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Model

The misses own the mean

A cache does not make things fast, it makes them sometimes fast, and the average is set by the failures.

Hit rate
fraction of requests served by the fast tier
Tier latencies
latency of the fast and the slow path

Recurring principle: Variance costs more than volume

How it behaves

One input on the horizontal axis, the others held fixed.

mean latency (ms)share of the mean from misses (%)
Data table
Mean latency by hit rate (hit 0.1 ms, miss 50 ms), and the share the misses cause
Hit rate hseriesMean latency (ms) · misses' share (%)
0.5mean latency (ms)25.1
0.506mean latency (ms)24.7
0.512mean latency (ms)24.4
0.519mean latency (ms)24.1
0.525mean latency (ms)23.8
0.531mean latency (ms)23.5
0.537mean latency (ms)23.2
0.544mean latency (ms)22.9
0.55mean latency (ms)22.6
0.556mean latency (ms)22.2
0.562mean latency (ms)21.9
0.569mean latency (ms)21.6
0.575mean latency (ms)21.3
0.581mean latency (ms)21
0.587mean latency (ms)20.7
0.594mean latency (ms)20.4
0.6mean latency (ms)20.1
0.606mean latency (ms)19.8
0.612mean latency (ms)19.4
0.619mean latency (ms)19.1
0.625mean latency (ms)18.8
0.631mean latency (ms)18.5
0.637mean latency (ms)18.2
0.643mean latency (ms)17.9
0.65mean latency (ms)17.6
0.656mean latency (ms)17.3
0.662mean latency (ms)17
0.668mean latency (ms)16.6
0.675mean latency (ms)16.3
0.681mean latency (ms)16
0.687mean latency (ms)15.7
0.693mean latency (ms)15.4
0.7mean latency (ms)15.1
0.706mean latency (ms)14.8
0.712mean latency (ms)14.5
0.718mean latency (ms)14.2
0.725mean latency (ms)13.8
0.731mean latency (ms)13.5
0.737mean latency (ms)13.2
0.743mean latency (ms)12.9
0.75mean latency (ms)12.6
0.756mean latency (ms)12.3
0.762mean latency (ms)12
0.768mean latency (ms)11.7
0.774mean latency (ms)11.4
0.781mean latency (ms)11
0.787mean latency (ms)10.7
0.793mean latency (ms)10.4
0.799mean latency (ms)10.1
0.806mean latency (ms)9.8
0.812mean latency (ms)9.49
0.818mean latency (ms)9.18
0.824mean latency (ms)8.86
0.831mean latency (ms)8.55
0.837mean latency (ms)8.24
0.843mean latency (ms)7.93
0.849mean latency (ms)7.62
0.856mean latency (ms)7.31
0.862mean latency (ms)7
0.868mean latency (ms)6.69
0.874mean latency (ms)6.37
0.88mean latency (ms)6.06
0.887mean latency (ms)5.75
0.893mean latency (ms)5.44
0.899mean latency (ms)5.13
0.905mean latency (ms)4.82
0.912mean latency (ms)4.51
0.918mean latency (ms)4.2
0.924mean latency (ms)3.88
0.93mean latency (ms)3.57
0.937mean latency (ms)3.26
0.943mean latency (ms)2.95
0.949mean latency (ms)2.64
0.955mean latency (ms)2.33
0.962mean latency (ms)2.02
0.968mean latency (ms)1.71
0.974mean latency (ms)1.39
0.98mean latency (ms)1.08
0.987mean latency (ms)0.772
0.993mean latency (ms)0.461
0.999mean latency (ms)0.15
0.5share of the mean from misses (%)99.8
0.506share of the mean from misses (%)99.8
0.512share of the mean from misses (%)99.8
0.519share of the mean from misses (%)99.8
0.525share of the mean from misses (%)99.8
0.531share of the mean from misses (%)99.8
0.537share of the mean from misses (%)99.8
0.544share of the mean from misses (%)99.8
0.55share of the mean from misses (%)99.8
0.556share of the mean from misses (%)99.8
0.562share of the mean from misses (%)99.7
0.569share of the mean from misses (%)99.7
0.575share of the mean from misses (%)99.7
0.581share of the mean from misses (%)99.7
0.587share of the mean from misses (%)99.7
0.594share of the mean from misses (%)99.7
0.6share of the mean from misses (%)99.7
0.606share of the mean from misses (%)99.7
0.612share of the mean from misses (%)99.7
0.619share of the mean from misses (%)99.7
0.625share of the mean from misses (%)99.7
0.631share of the mean from misses (%)99.7
0.637share of the mean from misses (%)99.6
0.643share of the mean from misses (%)99.6
0.65share of the mean from misses (%)99.6
0.656share of the mean from misses (%)99.6
0.662share of the mean from misses (%)99.6
0.668share of the mean from misses (%)99.6
0.675share of the mean from misses (%)99.6
0.681share of the mean from misses (%)99.6
0.687share of the mean from misses (%)99.6
0.693share of the mean from misses (%)99.5
0.7share of the mean from misses (%)99.5
0.706share of the mean from misses (%)99.5
0.712share of the mean from misses (%)99.5
0.718share of the mean from misses (%)99.5
0.725share of the mean from misses (%)99.5
0.731share of the mean from misses (%)99.5
0.737share of the mean from misses (%)99.4
0.743share of the mean from misses (%)99.4
0.75share of the mean from misses (%)99.4
0.756share of the mean from misses (%)99.4
0.762share of the mean from misses (%)99.4
0.768share of the mean from misses (%)99.3
0.774share of the mean from misses (%)99.3
0.781share of the mean from misses (%)99.3
0.787share of the mean from misses (%)99.3
0.793share of the mean from misses (%)99.2
0.799share of the mean from misses (%)99.2
0.806share of the mean from misses (%)99.2
0.812share of the mean from misses (%)99.1
0.818share of the mean from misses (%)99.1
0.824share of the mean from misses (%)99.1
0.831share of the mean from misses (%)99
0.837share of the mean from misses (%)99
0.843share of the mean from misses (%)98.9
0.849share of the mean from misses (%)98.9
0.856share of the mean from misses (%)98.8
0.862share of the mean from misses (%)98.8
0.868share of the mean from misses (%)98.7
0.874share of the mean from misses (%)98.6
0.88share of the mean from misses (%)98.5
0.887share of the mean from misses (%)98.5
0.893share of the mean from misses (%)98.4
0.899share of the mean from misses (%)98.2
0.905share of the mean from misses (%)98.1
0.912share of the mean from misses (%)98
0.918share of the mean from misses (%)97.8
0.924share of the mean from misses (%)97.6
0.93share of the mean from misses (%)97.4
0.937share of the mean from misses (%)97.1
0.943share of the mean from misses (%)96.8
0.949share of the mean from misses (%)96.4
0.955share of the mean from misses (%)95.9
0.962share of the mean from misses (%)95.2
0.968share of the mean from misses (%)94.3
0.974share of the mean from misses (%)93
0.98share of the mean from misses (%)91
0.987share of the mean from misses (%)87.2
0.993share of the mean from misses (%)78.5
0.999share of the mean from misses (%)33.4

Worked examples, recomputed

Every number the mechanisms quote for this relationship is recomputed from it, so none of them disagrees with it.

Where it appears

Each mechanism states it in its own names. The general symbol each name stands for is shown with it.

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