Law

Dependent calls pay every round trip

Latency decides how fast a chain of dependent steps finishes; bandwidth decides how much independent work you can push.

t \geq dependent calls \times RTT

Recurring principle: Fixed cost per operation

How it behaves

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

same region (1 ms)cross-region (80–100 ms)

Data table

Time spent waiting, by dependent calls
Dependent calls	series	Time waiting
1	same region (1 ms)	1 ms
1.61	same region (1 ms)	1.61 ms
2.23	same region (1 ms)	2.23 ms
2.84	same region (1 ms)	2.84 ms
3.45	same region (1 ms)	3.45 ms
4.06	same region (1 ms)	4.06 ms
4.67	same region (1 ms)	4.68 ms
5.29	same region (1 ms)	5.29 ms
5.9	same region (1 ms)	5.9 ms
6.51	same region (1 ms)	6.51 ms
7.13	same region (1 ms)	7.13 ms
7.74	same region (1 ms)	7.74 ms
8.35	same region (1 ms)	8.35 ms
8.96	same region (1 ms)	8.96 ms
9.57	same region (1 ms)	9.57 ms
10.2	same region (1 ms)	10.2 ms
10.8	same region (1 ms)	10.8 ms
11.4	same region (1 ms)	11.4 ms
12	same region (1 ms)	12 ms
12.6	same region (1 ms)	12.6 ms
13.3	same region (1 ms)	13.3 ms
13.9	same region (1 ms)	13.9 ms
14.5	same region (1 ms)	14.5 ms
15.1	same region (1 ms)	15.1 ms
15.7	same region (1 ms)	15.7 ms
16.3	same region (1 ms)	16.3 ms
16.9	same region (1 ms)	16.9 ms
17.5	same region (1 ms)	17.5 ms
18.1	same region (1 ms)	18.1 ms
18.8	same region (1 ms)	18.8 ms
19.4	same region (1 ms)	19.4 ms
20	same region (1 ms)	20 ms
20.6	same region (1 ms)	20.6 ms
21.2	same region (1 ms)	21.2 ms
21.8	same region (1 ms)	21.8 ms
22.4	same region (1 ms)	22.4 ms
23.1	same region (1 ms)	23.1 ms
23.7	same region (1 ms)	23.7 ms
24.3	same region (1 ms)	24.3 ms
24.9	same region (1 ms)	24.9 ms
25.5	same region (1 ms)	25.5 ms
26.1	same region (1 ms)	26.1 ms
26.7	same region (1 ms)	26.7 ms
27.3	same region (1 ms)	27.3 ms
27.9	same region (1 ms)	27.9 ms
28.6	same region (1 ms)	28.6 ms
29.2	same region (1 ms)	29.2 ms
29.8	same region (1 ms)	29.8 ms
30.4	same region (1 ms)	30.4 ms
31	same region (1 ms)	31 ms
31.6	same region (1 ms)	31.6 ms
32.2	same region (1 ms)	32.2 ms
32.9	same region (1 ms)	32.9 ms
33.5	same region (1 ms)	33.5 ms
34.1	same region (1 ms)	34.1 ms
34.7	same region (1 ms)	34.7 ms
35.3	same region (1 ms)	35.3 ms
35.9	same region (1 ms)	35.9 ms
36.5	same region (1 ms)	36.5 ms
37.1	same region (1 ms)	37.1 ms
37.8	same region (1 ms)	37.8 ms
38.4	same region (1 ms)	38.4 ms
39	same region (1 ms)	39 ms
39.6	same region (1 ms)	39.6 ms
40.2	same region (1 ms)	40.2 ms
40.8	same region (1 ms)	40.8 ms
41.4	same region (1 ms)	41.4 ms
42	same region (1 ms)	42 ms
42.6	same region (1 ms)	42.6 ms
43.3	same region (1 ms)	43.3 ms
43.9	same region (1 ms)	43.9 ms
44.5	same region (1 ms)	44.5 ms
45.1	same region (1 ms)	45.1 ms
45.7	same region (1 ms)	45.7 ms
46.3	same region (1 ms)	46.3 ms
46.9	same region (1 ms)	46.9 ms
47.5	same region (1 ms)	47.5 ms
48.2	same region (1 ms)	48.2 ms
48.8	same region (1 ms)	48.8 ms
49.4	same region (1 ms)	49.4 ms
50	same region (1 ms)	50 ms
1	cross-region (80–100 ms)	90 ms
1.61	cross-region (80–100 ms)	145 ms
2.23	cross-region (80–100 ms)	200 ms
2.84	cross-region (80–100 ms)	255 ms
3.45	cross-region (80–100 ms)	311 ms
4.06	cross-region (80–100 ms)	366 ms
