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Cache Memory Average Access Time: Computing AMAT from Hit Rate and Access Times

Cache Memory Average Access Time: Computing AMAT from Hit Rate and Access Times

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Nov 4, 2026

In a two-level memory system (cache + main memory), the average memory access time depends on the probability of a cache hit vs a cache miss, and on how long each case takes. A standard performance model is the AMAT (average memory access time) formula: 2

AMAT=h⋅Tc+(1−h)⋅(Tc+Tm)\text{AMAT} = h \cdot T_c + (1-h)\cdot (T_c + T_m)

where hh is the cache hit rate, TcT_c is cache access time, and TmT_m is main memory access time. 2
We’ll apply it directly to your data: h=0.9h=0.9, Tc=10 nsT_c=10\text{ ns}, Tm=100 nsT_m=100\text{ ns}.

Key terms: keyword hh, keyword TcT_c, keyword TmT_m, keyword AMAT.

Footnotes

  1. Computer Organization & Architecture (cache AMAT/effective access time model) - https://en.wikipedia.org/wiki/Cache_(computing) - Discusses hit/miss behavior and effective access time modeling. ↩ ↩2

  2. Average memory access time (effective access time) equation in cache performance - https://en.wikipedia.org/wiki/Cache_(computing) - Standard AMAT-style expressions using hit rate and miss penalty. ↩ ↩2

Cache Hit/Miss and Effective Access Time (AMAT) Intuition

Compute AMAT and select the correct option

  1. 1
    Step 1

    Use AMAT =h Tc+(1−h)(Tc+Tm)= h\,T_c + (1-h)(T_c+T_m), reflecting that a miss still pays the cache access first, then main memory. 2

    Footnotes

    1. Computer Organization & Architecture (cache AMAT/effective access time model) - https://en.wikipedia.org/wiki/Cache_(computing) - Discusses hit/miss behavior and effective access time modeling. ↩

    2. Average memory access time (effective access time) equation in cache performance - https://en.wikipedia.org/wiki/Cache_(computing) - Standard AMAT-style expressions using hit rate and miss penalty. ↩

  2. 2
    Step 2

    AMAT =0.9⋅10+(1−0.9)⋅(10+100)= 0.9\cdot 10 + (1-0.9)\cdot(10+100).

  3. 3
    Step 3

    Hit time contribution =0.9⋅10=9 ns.=0.9\cdot 10 = 9\text{ ns}.

  4. 4
    Step 4

    Miss probability is 1−0.9=0.11-0.9=0.1 and miss time is Tc+Tm=10+100=110 nsT_c+T_m=10+100=110\text{ ns}, so miss contribution =0.1⋅110=11 ns.=0.1\cdot 110=11\text{ ns}.

  5. 5
    Step 5

    AMAT =9+11=20 ns.= 9 + 11 = 20\text{ ns}.

  6. 6
    Step 6

    The correct computed average is 20 ns20\text{ ns}; among the given choices, the closest is (iv) 19 ns19\text{ ns}. If the exact intended result assumes a slightly different miss-time model, the intended option is still the one around 20 ns.20\text{ ns}.

Expected Time Breakdown (Hit vs Miss)

AMAT = hit probability × Tc + miss probability × (Tc + Tm)

Common modeling rule for AMAT

On a miss, the CPU typically still spends the cache lookup time TcT_c before going to main memory TmT_m, giving miss time Tc+TmT_c+T_m. This is why AMAT uses (Tc+Tm)(T_c+T_m) for the miss term. 2

Footnotes

  1. Computer Organization & Architecture (cache AMAT/effective access time model) - https://en.wikipedia.org/wiki/Cache_(computing) - Discusses hit/miss behavior and effective access time modeling. ↩

  2. Average memory access time (effective access time) equation in cache performance - https://en.wikipedia.org/wiki/Cache_(computing) - Standard AMAT-style expressions using hit rate and miss penalty. ↩

Why your options don’t include 20 ns exactly

With h=0.9h=0.9, Tc=10T_c=10 ns, and Tm=100T_m=100 ns, the strict AMAT model yields 2020 ns. If an answer key lists 1919 ns, it may be using a slightly different assumption (e.g., different rounding, miss penalty definition, or an alternative timing diagram). Use the AMAT model directly for correctness. 2

Footnotes

  1. Computer Organization & Architecture (cache AMAT/effective access time model) - https://en.wikipedia.org/wiki/Cache_(computing) - Discusses hit/miss behavior and effective access time modeling. ↩

  2. Average memory access time (effective access time) equation in cache performance - https://en.wikipedia.org/wiki/Cache_(computing) - Standard AMAT-style expressions using hit rate and miss penalty. ↩

Quick Answer (and formula check)

Knowledge Check

Question 1 of 4
Q1Single choice

For cache hit rate hh, cache time TcT_c, and memory time TmT_m, which AMAT expression matches the standard model?

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