![]() The balancer is the input and output vertices together with a set of intermediate vertices which represent splitters which have $1\leq$in-degree,out-degree$\leq$2 (one or two directed edges point to them and one or two coming from them) and the associated directed edges. The inputs being sources (in-degree=0) and the outputs being sinks (out-degree=0). We can represent the input belts and output belts as vertices of a directed graph. #Belt balancer factorio how toThe first idea is about how to represent the problem: I have some ideas on how to approach this problem, but am nowhere near having it solved. The question I have is the following: It always possible to create an $n$-belt balancer satisfying the universally throughput unlimited condition for any $n$? It not, for which $n$'s is it possible? (clearly, $n=2$ works because of how splitters behave) This basically means that the $n$-belt balancer is never a bottleneck no matter the current input or output limitations (which lanes are getting input/available for output). #Belt balancer factorio fullThen the full input on those $k$ input belts can be provided across the $k$ output belts (which have the same maximum throughput, hence no one output belt can handle more than one input belt's worth of throughput). The desired property called universally throughput unlimited is the following: Suppose only $k$ of the $n$ input belts are getting input (assume full input aka, input belts are assumed saturated), and that all but $k$ of the output belts are backlogged and have no throughput (already full of items and nothing is moving on those belts). They are frequently used in large factories to move large amounts of items to a variety of different areas in a manner where no one belt worth of items getting backlogged (more items coming at it than it can use) results in other projects not getting full throughput (or at least as much as they can use). So what is a $n$-belt balancer? It is a configuration of belts (which move items around), and splitters (which take two belts in and balance their items on the two belts on the output side), which will balance the input of all $n$ input belts across all $n$ output belts. In it, the poster is examining an $8$-belt balancer (more on that to come) which he shows fails to satisfy a desirable property, which he called universally throughput unlimited. So this question is inspired by the following thread: ![]()
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