Average memory access time with cache: Main memory access is 100 ns and cache access is 10 ns with a 0.95 hit ratio. What is the effective average access time?

Introduction / Context:Caches exploit temporal and spatial locality to reduce the average memory access time (AMAT). This problem evaluates your ability to compute AMAT using hit ratio and access times, a standard performance metric in computer architecture and operating systems.

Given Data / Assumptions:

• Main memory access time ≈ 100 ns (practically, not ms, since millisecond-level main memory would be unrealistic; we proceed with the standard nanosecond scale for DRAM).
• Cache access time = 10 ns.
• Cache hit ratio H = 0.95 (i.e., miss ratio M = 0.05).
• On a miss, assume the cache lookup cost still occurs, followed by a main memory access (serial miss penalty model): miss service time ≈ 10 ns + 100 ns = 110 ns.

Concept / Approach:Average memory access time AMAT is computed as: AMAT = H * (cache time) + (1 − H) * (miss service time). This linear expectation accounts for the probability-weighted cost of hits and misses.

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