Belady's Anomaly in Page Replacement Algorithms: Understanding Counter-Intuitive Behavior
Explore Belady's anomaly, a phenomenon where increasing the number of available memory frames in a FIFO (First-In, First-Out) page replacement algorithm can paradoxically increase the number of page faults. This guide explains the causes of Belady's anomaly and its implications for memory management.
Belady's Anomaly in Page Replacement Algorithms
Understanding Belady's Anomaly
In most page replacement algorithms (like Least Recently Used - LRU and Optimal), increasing the number of available memory frames generally leads to a reduction in page faults (times when a page needs to be loaded from disk). However, Belady's anomaly describes a situation where, for the First-In, First-Out (FIFO) algorithm, increasing the number of frames can paradoxically *increase* the number of page faults. This counter-intuitive behavior occurs in certain reference string patterns.
Example Illustrating Belady's Anomaly
Let's examine a reference string (a sequence of page requests): 0 1 5 3 0 1 4 0 1 5 3 4. We'll analyze the FIFO algorithm with different numbers of frames:
Case 1: 3 Frames
| Request | Frame 1 | Frame 2 | Frame 3 | Miss/Hit |
|---|---|---|---|---|
| 0 | 0 | - | - | Miss |
| 1 | 0 | 1 | - | Miss |
| 5 | 0 | 1 | 5 | Miss |
| 3 | 0 | 1 | 3 | Miss |
| 0 | 0 | 1 | 3 | Hit |
| 1 | 0 | 1 | 3 | Hit |
| 4 | 0 | 1 | 4 | Miss |
| 0 | 0 | 1 | 4 | Hit |
| 1 | 0 | 1 | 4 | Hit |
| 5 | 0 | 1 | 5 | Miss |
| 3 | 0 | 1 | 3 | Miss |
| 4 | 0 | 1 | 4 | Hit |
Number of page faults: 9
Case 2: 4 Frames
| Request | Frame 1 | Frame 2 | Frame 3 | Frame 4 | Miss/Hit |
|---|---|---|---|---|---|
| 0 | 0 | - | - | - | Miss |
| 1 | 0 | 1 | - | - | Miss |
| 5 | 0 | 1 | 5 | - | Miss |
| 3 | 0 | 1 | 5 | 3 | Miss |
| 0 | 0 | 1 | 5 | 3 | Hit |
| 1 | 0 | 1 | 5 | 3 | Hit |
| 4 | 0 | 1 | 5 | 4 | Miss |
| 0 | 0 | 1 | 5 | 4 | Hit |
| 1 | 0 | 1 | 5 | 4 | Hit |
| 5 | 0 | 1 | 5 | 4 | Hit |
| 3 | 0 | 1 | 5 | 3 | Hit |
| 4 | 0 | 1 | 5 | 4 | Hit |
Number of page faults: 10
In this example, increasing the number of frames from 3 to 4 *increases* the number of page faults, demonstrating Belady's anomaly.