Model

What variance costs in money

It is the price of variance, now written in money.

price \div mean demand \approx \frac{peak / mean}{ρ _{target}}

$ρ_{target}$: Target utilization; kept well below 1 for latency (0.6–0.7)

Recurring principle: Variance costs more than volume

How it behaves

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

ρ target 0.65ρ target 0.9 (batch)

Data table

Provisioned ÷ mean demand, by burstiness
Peak ÷ mean	series	Provisioned ÷ mean demand
1	ρ target 0.65	1.54×
1.11	ρ target 0.65	1.71×
1.23	ρ target 0.65	1.88×
1.34	ρ target 0.65	2.06×
1.45	ρ target 0.65	2.23×
1.56	ρ target 0.65	2.4×
1.68	ρ target 0.65	2.58×
1.79	ρ target 0.65	2.75×
1.9	ρ target 0.65	2.92×
2.01	ρ target 0.65	3.1×
2.13	ρ target 0.65	3.27×
2.24	ρ target 0.65	3.44×
2.35	ρ target 0.65	3.62×
2.46	ρ target 0.65	3.79×
2.58	ρ target 0.65	3.96×
2.69	ρ target 0.65	4.13×
2.8	ρ target 0.65	4.31×
2.91	ρ target 0.65	4.48×
3.02	ρ target 0.65	4.65×
3.14	ρ target 0.65	4.83×
3.25	ρ target 0.65	5×
3.36	ρ target 0.65	5.17×
3.48	ρ target 0.65	5.35×
3.59	ρ target 0.65	5.52×
3.7	ρ target 0.65	5.69×
3.81	ρ target 0.65	5.87×
3.92	ρ target 0.65	6.04×
4.04	ρ target 0.65	6.21×
4.15	ρ target 0.65	6.38×
4.26	ρ target 0.65	6.56×
4.38	ρ target 0.65	6.73×
4.49	ρ target 0.65	6.9×
4.6	ρ target 0.65	7.08×
4.71	ρ target 0.65	7.25×
4.83	ρ target 0.65	7.42×
4.94	ρ target 0.65	7.6×
5.05	ρ target 0.65	7.77×
5.16	ρ target 0.65	7.94×
5.28	ρ target 0.65	8.12×
5.39	ρ target 0.65	8.29×
5.5	ρ target 0.65	8.46×
5.61	ρ target 0.65	8.63×
5.72	ρ target 0.65	8.81×
5.84	ρ target 0.65	8.98×
5.95	ρ target 0.65	9.15×
6.06	ρ target 0.65	9.33×
6.17	ρ target 0.65	9.5×
6.29	ρ target 0.65	9.67×
6.4	ρ target 0.65	9.85×
6.51	ρ target 0.65	10×
6.63	ρ target 0.65	10.2×
6.74	ρ target 0.65	10.4×
6.85	ρ target 0.65	10.5×
6.96	ρ target 0.65	10.7×
7.08	ρ target 0.65	10.9×
7.19	ρ target 0.65	11.1×
7.3	ρ target 0.65	11.2×
7.41	ρ target 0.65	11.4×
7.53	ρ target 0.65	11.6×
7.64	ρ target 0.65	11.8×
7.75	ρ target 0.65	11.9×
7.86	ρ target 0.65	12.1×
7.97	ρ target 0.65	12.3×
8.09	ρ target 0.65	12.4×
8.2	ρ target 0.65	12.6×
8.31	ρ target 0.65	12.8×
8.43	ρ target 0.65	13×
8.54	ρ target 0.65	13.1×
8.65	ρ target 0.65	13.3×
8.76	ρ target 0.65	13.5×
8.88	ρ target 0.65	13.7×
8.99	ρ target 0.65	13.8×
9.1	ρ target 0.65	14×
9.21	ρ target 0.65	14.2×
9.32	ρ target 0.65	14.3×
9.44	ρ target 0.65	14.5×
9.55	ρ target 0.65	14.7×
9.66	ρ target 0.65	14.9×
9.78	ρ target 0.65	15×
9.89	ρ target 0.65	15.2×
10	ρ target 0.65	15.4×
1	ρ target 0.9 (batch)	1.11×
1.11	ρ target 0.9 (batch)	1.24×
1.23	ρ target 0.9 (batch)	1.36×
1.34	ρ target 0.9 (batch)	1.49×
1.45	ρ target 0.9 (batch)	1.61×
1.56	ρ target 0.9 (batch)	1.74×
1.68	ρ target 0.9 (batch)	1.86×
