GATE CS 2014 Set 1 — Question 54
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Computer Organization & Architecture → Memory Hierarchy & Cache → Cache Replacement Policies
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Question
An access sequence of cache block addresses is of length N and contains n unique block addresses. The number of unique block addresses between two consecutive accesses to the same block address is bounded above by k. What is the miss ratio if the access sequence is passed through a cache of associativity exercising least-recently-used replacement policy?
Correct answer
(A) n/N
Solution
The problem describes a scenario where the cache is large enough to capture the locality of the reference string.
Total Accesses =
Miss Ratio =
1.Compulsory Misses: There are unique block addresses. The first access to each unique block will always result in a miss (compulsory miss). Thus, there are at least misses.
2.Capacity/Conflict Misses: The condition states that the number of unique blocks between consecutive accesses to the same block is bounded by , and the associativity . In an LRU cache, if the number of unique intervening blocks is less than the cache size (or associativity set size), the block will remain in the cache and the subsequent access will be a hit.
Assuming the condition is sufficient to prevent capacity misses for the given reuse distance (strictly speaking, stack depth is if there are unique intervening blocks, but in the context of such problems, this implies hits on re-access), all accesses after the first one for each block are hits.Total Misses = Compulsory Misses = Total Accesses =
Miss Ratio =
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