consider the following page reference string 7,0,1,2,0,3,0,4,2,3,0,3,2,1,2,0,1,7,0,1 how many page faults occur for the FIFO replacement algorithms, assuming three frames? discuss page fault rate always decrease with increase number of frames.
Answers
Answer:Initially all slots are empty, so when 1, 3, 0 came they are allocated to the empty slots —> 3 Page Faults.
when 3 comes, it is already in memory so —> 0 Page Faults.
Then 5 comes, it is not available in memory so it replaces the oldest page slot i.e 1. —>1 Page Fault.
6 comes, it is also not available in memory so it replaces the oldest page slot i.e 3 —>1 Page Fault.
Finally when 3 come it is not avilable so it replaces 0 1 page fault
Belady’s anomaly – Belady’s anomaly 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. For example, if we consider reference string 3, 2, 1, 0, 3, 2, 4, 3, 2, 1, 0, 4 and 3 slots, we get 9 total page faults, but if we increase slots to 4, we get 10 page faults.
Optimal Page replacement –
In this algorithm, pages are replaced which would not be used for the longest duration of time in the future.
Example-2:Consider the page references 7, 0, 1, 2, 0, 3, 0, 4, 2, 3, 0, 3, 2, with 4 page frame. Find number of page fault.
Initially all slots are empty, so when 7 0 1 2 are allocated to the empty slots —> 4 Page faults
0 is already there so —> 0 Page fault.
when 3 came it will take the place of 7 because it is not used for the longest duration of time in the future.—>1 Page fault.
0 is already there so —> 0 Page fault..
4 will takes place of 1 —> 1 Page Fault.
Now for the further page reference string —> 0 Page fault because they are already available in the memory.
Optimal page replacement is perfect, but not possible in practice as the operating system cannot know future requests. The use of Optimal Page replacement is to set up a benchmark so that other replacement algorithms can be analyzed against it.
Least Recently Used –
In this algorithm page will be replaced which is least recently used.
Example-3Consider the page reference string 7, 0, 1, 2, 0, 3, 0, 4, 2, 3, 0, 3, 2 with 4 page frames.Find number of page faults.
Initially all slots are empty, so when 7 0 1 2 are allocated to the empty slots —> 4 Page faults
0 is already their so —> 0 Page fault.
when 3 came it will take the place of 7 because it is least recently used —>1 Page fault
0 is already in memory so —> 0 Page fault.
4 will takes place of 1 —> 1 Page Fault
Explanation:
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Q) consider the following page reference string 7,0,1,2,0,3,0,4,2,3,0,3,2,1,2,0,1,7,0,1 how many page faults occur for the FIFO replacement algorithms, assuming three frames? discuss page fault rate always decrease with increase number of frames.
a) 17.
b) 14.
c) 16.
d) 15.
Option (d) 15 is the right answer here.
- For the page replacement process, the easiest and simple algorithm used is FIFO.
- In FIFO all the pages are arranged in a queue, and the page that came first will be the first one in the queue.
- Whenever a page needs to replace the last and new addition will be replaced.
- When a page in the virtual space address is accessed then a page fault happens.
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