1.79	ρ target 0.9 (batch)	1.99×
1.9	ρ target 0.9 (batch)	2.11×
2.01	ρ target 0.9 (batch)	2.24×
2.13	ρ target 0.9 (batch)	2.36×
2.24	ρ target 0.9 (batch)	2.49×
2.35	ρ target 0.9 (batch)	2.61×
2.46	ρ target 0.9 (batch)	2.74×
2.58	ρ target 0.9 (batch)	2.86×
2.69	ρ target 0.9 (batch)	2.99×
2.8	ρ target 0.9 (batch)	3.11×
2.91	ρ target 0.9 (batch)	3.24×
3.02	ρ target 0.9 (batch)	3.36×
3.14	ρ target 0.9 (batch)	3.49×
3.25	ρ target 0.9 (batch)	3.61×
3.36	ρ target 0.9 (batch)	3.74×
3.48	ρ target 0.9 (batch)	3.86×
3.59	ρ target 0.9 (batch)	3.99×
3.7	ρ target 0.9 (batch)	4.11×
3.81	ρ target 0.9 (batch)	4.24×
3.92	ρ target 0.9 (batch)	4.36×
4.04	ρ target 0.9 (batch)	4.49×
4.15	ρ target 0.9 (batch)	4.61×
4.26	ρ target 0.9 (batch)	4.74×
4.38	ρ target 0.9 (batch)	4.86×
4.49	ρ target 0.9 (batch)	4.99×
4.6	ρ target 0.9 (batch)	5.11×
4.71	ρ target 0.9 (batch)	5.24×
4.83	ρ target 0.9 (batch)	5.36×
4.94	ρ target 0.9 (batch)	5.49×
5.05	ρ target 0.9 (batch)	5.61×
5.16	ρ target 0.9 (batch)	5.74×
5.28	ρ target 0.9 (batch)	5.86×
5.39	ρ target 0.9 (batch)	5.99×
5.5	ρ target 0.9 (batch)	6.11×
5.61	ρ target 0.9 (batch)	6.24×
5.72	ρ target 0.9 (batch)	6.36×
5.84	ρ target 0.9 (batch)	6.49×
5.95	ρ target 0.9 (batch)	6.61×
6.06	ρ target 0.9 (batch)	6.74×
6.17	ρ target 0.9 (batch)	6.86×
6.29	ρ target 0.9 (batch)	6.99×
6.4	ρ target 0.9 (batch)	7.11×
6.51	ρ target 0.9 (batch)	7.24×
6.63	ρ target 0.9 (batch)	7.36×
6.74	ρ target 0.9 (batch)	7.49×
6.85	ρ target 0.9 (batch)	7.61×
6.96	ρ target 0.9 (batch)	7.74×
7.08	ρ target 0.9 (batch)	7.86×
7.19	ρ target 0.9 (batch)	7.99×
7.3	ρ target 0.9 (batch)	8.11×
7.41	ρ target 0.9 (batch)	8.24×
7.53	ρ target 0.9 (batch)	8.36×
7.64	ρ target 0.9 (batch)	8.49×
7.75	ρ target 0.9 (batch)	8.61×
7.86	ρ target 0.9 (batch)	8.74×
7.97	ρ target 0.9 (batch)	8.86×
8.09	ρ target 0.9 (batch)	8.99×
8.2	ρ target 0.9 (batch)	9.11×
8.31	ρ target 0.9 (batch)	9.24×
8.43	ρ target 0.9 (batch)	9.36×
8.54	ρ target 0.9 (batch)	9.49×
8.65	ρ target 0.9 (batch)	9.61×
8.76	ρ target 0.9 (batch)	9.74×
8.88	ρ target 0.9 (batch)	9.86×
8.99	ρ target 0.9 (batch)	9.99×
9.1	ρ target 0.9 (batch)	10.1×
9.21	ρ target 0.9 (batch)	10.2×
9.32	ρ target 0.9 (batch)	10.4×
9.44	ρ target 0.9 (batch)	10.5×
9.55	ρ target 0.9 (batch)	10.6×
9.66	ρ target 0.9 (batch)	10.7×
9.78	ρ target 0.9 (batch)	10.9×
9.89	ρ target 0.9 (batch)	11×
10	ρ target 0.9 (batch)	11.1×

Worked examples, recomputed

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

peak/mean = 3, ρ = 0.65 → ≈ 4.6×, about 5×

Where it appears

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

Cost Mechanics
What is metered, and what is the smallest increment you are charged for?
$(peak \div mean) \div ρ_{target}$
Read it in place →