Question

Consider an initially empty memory cache consisting of four pages. How many page misses does the LRU algorithm incur on the following page request sequence: (2, 3, 4, 1, 2, 5, 1, 3, 5, 4, 1, 2, 3)?

Short answer

9 page misses

Step-by-step solution

Understanding LRU (Least Recently Used) Algorithm

The LRU algorithm replaces the page that has not been used for the longest time. We will keep track of the pages in the cache and the order of their usage to apply the LRU algorithm.

Initialize the Cache

Start with an initially empty cache that can hold 4 pages.

Process the First Request (2)

The cache is empty, so page 2 is added. Page miss count is now 1. Cache: [2]

Process the Second Request (3)

Page 3 is not in the cache, so it is added. Page miss count is now 2. Cache: [2, 3]

Process the Third Request (4)

Page 4 is not in the cache, so it is added. Page miss count is now 3. Cache: [2, 3, 4]

Process the Fourth Request (1)

Page 1 is not in the cache, so it is added. Page miss count is now 4. Cache: [2, 3, 4, 1]

Process the Fifth Request (2)

Page 2 is in the cache, so it is moved to the most recently used position. Page miss count remains 4. Cache: [3, 4, 1, 2]

Process the Sixth Request (5)

Page 5 is not in the cache. Replace the least recently used page (3) with page 5. Page miss count is now 5. Cache: [4, 1, 2, 5]

Process the Seventh Request (1)

Page 1 is in the cache, so it is moved to the most recently used position. Page miss count remains 5. Cache: [4, 2, 5, 1]

Process the Eighth Request (3)

Page 3 is not in the cache. Replace the least recently used page (4) with page 3. Page miss count is now 6. Cache: [2, 5, 1, 3]

Process the Ninth Request (5)

Page 5 is in the cache, so it is moved to the most recently used position. Page miss count remains 6. Cache: [2, 1, 3, 5]

Process the Tenth Request (4)

Page 4 is not in the cache. Replace the least recently used page (2) with page 4. Page miss count is now 7. Cache: [1, 3, 5, 4]

Process the Eleventh Request (1)

Page 1 is in the cache, so it is moved to the most recently used position. Page miss count remains 7. Cache: [3, 5, 4, 1]

Process the Twelfth Request (2)

Page 2 is not in the cache. Replace the least recently used page (3) with page 2. Page miss count is now 8. Cache: [5, 4, 1, 2]

Process the Thirteenth Request (3)

Page 3 is not in the cache. Replace the least recently used page (5) with page 3. Page miss count is now 9. Cache: [4, 1, 2, 3]

Key concepts

Page Replacement Algorithms

Page replacement algorithms are critical in managing how pages are loaded into cache memory when it becomes full. These algorithms help in deciding which page should be replaced when a new page needs to be loaded.
One popular method is the Least Recently Used (LRU) algorithm. Different algorithms serve different purposes and may lead to varying performance levels depending on the context.
Some commonly known page replacement algorithms include:

• FIFO (First-In-First-Out)
• Optimal Page Replacement
• Random Page Replacement
• LRU (Least Recently Used)

The goal is to minimize page faults or

Cache Memory

Cache memory is a small, high-speed storage used to store frequently accessed data.
This helps in speeding up data retrieval processes and improving overall system performance.
When a processor needs data, it first checks the cache. If the data is found, this is called a 'cache hit'. If not, it's a 'cache miss', and the system must retrieve the data from slower memory.
Cache memory is crucial for high-performance computing and is organized in levels: L1, L2, and L3. The higher the level, the larger and slower the cache. Efficient use of cache memory can significantly affect performance and user experience.

Least Recently Used (LRU) Algorithm

The LRU algorithm is designed to keep the most recently accessed pages in the cache.
It works by replacing the least recently used page whenever a new page needs to be loaded into the cache. The method relies on tracking page usage over time.
Here's how the LRU algorithm works step-by-step:

• Start with an empty cache.
• For each page request, check if the page is in the cache.
• If it is, move it to the most recently used position.
• If it's not, add it to the cache and replace the least recently used page if the cache is full.

This ensures that the cache keeps the most relevant data, thereby optimizing the chances of a 'cache hit'.

Page Miss Count

Page miss count refers to the number of times a requested page is not found in the cache and must be retrieved from slower memory.
In the given exercise, we can understand how the LRU algorithm impacts the page miss count. Initially, the pages are loaded into an empty cache, resulting in a series of page misses.
Once the cache is full, the LRU algorithm replaces the least recently used page to make room for new ones. By tracking these operations step-by-step, we can compute the total page miss count.
A key aspect of improving system performance is minimizing the page miss count, which is why efficient page replacement algorithms like LRU are so important.