## Page-Replacement-Algorithm

 Question 1

Recall that Belady’s anomaly is that the page-fault rate may increase as the number of allocated frames increases. Now, consider the following statements:

S1: Random page replacement algorithm (where a page chosen at random is replaced) suffers from Belady’s anomaly
S2: LRU page replacement algorithm suffers from Belady’s anomaly

Which of the following is CORRECT?

 A S1 is true, S2 is true B S1 is true, S2 is false C S1 is false, S2 is true D S1 is false, S2 is false
Operating-Systems       Page-Replacement-Algorithm       Gate 2017 set-01
Question 1 Explanation:
FIFO may suffer from Belady's anomaly not always FIFO suffer from Belady's anomaly.
Page replacement algorithm suffers from Belady's anomaly when it is not a stack algorithm.
S1: Random page replacement algorithm is not a stack algorithm. So, S1 is true.
S2: LRU is a stack algorithm. Therefore, it doesn't suffer from Belady's anomaly. S2 is false.
 Question 2

Consider a computer system with ten physical page frames. The system is provided with an access sequence (a1,a2,…,a20,a1,a2,…,a20), where each ai is a distinct virtual page number. The difference in the number of page faults between the last-in-ﬁrst-out page replacement policy and the optimal page replacement policy is ___________.

 A 1 B 2 C 3 D 4
Operating-Systems       Page-Replacement-Algorithm       2016 set-01
Question 2 Explanation:
We have to calculate the difference between the last-in-first-out page replacement policy and the optimal page replacement policy.
First we can consider LIFO (Last In First Out) →
a1 to a10 will result in page faults = 10 page faults,
Then a11 will replace a10 (last in is a10), a12 replace a11 and ...till a20 = 10 page faults and a20 will be top of stack and a9…a1 are remained as such.
Then a1 to a9 are already there.
So, 0 page faults from a1 to a9.
a10 will replace a20, a11 will replace a10 and so on = So 11 page faults.
So total faults will be 10+10+11 = 31.
Second Optimal Page Replacement Policy →
a1 to a10 = 10 page faults,
a11 will replace a10 because among a1 to a10, a10 will be used later, a12 will replace a11 and so on = 10 page faults.
a20 will be top of stack and a9…a1 are remained as such.
a1 to a9 = 0 page fault. a10 will replace a1 because it will not be used afterwards and so on, a10 to a19 will have 10 page faults.
So no page fault for a20.
Total = 10+ 10 +10 = 30.
So the difference between LIFO - Optimal = 1
 Question 3

In which one of the following page replacement algorithms it is possible for the page fault rate to increase even when the number of allocated frames increases?

 A LRU (Least Recently Used) B OPT (Optimal Page Replacement) C MRU (Most Recently Used) D FIFO (First In First Out)
Operating-Systems       Page-Replacement-Algorithm       GATE 2016 set-2
Question 3 Explanation:
To answer the question you have to know about Belady’s anomaly.
In Belady’s anomaly is the phenomenon in which increasing the number of page frames results in an increase in the number of page faults for certain memory access patterns proves that it is possible to have more page faults when increasing the number of page frames while using the First in First Out (FIFO) page replacement algorithm.
In some situations, FIFO page replacement gives more page faults when increasing the number of page frames.
 Question 4

Consider a main memory with five page frames and the following sequence of page references: 3, 8, 2, 3, 9, 1, 6, 3, 8, 9, 3, 6, 2, 1, 3. Which one of the following is true with respect to page replacement policies First-In-First Out (FIFO) and Least Recently Used (LRU)?

 A Both incur the same number of page faults B FIFO incurs 2 more page faults than LRU C LRU incurs 2 more page faults than FIFO D FIFO incurs 1 more page faults than LRU
Operating-Systems       Page-Replacement-Algorithm       GATE 2015 (Set-01)
Question 4 Explanation:

∴ Number of page faults = 9

∴ Number of page faults = 9
 Question 5
Assume that there are 3 page frames which are initially empty. If the page reference string is 1, 2, 3, 4, 2, 1, 5, 3, 2, 4, 6, the number of page faults using the optimal replacement policy is__________.
 A 7 B 8 C 9 D 10
Operating-Systems       Page-Replacement-Algorithm       GATE 2014(Set-01)
Question 5 Explanation:

Total 7 faults are there.
 Question 6
A computer has twenty physical page frames which contain pages numbered 101 through 120. Now a program accesses the pages numbered 1, 2, …, 100 in that order, and repeats the access sequence THRICE. Which one of the following page replacement policies experiences the same number of page faults as the optimal page replacement policy for this program?
 A Least-recently-used B First-in-first-out C Last-in-first-out D Most-recently-used
Operating-Systems       Page-Replacement-Algorithm       Gate 2014 Set -02
Question 6 Explanation:
The current status of 20 frames shows page numbers from 101 to 120. Implementation of optimal page replacement policy for above given page reference string would be as follows:

