Operating system (OS) use memory management to allocate physical memory (page frames) to running processes. One key aspect of memory management in OS is the use of page replacement algorithms to determine which pages to evict from memory when new pages need to be loaded. However, increasing the number of page frames allocated to a process can sometimes lead to an increase in the number of page faults, this phenomenon is known as Belady’s anomaly in OS. We will discuss topics related to Belady’s Anomaly in this article, such as: What is Belady’s Anomaly in OS, Why does it happen, Examples of Belady’s Anomaly in OS, and how to Eliminate Belady’s Anomaly in OS.
What is Belady’s Anomaly in OS?
Belady’s anomaly in OS is a phenomenon where increasing the number of page frames assigned to a process can actually lead to an increase in the number of page faults.
Page faults occur when a program accesses a memory page that is not currently in physical memory, and the operating system must retrieve it from the disk. In an attempt to reduce the number of page faults, operating systems use various page replacement algorithms to determine which pages to keep in memory and which to evict.
Belady’s anomaly occurs when increasing the number of page frames assigned to a process using certain paging algorithms can cause the algorithm to evict pages prematurely, increasing the number of page faults. This is counterintuitive because one would expect that assigning more memory to a process would improve its performance.
Here are some of the most common page replacement algorithms where Belady’s Anomaly occurs: FIFO Algorithm, Second Chance Algorithm, and Random Page Replacement Algorithm.
Why does Belady’s Anomaly Occur?
Belady’s Anomaly occurs when an algorithm fails to follow the stack property. These issues do not exist with LRU and Optimal Page Replacement because they are stack-based algorithms. Stack-based algorithms are algorithms that follow the stack property. In these algorithms, the number of page faults decreases as the frame size grows. As a result, page replacement algorithms can allocate priority to pages regardless of the number of frames in the main memory.
Graph of Belady’s Anomaly
When the number of frames is increased, the number of page faults should decrease. However, "Belady’s Anomaly" happens when page faults increase despite increasing the number of frames. Let us visualize this condition using a graph:
The page fault is greatest in the above figure when the number of frames is 1. Following that, as the number of frames increases, the number of page faults does not increase and remains constant until the number of frames is 2. The number of faults decreased at point 3. But, at point 4, the number of faults again increased even if the frames were increased. At this moment, we can see "Belady’s Anomaly".
Examples of Belady’s Anomaly
Let us now look at a demonstration of Belady’s Anomaly. Take a look at the following page reference string:
1, 2, 3, 4, 1, 2, 5, 1, 2, 3, 4, 5
Let’s look at the page frames through the lens of the FIFO replacement algorithm. To begin, let us assume that the number of possible page frames is 3. The following table illustrates this situation.
| 1 | 1 | 1 | 2 | 3 | 4 | 1 | 1 | 1 | 2 | 5 | 5 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 2 | 2 | 3 | 4 | 1 | 2 | 2 | 2 | 5 | 3 | 3 | |
| 3 | 4 | 1 | 2 | 5 | 5 | 5 | 3 | 4 | 4 | ||
| PF | PF | PF | PF | PF | PF | PF | X | X | PF | PF | X |
Note: PF means Page Fault
Here, the number of page faults is 1+1+1+1+1+1+1+1+1 = 9.
When three-page frames are available, the total number of page faults equals 9, as seen above. Let’s look at another example with four-page frames:
| 1 | 1 | 1 | 1 | 1 | 1 | 2 | 3 | 4 | 5 | 1 | 2 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 2 | 2 | 2 | 2 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | |
| 3 | 3 | 3 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | ||
| 4 | 4 | 4 | 5 | 1 | 2 | 3 | 4 | 5 | |||
| PF | PF | PF | PF | X | X | PF | PF | PF | PF | PF | PF |
Note: PF means Page Fault
Here, the number of page faults is 1+1+1+1+1+1+1+1+1+1 = 10
We can see that as the number of frames increases from 3 to 4, page faults also increase from 9 to 10.
Elimination of Belady’s Anomaly in OS
A stack-based algorithm can be used to eliminate Belady’s Algorithm. Here are some examples of such algorithms:
- Optimal Page Replacement Algorithm
- Least Recently Used (LRU) Algorithm
These algorithms are based on the idea that if a page is not used for long period of time, it is not used frequently. So, it is better to erase this page from memory. Memory management can be improved in this manner, and Belady’s Anomaly can be avoided.
Summary
Here is a summary of key points related to Belady’s Anomaly in OS.
- The scenario known as Belady’s Anomaly occurs when the "number of frames becomes directly proportional to the number of page faults."
- Belady’s Anomaly happens on the FIFO algorithm.
- A "stack-based algorithm" can be used to reduce Belady’s Anomaly in OS.
- Stack-based algorithms create a priority list of the most frequently used pages and efficiently retrieve them.
- The Least Recently Used (LRU) algorithm is one example of a stack-based algorithm.
FAQs
Here are some frequently asked questions related to Belady’s Anomaly in OS.
Q1: What is Belady’s anomaly in OS?
Answer: Belady’s anomaly is a phenomenon that occurs in operating systems that use page replacement algorithms, where increasing the number of page frames may result in an increase in the number of page faults.
Q2: Why is Belady’s anomaly a problem in operating systems that use page replacement algorithms?
Answer: Belady’s anomaly is a problem because it is counterintuitive and goes against the basic idea of page replacement algorithms, which is to reduce the number of page faults.
Q3: Is Belady’s anomaly a problem in all page replacement algorithms?
Answer: No, Belady’s anomaly is not a problem in all page replacement algorithms. It is specific to certain algorithms like FIFO and FCFS.
Q4: Can Belady’s anomaly occur in real-world scenarios, or is it a theoretical problem?
Answer: Belady’s anomaly can occur in real-world scenarios and has been observed in various computer systems.
Q5: Can Belady’s anomaly be eliminated completely in a page replacement algorithm?
Answer: No, Belady’s anomaly cannot be completely eliminated in a page replacement algorithm, but it can be minimized by using certain algorithms.
Q6: How do stack-based algorithms eliminate Belady’s anomaly?
Answer: Stack-based algorithms eliminate Belady’s anomaly by maintaining a stack of page frames and replacing the least recently used page.
Q7: Can the choice of the page replacement algorithm affect the severity of Belady’s anomaly?
Answer: Yes, the choice of the page replacement algorithm can affect the severity of Belady’s anomaly.