence it generates a page fault at every outer loop iteration, with a total of 100
page faults. So algorithm B has better spatial locality. Note that page
replacement algorithm doesn’t matter here since the physical memory is so
small.
8
Illustration
 Consider a 4x4 array example. Each row fits in a
page. Algorithm B walks the array one row at a time
(left), while Algorithm A walks the array one column
at a time.
0
1
2
3
0
1
2
3
0
Page 1 0
Page 1
1
Page 2 1
Page 2
2
Page 3 2
Page 3
3
Page 4 3
Page 4
Algorithm B
Algorithm A
9
Page Replacement II
 Consider a physical memory with 3 page
frames. Each column represents a timestep. If there is no page fault during that
time-step, leave the column blank.
Consider FIFO, OPT, LRU, and CLOCK.
A
B
C
D
D
E
E
C
B
A
D
E
C
B
A
1
2
3
10
FIFO
A
B
C
D
D
E
E
C
B
A
D
E
C
B
A
A
B
C
D
D
E
E
C
B
A
D
E
C
B
A
1
2
3
1
2
3
A
D
B
A
E
C
C
D
B
B
E
A
 13 page faults
11
OPT
A
B
C
D
D
E
E
C
B
A
D
E
C
B
A
A
B
C
D
D
E
E
C
B
A
D
E
C
B
A
B
A
1
2
3
1
2
3
A
D
E
B
A
D
C
 9 page faults (the last two page faults could choose to
replace any physical page.)
12
LRU
A
B
C
D
D
E
E
C
B
A
D
E
C
B
A
A
B
C
D
D
E
E
C
B
A
D
E
C
B
A
1
2
3
1
2
3
A
D
B
B
E
E
C
A
D
A
B
C
 12 page faults
13
CLOCK
A
B
C
D
D
E
E
C
B
A
D
E
C
B
A
A
B
C
D
D
E
E
C
B
A
D
E
C
B
A
1
2
3
1
2
3
A
D
B
B
E
C
E
A
A
C
D
B
 12 page faults
14
Page Replacement III
 Consider a physical memory with 3 page
frames. Each column represents a time-step. If
there is no page fault during that time-step,
leave the column blank. Consider FIFO, OPT,
LRU, and CLOCK.
A
B
A
C
D
E
F
A
B
C
F
A
E
F
1
2
3
4
15
FIFO
A
B
A
C
D
E
F
A
B
C
F
A
E
F
A
B
A
C
D
E
F
A
B
C
F
A
E
F
1
2
3
4
1
2
A
E
B
3
4
C
F
C
E
A
D
F
B
 11 page faults
16
LRU
A
B
A
C
D
E
F
A
B
C
F
A
E
F
A
B
A
C
D
E
F
A
B
C
F
A
E
F
1
2
3
4
1
2
A
F
B
3
4
E
C
C
A
D
B
E
 10 page faults
17
CLOCK
A
B
A
C
D
E
F
A
B
C
F
A
E
F
A
B
A
C
D
E
F
A
B
C
F
A
E
F
1
2
3
4
1
2
3
4
A
E
B
C
F
C
A
D
B
E
 10 Page faults.
18