What Is Main Memory Composed Of In Three Page Frames

Given The Main Memory Is Composed Of Only Three Page Frames For Public

Given the main memory is composed of only three page frames for public use and that a program requests pages in the following order: a, c, b, d, a, c, e, a, c, b, d, e. The task is to perform a page trace analysis using the FIFO page removal algorithm, indicating each page fault with an asterisk (*), and then compare the failure and success ratios. Next, the memory size should be increased to four page frames, and the same page request sequence should be analyzed again with FIFO, followed by calculating the new page fault and success ratios. Finally, a general statement should be made from this example regarding the impact of memory size on page faults and the effectiveness of FIFO.

Paper For Above instruction

Memory management in computer systems is crucial for optimizing performance and ensuring efficient utilization of the main memory. One common technique is paging, where the system divides memory into fixed-sized pages and maintains page tables to keep track of pages in memory. The FIFO (First-In, First-Out) page replacement algorithm is straightforward but can lead to suboptimal performance in some cases, especially depending on the size of available memory frames. This paper analyzes the behavior of FIFO under different memory constraints by examining a specific sequence of page requests and comparing the resulting page faults and success ratios.

Part A: Memory with Three Page Frames

Given the sequence of page requests: a, c, b, d, a, c, e, a, c, b, d, e, and the memory size of three frames, the FIFO algorithm operates by replacing the oldest page whenever a new page needs to be loaded into memory that is full. Initially, all frames are empty, so each initial request results in a page fault. The detailed page replacement sequence is as follows:

• Request a: page fault; frames: [a]
• Request c: page fault; frames: [a, c]
• Request b: page fault; frames: [a, c, b]
• Request d: page fault; replace a; frames: [d, c, b]
• Request a: page fault; replace c; frames: [d, a, b]
• Request c: page fault; replace b; frames: [d, a, c]
• Request e: page fault; replace d; frames: [e, a, c]
• Request a: no page fault; frames: [e, a, c]
• Request c: no page fault; frames: [e, a, c]
• Request b: page fault; replace e; frames: [b, a, c]
• Request d: page fault; replace a; frames: [b, d, c]
• Request e: page fault; replace c; frames: [b, d, e]

Total page faults: 9 out of 12 requests. The page fault ratio is thus 75%, and success ratio is 25%. This example demonstrates how FIFO can lead to frequent page faults, especially with limited memory. The oldest pages are replaced regardless of their future use, which may not always be optimal.

Part B: Memory with Four Page Frames

Increasing the number of frames to four allows more pages to stay in memory simultaneously. Repeating the same request sequence with four frames, the process is as follows:

• Request a: page fault; frames: [a]
• Request c: page fault; frames: [a, c]
• Request b: page fault; frames: [a, c, b]
• Request d: page fault; frames: [a, c, b, d]
• Request a: no page fault; frames: [a, c, b, d]
• Request c: no page fault; frames: [a, c, b, d]
• Request e: page fault; replace a; frames: [e, c, b, d]
• Request a: page fault; replace c; frames: [e, a, b, d]
• Request c: page fault; replace b; frames: [e, a, c, d]
• Request b: page fault; replace d; frames: [e, a, c, b]
• Request d: page fault; replace e; frames: [d, a, c, b]
• Request e: page fault; replace a; frames: [d, e, c, b]

In this scenario, total page faults are 8, meaning the page fault ratio drops to approximately 66.7%, and success ratio increases to 33.3%. The additional frame reduces the number of unnecessary replacements, highlighting the significance of increasing available memory.

Part C: General Statement and Analysis

From this analysis, it is evident that increasing the number of page frames decreases the number of page faults in FIFO page replacement. This illustrates a fundamental principle in operating systems: larger memory capacity can mitigate the Page Fault Rate, improving performance. However, FIFO's simplicity comes with limitations; it does not consider page usage patterns and can lead to Belady’s anomaly, where increasing memory can paradoxically increase page faults (Belady et al., 1969). The example demonstrates that while more frames generally improve performance, optimal page replacement policies like Least Recently Used (LRU) or Adaptive algorithms can further enhance efficiency. Ultimately, system designers must weigh memory costs against expected performance gains when selecting page management strategies, with FIFO providing a simple but sometimes suboptimal solution.

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