Model

Admitting traffic to a cold cache

A cache restart must never start cold: admit traffic as the hit rate climbs.

(1 - h (t)) λ (t) < origin capacity ⟺ λ (t) < \frac{capacity}{1 - h ( t )}

$h (t)$: Hit rate; the hit rate at time t, read from the miss-ratio curve as the cache fills

How it behaves

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

Data table

Traffic the origin can absorb, by hit rate (origin 1,500 reads/s)
Hit rate as the cache fills	Traffic you may admit (per second)
0	1.5K
0.012	1.52K
0.025	1.54K
0.037	1.56K
0.049	1.58K
0.061	1.6K
0.074	1.62K
0.086	1.64K
0.098	1.66K
0.11	1.69K
0.123	1.71K
0.135	1.73K
0.147	1.76K
0.159	1.78K
0.171	1.81K
0.184	1.84K
0.196	1.87K
0.208	1.89K
0.221	1.92K
0.233	1.96K
0.245	1.99K
0.257	2.02K
0.269	2.05K
0.282	2.09K
0.294	2.12K
0.306	2.16K
0.319	2.2K
0.331	2.24K
0.343	2.28K
0.355	2.33K
0.367	2.37K
0.38	2.42K
0.392	2.47K
0.404	2.52K
0.416	2.57K
0.429	2.63K
0.441	2.68K
0.453	2.74K
0.466	2.81K
0.478	2.87K
0.49	2.94K
0.502	3.01K
0.514	3.09K
0.527	3.17K
0.539	3.25K
0.551	3.34K
0.564	3.44K
0.576	3.54K
0.588	3.64K
0.6	3.75K
0.613	3.87K
0.625	4K
0.637	4.13K
0.649	4.28K
0.661	4.43K
0.674	4.6K
0.686	4.78K
0.698	4.97K
0.71	5.18K
0.723	5.41K
0.735	5.66K
0.747	5.93K
0.759	6.24K
0.772	6.57K
0.784	6.94K
0.796	7.36K
0.808	7.83K
0.821	8.37K
0.833	8.98K
0.845	9.69K
0.857	10.5K
0.87	11.5K
0.882	12.7K
0.894	14.2K
0.906	16K
0.919	18.5K
0.931	21.7K
0.943	26.4K
0.956	33.7K
0.968	46.5K
0.98	75K

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

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

Caching
What happens when we deliberately keep a second copy of data that no protocol forces to be correct?
$(1 - h (t)) \cdot λ (t) < origin capacity$
Read it in place →