The Huffman encoder and inventory contango

Or shortages and overflow in the inventory network.  There is an intimate connection.

The Huffman encoder generates semi random sequences of typical measurements when it is fed a uniform random fixed value stream.  Most of the values take the short path,straight to consumer, and they take fewer shipments, or use fewer carrier bits.  The seldom shipped, more complex products take the longer path through the network.

But, you see, the Huffman encoder has designed the network so that none of the paths clog up when generating the typical sequence.  It quantized the original random values such that the total number of shipments is minimized.  So, by design the network generates typical results without clogging up.

So, you are a shipper, and want to be i the business of shipping complex products into complex assemblies.   Huffman encode the sector shipping billings up to a small precision, say 5 bits.  Then you have the typical set of shipments, find the  sequence element  that matches your relative truck size and make money.
Proof

One has to define the minimal, binary spanning tree that decodes the typical set.  Then, any other spanning tree that attempted to generate the typical set would occasionally have multiple input bunch up, overlapping, in the network, unless we assume Newtonian queue management.  Thus, there is one minimal spanning tree that matches given precision to some  semi random, repeating sequence.  This is the reverse of the Shannon entropy idea.  Shannon says there is a large enough encoding tree for any sequence up to some precision.  In this case, we set the precision, and that defines the limits on the sequence.  The precision is highly quantized in queuing systems because queue sizes are small if they have any significance.  In other words, the cost of waiting at the third position goes way up because of lost opportunity, after that, tings get  slightly worser per queue length.  This is always true on natural systems because their is no such thing as sitting still.

The lock, the Gibbs stae lock occurs because natures queues can never become empty of overflowed, and the only solution is constant motion.  Processes occur if they are slightly under sampled, and the lissing effect id what causes motion.  Nature is slightly under sampled precisely because the Shannon condition is a perfect lock, and the quantization wells have to leak. Its combinatorics, there is no empty space, or queue reservation by imaginary numbers.  The network always has loops, the  aliasing effect,  and they cannot all be closed.