Model

Unanimity multiplies unavailability

Atomic commit needs every participant up; consensus needs only a majority. Replication improves the base, not the exponent.

A_{all} = A^{n}, downtime \approx n (1 - A)

$A$: Availability; availability of one participant
$n$: Participants; participants that must all be up

Recurring principle: Independence is assumed

How it behaves

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

each 99.9%each 99.99%

Data table

Availability of an all-participants commit, by participants
Participants n	series	Availability
1	each 99.9%	99.9%
1.05	each 99.9%	99.9%
1.1	each 99.9%	99.9%
1.16	each 99.9%	99.9%
1.22	each 99.9%	99.9%
1.28	each 99.9%	99.9%
1.34	each 99.9%	99.9%
1.41	each 99.9%	99.9%
1.48	each 99.9%	99.9%
1.55	each 99.9%	99.8%
1.63	each 99.9%	99.8%
1.71	each 99.9%	99.8%
1.8	each 99.9%	99.8%
1.89	each 99.9%	99.8%
1.98	each 99.9%	99.8%
2.08	each 99.9%	99.8%
2.19	each 99.9%	99.8%
2.3	each 99.9%	99.8%
2.41	each 99.9%	99.8%
2.53	each 99.9%	99.7%
2.66	each 99.9%	99.7%
2.79	each 99.9%	99.7%
2.93	each 99.9%	99.7%
3.08	each 99.9%	99.7%
3.23	each 99.9%	99.7%
3.4	each 99.9%	99.7%
3.57	each 99.9%	99.6%
3.74	each 99.9%	99.6%
3.93	each 99.9%	99.6%
4.13	each 99.9%	99.6%
4.34	each 99.9%	99.6%
4.55	each 99.9%	99.5%
4.78	each 99.9%	99.5%
5.02	each 99.9%	99.5%
5.27	each 99.9%	99.5%
5.54	each 99.9%	99.4%
5.81	each 99.9%	99.4%
6.11	each 99.9%	99.4%
6.41	each 99.9%	99.4%
6.73	each 99.9%	99.3%
7.07	each 99.9%	99.3%
7.43	each 99.9%	99.3%
7.8	each 99.9%	99.2%
8.19	each 99.9%	99.2%
8.6	each 99.9%	99.1%
9.03	each 99.9%	99.1%
9.48	each 99.9%	99.1%
9.96	each 99.9%	99%
10.5	each 99.9%	99%
11	each 99.9%	98.9%
11.5	each 99.9%	98.9%
12.1	each 99.9%	98.8%
12.7	each 99.9%	98.7%
13.4	each 99.9%	98.7%
14	each 99.9%	98.6%
14.7	each 99.9%	98.5%
15.5	each 99.9%	98.5%
16.2	each 99.9%	98.4%
17.1	each 99.9%	98.3%
17.9	each 99.9%	98.2%
18.8	each 99.9%	98.1%
19.7	each 99.9%	98%
20.7	each 99.9%	97.9%
21.8	each 99.9%	97.8%
22.9	each 99.9%	97.7%
24	each 99.9%	97.6%
25.2	each 99.9%	97.5%
26.5	each 99.9%	97.4%
27.8	each 99.9%	97.3%
29.2	each 99.9%	97.1%
30.7	each 99.9%	97%
32.2	each 99.9%	96.8%
33.8	each 99.9%	96.7%
35.5	each 99.9%	96.5%
37.3	each 99.9%	96.3%
39.2	each 99.9%	96.2%
41.1	each 99.9%	96%
43.2	each 99.9%	95.8%
45.3	each 99.9%	95.6%
47.6	each 99.9%	95.3%
50	each 99.9%	95.1%
1	each 99.99%	100%
1.05	each 99.99%	100%
1.1	each 99.99%	100%
1.16	each 99.99%	100%
1.22	each 99.99%	100%
1.28	each 99.99%	100%
1.34	each 99.99%	100%
1.41	each 99.99%	100%
1.48	each 99.99%	100%
1.55	each 99.99%	100%
1.63	each 99.99%	100%
1.71	each 99.99%	100%
1.8	each 99.99%	100%
1.89	each 99.99%	100%
1.98	each 99.99%	100%
2.08	each 99.99%	100%
2.19	each 99.99%	100%
2.3	each 99.99%	100%
2.41	each 99.99%	100%
2.53	each 99.99%	100%
2.66	each 99.99%	100%
2.79	each 99.99%	100%
2.93	each 99.99%	100%
3.08	each 99.99%	100%
3.23	each 99.99%	100%
3.4	each 99.99%	100%
3.57	each 99.99%	100%
3.74	each 99.99%	100%
3.93	each 99.99%	100%
4.13	each 99.99%	100%
4.34	each 99.99%	100%
4.55	each 99.99%	100%
4.78	each 99.99%	100%
5.02	each 99.99%	99.9%
5.27	each 99.99%	99.9%
5.54	each 99.99%	99.9%
5.81	each 99.99%	99.9%
6.11	each 99.99%	99.9%
6.41	each 99.99%	99.9%
6.73	each 99.99%	99.9%
7.07	each 99.99%	99.9%
7.43	each 99.99%	99.9%
7.8	each 99.99%	99.9%
8.19	each 99.99%	99.9%
8.6	each 99.99%	99.9%
9.03	each 99.99%	99.9%
9.48	each 99.99%	99.9%
9.96	each 99.99%	99.9%
10.5	each 99.99%	99.9%
11	each 99.99%	99.9%
11.5	each 99.99%	99.9%
12.1	each 99.99%	99.9%
12.7	each 99.99%	99.9%
13.4	each 99.99%	99.9%
14	each 99.99%	99.9%
14.7	each 99.99%	99.9%
15.5	each 99.99%	99.8%
16.2	each 99.99%	99.8%
17.1	each 99.99%	99.8%
17.9	each 99.99%	99.8%
18.8	each 99.99%	99.8%
19.7	each 99.99%	99.8%
20.7	each 99.99%	99.8%
21.8	each 99.99%	99.8%
22.9	each 99.99%	99.8%
24	each 99.99%	99.8%
25.2	each 99.99%	99.7%
26.5	each 99.99%	99.7%
27.8	each 99.99%	99.7%
29.2	each 99.99%	99.7%
30.7	each 99.99%	99.7%
32.2	each 99.99%	99.7%
33.8	each 99.99%	99.7%
35.5	each 99.99%	99.6%
37.3	each 99.99%	99.6%
39.2	each 99.99%	99.6%
41.1	each 99.99%	99.6%
43.2	each 99.99%	99.6%
45.3	each 99.99%	99.5%
47.6	each 99.99%	99.5%
50	each 99.99%	99.5%

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.

Transactions & Concurrency Control
What happens when many users change the same data at the same time, and how do we keep the result correct?
$0.99 9^{10} \approx 0.990$
Read it in place →
Distributed Systems Coordination
Who is allowed to decide, and how does everyone else learn the decision without asking?
$p^{N}$
p (shard availability) = $A$ · N (shards) = $n$
Read it in place →
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?
$a^{N}$
a = $A$ · N (hard dependencies) = $n$
Read it in place →
Cost Mechanics
What is metered, and what is the smallest increment you are charged for?
$(1 - p)^{n}$
1 − p (survives the hour) = $A$ · n (nodes) = $n$
Read it in place →