The document discusses the First-In-First-Out (FIFO) page replacement algorithm and introduces Belady's anomaly, where increasing the number of allocated frames can sometimes lead to more page faults. It highlights the optimal page-replacement algorithm, which minimizes page faults by replacing the page that will not be used for the longest time, demonstrating its superior performance compared to FIFO. The document also outlines an assignment to explain the FIFO algorithm and compare it with the optimal algorithm.

1. Operating System 39
First-In-First-Out (FIFO) Algorithm
Prof Neeraj Bhargava
Vaibhav Khanna
Department of Computer Science
School of Engineering and Systems Sciences
Maharshi Dayanand Saraswati University Ajmer

2. First-In-First-Out (FIFO) Algorithm
• Reference string:
7,0,1,2,0,3,0,4,2,3,0,3,0,3,2,1,2,0,1,7,0,1
• 3 frames (3 pages can be in memory at a time per
process)
• Can vary by reference string: consider
1,2,3,4,1,2,5,1,2,3,4,5
– Adding more frames can cause more page faults!
• Belady’s Anomaly
• How to track ages of pages?
– Just use a FIFO queue
15 page faults

3. First-In-First-Out (FIFO) Algorithm

4. FIFO Illustrating Belady’s Anomaly

5. FIFO Illustrating Belady’s Anomaly
• Figure shows the curve of page faults versus
the number of available frames.
• We notice that the number of faults for four
frames (=10) is greater than the number of
faults for three frames (=9)! This result is most
unexpected and is known as Belady’s anomaly.

6. • Belady’s anomaly reflects the fact that, for
some page-replacement algorithms, the page-
fault rate may increase as the number of
allocated frames increases.
• We would expect that giving more memory to
a process would improve its performance.
• In some early research, investigators noticed
that this assumption was not always true.
Belady’s anomaly was discovered as a result

7. Optimal Algorithm
• One result of the discovery of Belady’s anomaly was
the search for an optimal page-replacement algorithm.
• An optimal page-replacement algorithm has the lowest
page-fault rate of all algorithms.
• An optimal algorithm will never suffer from Belady’s
anomaly.
• An optimal page-replacement algorithm exists, and has
been called OPT or MIN. Stated simply, it is:
• Replace the page that will not be used for the longest
period of time.

8. Optimal Algorithm
• Replace page that will not be used for longest
period of time
– 9 is optimal for the example
• How do you know this?
– Can’t read the future
• Used for measuring how well your algorithm
performs

10. Optimal Algorithm
• Use of this page-replacement algorithm guarantees the lowest
possible page-fault rate for a fixed number of frames
• For example, on our sample reference string, the optimal page-
replacement algorithm would yield nine page faults, as shown in
Figure .
• The reference to page 2 replaces page 7, because 7 will not be used
until reference 18, whereas page 0 will be used at 5, and page 1 at
14. The reference to page 3 replaces page 1, as page 1 will be the
last of the three pages in memory to be referenced again.
• With only nine page faults, optimal replacement is much better
than a FIFO algorithm, which had 15 faults.
• Unfortunately, the optimal page-replacement algorithm is
extremely difficult to implement because it requires prior
knowledge of the reference string and therefore, is often used for
comparison purpose alone

11. Assignment
• Explain the working of FIFO Algorithm
• How is optimal Algorithm different from FIFO