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Belady’s Anomaly

Last Updated on December 29, 2023 by Ankit Kochar

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. In virtual memory systems, where data is stored on disk and brought into physical memory as needed, the choice of which page to evict from memory becomes crucial. Belady’s Anomaly draws attention to the counterintuitive situation where increasing the number of available page frames for storage may lead to an increase in the number of page faults, negatively impacting system performance.

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

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

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.

Belady’s Anomaly remains a significant concept in the field of operating systems, influencing the design and evaluation of page replacement algorithms. While subsequent research has proposed various algorithms aiming to mitigate or avoid the anomaly, its presence underscores the complexity and non-linear nature of memory management in computer systems. As technology continues to advance, understanding and addressing such anomalies will be crucial for optimizing the performance of modern computing systems.

FAQs related to Belady’s Anomaly

Here are some frequently asked questions related to Belady’s Anomaly in OS.

1. 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.

2. How does Belady’s Anomaly affect computer systems?
Belady’s Anomaly highlights the unexpected consequences in the performance of page replacement algorithms. It emphasizes that simply increasing the amount of physical memory available for storing pages does not always lead to better performance and can, in fact, result in more page faults.

3. Who discovered Belady’s Anomaly?
Belady’s Anomaly is named after Lester Belady, a computer scientist who first observed and documented this phenomenon in 1969. His work has been influential in the field of operating systems and memory management.

4. Are there solutions to mitigate Belady’s Anomaly?
Various page replacement algorithms have been proposed to mitigate or minimize Belady’s Anomaly. These algorithms aim to improve the efficiency of page replacement strategies and better adapt to dynamic changes in the system’s memory requirements.

5. Why is Belady’s Anomaly important in the context of operating systems?
Belady’s Anomaly is crucial in understanding the complexities of memory management in operating systems. It highlights that the relationship between the number of page frames and system performance is not always straightforward, emphasizing the need for sophisticated algorithms to optimize memory usage.

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