GATE CS 2016 Set 2 — Question 60
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Computer Organization & Architecture → Memory Hierarchy & Cache → Cache Numericals
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Question
A file system uses an in-memory cache to cache disk blocks. The miss rate of the cache is shown in the figure. The latency to read a block from the cache is ms and to read a block from the disk is ms. Assume that the cost of checking whether a block exists in the cache is negligible. Available cache sizes are in multiples of MB.
The smallest cache size required to ensure an average read latency of less than ms is _______ MB.
The smallest cache size required to ensure an average read latency of less than ms is _______ MB.
Correct answer
30 to 30
Solution
Let be the hit rate and be the miss rate ().
Cache access time ms.
Disk access time ms.
Average read latency is given by:We require ms:So, the miss rate must be less than .Looking at the graph provided in the question:
Cache access time ms.
Disk access time ms.
Average read latency is given by:We require ms:So, the miss rate must be less than .Looking at the graph provided in the question:
- At Cache Size = 10 MB, Miss Rate
- At Cache Size = 20 MB, Miss Rate
- At Cache Size = 30 MB, Miss Rate
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