Difference between revisions of "Branching factor"
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In a first approximation of [[convergent assembly]] organized into [[assembly layers]] <br> | In a first approximation of [[convergent assembly]] organized into [[assembly layers]] <br> | ||
each assembly chamber has exactly b<sup>2</sup> sub-chambers. <br> | each assembly chamber has exactly b<sup>2</sup> sub-chambers. <br> | ||
| − | These | + | These sub-chambers collectively prepare: |
* b<sup>3</sup> sub-parts in once full cycles time or equivalently | * b<sup>3</sup> sub-parts in once full cycles time or equivalently | ||
* b<sup>2</sup> sub-parts in b<sup>-1</sup> = 1/b of a full cycles time | * b<sup>2</sup> sub-parts in b<sup>-1</sup> = 1/b of a full cycles time | ||
Revision as of 13:40, 25 August 2022
Branching factor is a characteristic number for convergent assembly.
Let's abbreviate it with b here. (Otherwhere also used: n, B, ...)
In a first approximation of convergent assembly organized into assembly layers
each assembly chamber has exactly b2 sub-chambers.
These sub-chambers collectively prepare:
- b3 sub-parts in once full cycles time or equivalently
- b2 sub-parts in b-1 = 1/b of a full cycles time
Concrete visual example:
A chamber making 27 piece Rubiks cube like assemblies
has only 9 chambers in the next smaller sub-layer
but this sub-layer works with the 3-fold frequency,
so the throughput of the sub-layer matches with the throughput of the chamber atop.
("sub-layer" above refers to just the local patch of the sub-layer below one single chamber atop)
Pros and cons of higher branching factors
Benefits of higher branching factors are:
- More design freedom in parts – less constrained by the production process
- A bigger (better) assembly-motion-distance to transport-motion-distance ratio – in case there are slower operating stacked layers of same size
Downside of higher branching factors:
Given constant speed bigger branching factors lead to longer assembly times.
Doubled branching factor gives one eighth of the throughput.
It's a third power scaling law.
Misc notes
The branching factor can vary over a stack of layers.
When and how much to do that depends on the details of a concrete implementation.
Not factored in in a a first approximation of convergent assembly are eventual errors.
Since this is not compensated in space it needs to be compensated in time. That is: delays.
