Difference between revisions of "Branching factor"

Revision as of 06:45, 26 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.

Related

• Convergent assembly
• Math of convergent assembly
• Chamber to part size ratio
• Convergent assembly depth
• Error handling
• Level throughput balancing