4.67	cross-region (80–100 ms)	421 ms
5.29	cross-region (80–100 ms)	476 ms
5.9	cross-region (80–100 ms)	531 ms
6.51	cross-region (80–100 ms)	586 ms
7.13	cross-region (80–100 ms)	641 ms
7.74	cross-region (80–100 ms)	696 ms
8.35	cross-region (80–100 ms)	752 ms
8.96	cross-region (80–100 ms)	807 ms
9.57	cross-region (80–100 ms)	862 ms
10.2	cross-region (80–100 ms)	917 ms
10.8	cross-region (80–100 ms)	972 ms
11.4	cross-region (80–100 ms)	1.03 s
12	cross-region (80–100 ms)	1.08 s
12.6	cross-region (80–100 ms)	1.14 s
13.3	cross-region (80–100 ms)	1.19 s
13.9	cross-region (80–100 ms)	1.25 s
14.5	cross-region (80–100 ms)	1.3 s
15.1	cross-region (80–100 ms)	1.36 s
15.7	cross-region (80–100 ms)	1.41 s
16.3	cross-region (80–100 ms)	1.47 s
16.9	cross-region (80–100 ms)	1.52 s
17.5	cross-region (80–100 ms)	1.58 s
18.1	cross-region (80–100 ms)	1.63 s
18.8	cross-region (80–100 ms)	1.69 s
19.4	cross-region (80–100 ms)	1.74 s
20	cross-region (80–100 ms)	1.8 s
20.6	cross-region (80–100 ms)	1.85 s
21.2	cross-region (80–100 ms)	1.91 s
21.8	cross-region (80–100 ms)	1.96 s
22.4	cross-region (80–100 ms)	2.02 s
23.1	cross-region (80–100 ms)	2.07 s
23.7	cross-region (80–100 ms)	2.13 s
24.3	cross-region (80–100 ms)	2.18 s
24.9	cross-region (80–100 ms)	2.24 s
25.5	cross-region (80–100 ms)	2.29 s
26.1	cross-region (80–100 ms)	2.35 s
26.7	cross-region (80–100 ms)	2.41 s
27.3	cross-region (80–100 ms)	2.46 s
27.9	cross-region (80–100 ms)	2.52 s
28.6	cross-region (80–100 ms)	2.57 s
29.2	cross-region (80–100 ms)	2.63 s
29.8	cross-region (80–100 ms)	2.68 s
30.4	cross-region (80–100 ms)	2.74 s
31	cross-region (80–100 ms)	2.79 s
31.6	cross-region (80–100 ms)	2.85 s
32.2	cross-region (80–100 ms)	2.9 s
32.9	cross-region (80–100 ms)	2.96 s
33.5	cross-region (80–100 ms)	3.01 s
34.1	cross-region (80–100 ms)	3.07 s
34.7	cross-region (80–100 ms)	3.12 s
35.3	cross-region (80–100 ms)	3.18 s
35.9	cross-region (80–100 ms)	3.23 s
36.5	cross-region (80–100 ms)	3.29 s
37.1	cross-region (80–100 ms)	3.34 s
37.8	cross-region (80–100 ms)	3.4 s
38.4	cross-region (80–100 ms)	3.45 s
39	cross-region (80–100 ms)	3.51 s
39.6	cross-region (80–100 ms)	3.56 s
40.2	cross-region (80–100 ms)	3.62 s
40.8	cross-region (80–100 ms)	3.67 s
41.4	cross-region (80–100 ms)	3.73 s
42	cross-region (80–100 ms)	3.78 s
42.6	cross-region (80–100 ms)	3.84 s
43.3	cross-region (80–100 ms)	3.89 s
43.9	cross-region (80–100 ms)	3.95 s
44.5	cross-region (80–100 ms)	4 s
45.1	cross-region (80–100 ms)	4.06 s
45.7	cross-region (80–100 ms)	4.11 s
46.3	cross-region (80–100 ms)	4.17 s
46.9	cross-region (80–100 ms)	4.22 s
47.5	cross-region (80–100 ms)	4.28 s
48.2	cross-region (80–100 ms)	4.33 s
48.8	cross-region (80–100 ms)	4.39 s
49.4	cross-region (80–100 ms)	4.44 s
50	cross-region (80–100 ms)	4.5 s

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.

Physical Substrate & Performance Laws
Why do trade-offs exist at all?
$5 sequential round trips \geq 5 \times RTT$
Read it in place →
Cost Mechanics
What is metered, and what is the smallest increment you are charged for?
$20 \times 100 ms$
Read it in place →
Interfaces & Formats
What can two parties agree on when they cannot talk to each other?
$4 \times 80 ms = 320 ms$
Read it in place →