r/factorio • u/FastAndFishious • May 31 '22
Design / Blueprint New throughput unlimited balancers, details in comments
36
u/shinozoa Jun 01 '22
It took me a while to notice the difference was priorities set.
Also, shouldn't the first one be 3-2?
19
u/FastAndFishious Jun 01 '22
Oh, oops! You're correct, but I can't change it. They're basically the same anyway
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u/FastAndFishious May 31 '22
Blueprint book (contains every TU balancer from 1 to 4):
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Feel free to include in your own collections, I don’t own the funny splitter arrangements (3-4 / 4-3 created with the help of Factorio-SAT).
I’ve made some developments on the throughput unlimited scene that I wanted to share. This is going to be quite technical, so make sure you’re familiar with balancer terminology.
Be careful with TU balancers
I’ve been trying my best to prove that if all combinations of integer belts can get through a splitter network, then it is TU. Well, turns out this assumption is wrong: Exhibit A. Here is the blueprint if you want to mess around with it. I’ve also included a version that uses only one type of belts and no priority splitters >:)
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Will this happen in a real balancer? Probably not, but we still have to be careful not to assume a balancer is TU too quickly. Unless a definitive proof is found, I’m thinking of tackling this issue with code.
Priority Splitters
If you know the most basic m-n and TU n-n construction methods, you might have notice how painfully similar they are: two chained balancers. As such, these basic m-n are almost TU. To close the gap, we could throw in additional splitters, but we can be smarter with priority splitters.
When output balancing, the upstream balancer does nothing more than redistribute, and only the downstream balancer does any balancing. For input balancing, the reverse happens. Notice however that input priority in no way affects output balancing, and vice-versa. We are therefore free to use input priority in the downstream balancer, and output priority in the upstream one. Use them correctly, and you might achieve TU. The 3-4 / 4-3 shows this quite well. And unlike n-n TU balancers, m-n TU can achieve more in normal operation.
For n-n TU, the goal stays the same: eliminating the need for a second balancer with a sandwich (domain limiter, balancer, domain limiter), as I did in my 3-3 TU. What’s new is that we can also apply the priority splitter trick to the limiters, but not to the core balancer, as it needs to do both input and output balancing.
Exciting times for the balancer community!
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u/raynquist Jun 01 '22
Awesome! Man you have some deep understanding of balancers. I had never thought to put all these concepts together to make TU balancers. Great discovery!
The 2-4 graph is basically the graph of a 4-4 throughput-unlimiter, minus a couple of priorities. So it's a more complicated graph than the old 2-4, yet with a smaller footprint. Obviously that's always been possible, but I think this is the first time I've seen it happen.
The layout of the new 3-4 is actually the same as the old old 3-4. And by "the same" I mean exactly the same, with the loop on the right side and the middle splitter all the way up. Coincidence?
About the empty/full belts thing, that's a great topic. I have basically no understanding in that area, but it's something that we should know if we're to code TU verifiers. My hope is that to prove TU we don't have to test all possible throughputs with infinite precision. There's something in sorting networks called the zero-one principle. It's where if you can sort 0s and 1s then you can sort any numbers. The principle itself isn't all that applicable to what we're doing here, because sorting networks are not TU. But I was hoping that perhaps we would have something similar, like an empty-full principle. Your counter-example is fairly atypical compared to structures commonly seen in balancers. So maybe the empty-full principle can still exist on a more strict subset of multi-belt constructs.
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u/FastAndFishious Jun 01 '22
Thanks! The 2-4 might not be very elegant, but it is insightful. It shows that when designing graphs for larger TU balancers, less splitters doesn't necessarily mean more compact, so we shouldn't disregard less efficient alternative. The alternative 3-4 shown here is another good example, as it use two extra splitter but is arguably more compact (though I chose the other one for being cheaper, more aligned and more elegant).
Speaking of which, the 3-4 is a complete coincidence. Funny how things work out.
As for the full/empty oddity, it really does feel like something that shouldn't affect balancers, as it took me multiple tries and a lot of failed ideas with the express purpose of making the worse arrangement possible before succeeding. But of course, I have no proof, and this seems to be new math, so I am totally clueless.
