Model

The metastable band

The quantity that governs your exposure is not headroom. It is k. To leave the broken state you must push λ below C/k, not below C.

\frac{C}{k} < λ < C ⟺ \frac{1}{k} < ρ < 1

$λ$: Demand; the base arrival rate (useful demand)
$C$: Capacity; capacity
$k$: Amplification; units of work per unit of useful demand once retries fire, caches miss and timeouts trip

How it behaves

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

Data table

Utilization above which a broken state can sustain itself, by degraded amplification
Degraded amplification k	Vulnerable above this utilization
1	100%
1.11	89.9%
1.23	81.6%
1.34	74.8%
1.45	69%
1.56	64%
1.68	59.7%
1.79	55.9%
1.9	52.6%
2.01	49.7%
2.13	47.1%
2.24	44.7%
2.35	42.6%
2.46	40.6%
2.58	38.8%
2.69	37.2%
2.8	35.7%
2.91	34.3%
3.02	33.1%
3.14	31.9%
3.25	30.8%
3.36	29.7%
3.48	28.8%
3.59	27.9%
3.7	27%
3.81	26.2%
3.92	25.5%
4.04	24.8%
4.15	24.1%
4.26	23.5%
4.38	22.9%
4.49	22.3%
4.6	21.7%
4.71	21.2%
4.83	20.7%
4.94	20.3%
5.05	19.8%
5.16	19.4%
5.28	19%
5.39	18.6%
5.5	18.2%
5.61	17.8%
5.72	17.5%
5.84	17.1%
5.95	16.8%
6.06	16.5%
6.17	16.2%
6.29	15.9%
6.4	15.6%
6.51	15.4%
6.63	15.1%
6.74	14.8%
6.85	14.6%
6.96	14.4%
7.08	14.1%
7.19	13.9%
7.3	13.7%
7.41	13.5%
7.53	13.3%
7.64	13.1%
7.75	12.9%
7.86	12.7%
7.97	12.5%
8.09	12.4%
8.2	12.2%
8.31	12%
8.43	11.9%
8.54	11.7%
8.65	11.6%
8.76	11.4%
8.88	11.3%
8.99	11.1%
9.1	11%
9.21	10.9%
9.32	10.7%
9.44	10.6%
9.55	10.5%
9.66	10.3%
9.78	10.2%
9.89	10.1%
10	10%

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.

Emergent Failure Dynamics
What happens when nothing is broken, every component is healthy, and the system's own response to stress makes the stress worse?
$C / k < λ < C$
Read it in place →