# Page Replacement Algorithms | Important Results

## Page Replacement Algorithms-

Before you go through this article, make sure that you have gone through the previous article on Page Replacement Algorithms.

We have discussed-

• When a page fault occurs, the required page has to be brought from the secondary memory.
• If all the frames of main memory are already occupied, then a page has to be replaced.
• Page replacement algorithms help to decide which page should be replaced.

## Result-01: For a Reference String Consisting Of Repeated Sequence Of Page Numbers-

For such a reference string,

• Optimal page replacement algorithm replaces the most recently used page to minimize the page faults.
• This is because most recently page will be required after the longest time.
• Thus, Optimal page replacement algorithm acts as Most Recently Used (MRU) page replacement algorithm.

In other words,

• MRU page replacement algorithm will behave as Optimal page replacement algorithm.
• MRU page replacement algorithm gives the optimal performance.

## Example-

Consider the following reference string consisting of a repeated sequence of page numbers-

1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6

Here,

• Both Optimal and MRU page replacement algorithm replaces the most recently used page.
• Most recently used page will be required after the longest time.
• Hence, both these algorithms give the optimal performance.

Total number of page faults occurred = 12

## NOTES-

### Note-01:

• These are the minimum number of page faults that are possible.
• If any other page replacement algorithm is used, it will surely give rise to more number of page faults.
• FIFO and LRU page replacement algorithm give rise to 24 number of page faults.

### Note-02:

• CPU may generate such a reference string when executing loops.
• This is because while executing loops, same set of instructions have to be executed again and again.

### Note-03:

• Principle of locality states that the next reference would be most probably from the most recently used pages.
• Here, the behavior of Optimal page replacement algorithm contradicts with the principle of locality.
• Here, Optimal algorithm replaces the most recently used page to give the optimal performance.
• So, from here we can infer that principle of locality does not hold true in certain scenarios.

## Result-02: For a Reference String Where First Half String Is a Mirror Image Of Other Half-

For such a reference string,

• Optimal page replacement algorithm replaces the least recently used page or firstly arrived page to minimize page faults.
• This is because such a page will be required after the longest time.
• Thus, Optimal page replacement algorithm acts as LRU and FIFO page replacement algorithm.

In other words,

• LRU and FIFO page replacement algorithm will behave as Optimal page replacement algorithm.
• LRU and FIFO page replacement algorithm gives the optimal performance.

## Example-

Consider the following reference string where first half string is a mirror image of other half string-

1, 2, 3, 4, 5, 6, 7, 8, 9, 9, 8, 7, 6, 5, 4, 3, 2, 1

Here,

• Optimal, LRU and FIFO page replacement algorithms replaces the least recently used or firstly arrived page.
• Least recently used or firstly arrived page will be required after the longest time.
• Hence, all these algorithms give the optimal performance.

Total number of page faults occurred = 14

• These are the minimum number of page faults that are possible.
• If any other page replacement algorithm is used, it will surely give rise to more number of page faults.

## Remember-

• Optimal page replacement algorithm always gives the best performance in every scenario.
• This is because it foresees the future and takes the form of an algorithm which gives the best performance in that scenario.

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Summary
Article Name
Page Replacement Algorithms | Important Results
Description
Page replacement algorithms help to decide which page should be replaced when a page fault occurs and main memory is full. FIFO Page Replacement Algorithm, LRU Page Replacement Algorithm, Optimal Page Replacement Algorithm are famous page replacement algorithms.
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Gate Vidyalay
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