LRU page replacement algorithm

Prob. How many page faults will occur with a reference string 0,1,7,2,3,2,7,1,0,3?
There are four frames which are initially empty.
Use
  1. LRU Page replacement algorithm
Sol.


LRU Page replacement algorithm:


LRU stands for least recently used.
It replaces the page that has been referenced for longest time.
In FIFO Page replacement algorithm problem is, it may replace heavily used pages.

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Above table is an example of page frame, which is empty initially. And first page is 0.


So 0 will get added here, but there will be a page fault.


What is a page fault?
The page which is requested by the program is not present in the RAM, that means there is a page fault.


0 was not present in the page frame so there was a page fault.

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0
F


The next page is 1 and there is space for two more pages.So 0 will remain there and 1 will get added there.And again there will be a page fault.

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00
1
FF


The next page is 7, which is not in the page frame, but there is place for one more page, so 0 and 1 will remain there and 7 will get added. And there will be a page fault.

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000
11
7
FFF

The next page is 2, which is not in the page frame, but there is place for one more page, so 0, 1 and 7 will remain there and 2 will get added. And there will be a page fault.

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0000
111
77
2
FFFF


I have given red color when there is a page fault, and black color for rest of the pages, and green color for page hits.


Now the page frame is full, and the next page is 3 which is not there in the page frame. So we need to remove one page from the page frame, so we can add 3 there.


Now see in the table below,


2 is most recently used page, than 7 and than 1 and than 0.
So 0 will get removed, and 3 will get added there. And there will be a page fault because 3 was not present in the page frame. And 1, 7, and 2 will remain there.


The next page is 2, which is already present in the page frame. This is known as page hit.


What is page hit ?
The page which is requested by the program is already present in the RAM/page frame is known as page hit.


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000033
11111
7777
222
FFFFFH

The next page is 7, which is already present in the page frame. This is known as page hit.

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0000333
111111
77777
2222
FFFFFHH
The next page is 1, which is already present in the page frame. This is known as page hit.

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00003333
1111111
777777
22222
FFFFFHHH
The page frame is full, and the next page is 0 which is not there in the page frame. So we need to remove one page from the page frame, so we can add 0 there.


Now see in the table below,


1 is most recently used page, than 7 and than 2 and then 3.
So 3 will get removed, and 0 will get added there. And there will be a page fault because 0 was not present in the page frame. And 1, 7, and 2 will remain there.


The page frame is full, and the next page is 3 which is not there in the page frame. So we need to remove one page from the page frame, so we can add 3 there.


Now see in the table below,


0 is most recently used page, than 1 and than 7 and then 2.
So 2 will get removed, and 3 will get added there. And there will be a page fault because 3 was not present in the page frame. And 0, 1, and 7 will remain there.




Total pages present in the pages is = 10.

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Total page faults = 07.

FFFFF


FF


Total page hits = 03






HHH




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