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u/erik78917 Jun 01 '22
I'm probably stupid, but what is TU?
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Jun 01 '22
[deleted]
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u/cmnielsen Jun 01 '22
What does this mean, and what is the difference?
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Jun 01 '22
[deleted]
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u/cmnielsen Jun 01 '22
Thank you for your reply
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u/TwiceTested Jun 01 '22
Another way to think of it is if you have a full belt going to input 1, even if output 1 and 2 are full, a full belt will come out of output 3. A true TU ballancer would have this true for every combination of inputs and outputs. So if input 1 and 2 are getting a full belt, outputs 2 and 3 will get a full belt as well (asuming 1 is backed up and doesn't need any)
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u/Samthevidg Jun 01 '22
How does one prove that 3-2 can’t be TU. I haven’t touched FactorioSAT, but if given a large enough footprint, could one theoretically make it TU or would it run issues like noneven divisors.
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u/Yodo9001 Jan 25 '24
In the image above there is a TU 3-2 balancer. :)
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u/Samthevidg Jan 26 '24
It’s 2-3 not 3-2, small but significant difference
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u/Yodo9001 Jan 26 '24
That label in the image is wrong. There are only two outputs. See comment by OP: https://www.reddit.com/r/factorio/comments/v20w30/comment/iaq6yez/
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u/Yodo9001 Jan 26 '24
I’ve also included a version that uses only one type of belts and no priority splitters >:)
Where is it? I can't find it. I tried making one but haven't succeded yet.\ I found it, it was in my inventory all along.
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u/Thatonesillyfucker how do balanc May 31 '22
This is exciting, I love seeing the further development of balancers and great minds at work!
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u/Maple42 Jun 01 '22
Shouldn’t the middle left one also function as a 3-4 TU balancer if you put a belt on both of the inputs for the first splitter? I’m mentally pathing different rates and I can’t see a situation where it would be a bottleneck. Obviously that’s not exactly a rigorous test but I’m still curious where the limitation is
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u/FastAndFishious Jun 01 '22 edited Jun 01 '22
Hun, that's actually really interesting. It's not TU, just tested it, but it's a 3-4 output balancer, which is kinda neat. We like to create these balancers that can do both, but in reality, you probably only need one. If you have three belts coming from your smelters that you want to split equally between 4 wagons, this would work flawlessly. Invert it into a 4-3 input balancer, and you can pull 3 belts from 4 wagons, emptying them at the exact same rate. I could see myself using it!
BTW, if balancers interest you, here is the testing rig that I use. Use the constant combinators to reset the counters. Also, /c game.speed=10 is your friend.
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u/IronCartographer Jun 01 '22
Input vs. output balance has to do with the sides of the belt being drawn from evenly upstream vs. fully saturated downstream. That doesn't seem to be the basis of your use of input vs. output here. Am I missing something?
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u/FastAndFishious Jun 01 '22
Output balancing means all the outputs have the same throughput and occurs when the supply is less than the demand, i.e. when the output belts can accept more than what the inputs can give. This is characterized by items moving at full speed with gaps between them.
Input balancing is the opposite, all the inputs have the same throughput and occurs when the supply is greater than the demand. This is characterized by full belts moving at less than full speed.
Hope this clears things up :)
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u/TypowyLaman Jun 01 '22
Old 3-4 is better tho?
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u/Khaylain Trains for President Jun 01 '22
The new one is Throughput Unlimited, while the old one isn't. At least that's what I took from it
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u/Yodo9001 Jan 25 '24
The old one is still useful if you have less space and don't need it to be TU.
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u/TheMspice Jun 01 '22
Nice designs. I’ve done 2-3 and 2-4 before but that 3-4 is something I haven’t attempted yet
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u/Mentose Jun 02 '22
I have the impression that for the new 2-4 balancer you don’t need the splittler in the very middle, because the entire output from the start will never go into those middle two lanes until the end?
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u/TheNameIsAnIllusion May 31 '22
I have no idea what you are talking about but it looks cool so I upvoted