So, there would be 300 page faults in total (each access 100 page faults). Also it is visible that every time a replacement is done for the page which is most recently referred as it will be least recently referred in future. So, for the given page reference string optimal page replacement policy is working same as most recently used policy and thus number of page faults will be same in both of them.
 Question 7
A system uses 3 page frames for storing process pages in main memory. It uses the Least Recently Used (LRU) page replacement policy. Assume that all the page frames are initially empty. What is the total number of page faults that will occur while processing the page reference string given below?   4, 7, 6, 1, 7, 6, 1, 2, 7, 2
 A 6 B 7 C 8 D 9
Compiler-Design       Page-Replacement-Algorithm       Gate 2014 Set -03
Question 7 Explanation:
6 page faults will occur using LRU.
 Question 8
Consider a fully associative cache with 8 cache blocks (numbered 0-7) and the following sequence of memory block requests: 4, 3, 25, 8, 19, 6, 25, 8, 16, 35, 45, 22, 8, 3, 16, 25, 7 If LRU replacement policy is used, which cache block will have memory block 7?
 A 4 B 5 C 6 D 7
Operating-Systems       Page-Replacement-Algorithm       Gate 2004-IT
Question 8 Explanation:
When 45 comes, the cache contents are:
4, 3, 25, 8, 19, 6, 16, 35
CPU array (first element being least recently used)
[4, 3, 19, 6, 25, 8, 16, 35]
So, 45 replaces 4.
45, 3, 25, 8, 19, 6, 16, 35 [3, 19, 6, 25, 8, 16, 35, 45]
Similarly, 22 replaces 3 to give,
45, 22, 25, 8, 19, 6, 16, 35 [19, 6, 25, 8, 16, 35, 45, 22]
8 hits in cache.
45, 22, 25, 8, 19, 6, 16, 35 [19, 6, 25, 16, 35, 45, 22, 8]
3 replaces 19,
45, 22, 25, 8, 3, 6, 16, 35 [6, 25, 16, 35, 45, 22, 8, 3]
16 and 25 hits in cache,
45, 22, 25, 8, 3, 6, 16, 35 [6, 35, 45, 22, 8, 3, 16, 25]
Finally, 7 replaces 6, which is in block 5.
 Question 9
Which of the following page replacement algorithms suffers from Belady’s anamoly?
 A Optimal replacement B LRU C FIFO D Both (A) and (C)
Operating-Systems       Page-Replacement-Algorithm       Gate-1995
Question 9 Explanation:
FIFO is suffers from Belady's Anamoly.
 Question 10

 A 13 B 8 C 7 D 10
Operating-Systems       Page-Replacement-Algorithm       Gate-1995
Question 10 Explanation:
Page are fitted in frames, so first we need to determine the pages but given request are just the record request in decimal. We can assume that first page to address from 0000 to 0099 and page 2 contains records from 0100 to 0199 and so on (it is given in question that each page contains 100 records) and so on. So page request string is
01, 02, 04, 04, 05, 05, 05, 01, 02, 02, 02, 03, 03.
Clearly 7 page faults.
 Question 11
A memory page containing a heavily used variable that was initialized very early and is in constant use is removed when
 A LRU page replacement algorithm is used B FIFO page replacement algorithm is used C LFU page replacement algorithm is used D None of the above
Operating-Systems       Page-Replacement-Algorithm       Gate-1994
Question 11 Explanation:
In FIFO, whichever comes first that can be removed first. If the variable was initialized very early, it is in set of first pages. So it was removed.
In LRU which can eliminate (or) removed which is least recently used.
In LFU the frequency of the page is more. So it is in constant use so cannot be replaced.
 Question 12

 A either first fit or best fit policy (any one) B first fit but not best fit policy C best fit but first fit policy D None of the above
Operating-Systems       Page-Replacement-Algorithm       Gate-1994
Question 12 Explanation:
In first fit, block request will be satisfied from the first free block that fits it.
So, request for 300 will be satisfied by 350 size block reducing the free size to 50.
Request for 25, satisfied by 125 size block, reducing it to 125.
Request for 125 satisfied by the 125 size block.
And request for 50 satisfied by 50 size block.
So, all requests can be satisfied.
In best fit strategy, a block request is satisfied by the smallest block in which can fit it. So, request for 300 will be satisfied by 350 size block reducing the free size to 50.
Request for 25, satisfied by 50 size block as its the smallest size that fits 25, reducing it to 25.
Request for 125, satisfied by 150 size block, reducing it to 25.
Now, request for 50 cannot be satisfied as the two 25 size blocks are not contiguous.
 Question 13
Which page replacement policy sometimes leads to more page faults when size of memory is increased?
 A FIFO
Operating-Systems       Page-Replacement-Algorithm       Gate-1992
Question 13 Explanation:
FIFO, because it sometimes leads to more page faults when size of memory is increased.
There are 13 questions to complete.
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