Quantizing the gold deliveries, for example

Ifyou run the gold coin franchise for the pit, then you are moving gold around the major industrial cities, and you guarantee three days delivery,.

So the trading pit manages two queues, gold in and gold out.  Looking back three days, the pit boss can determine a good estimate of the price compression tree, the set of basket size of the form: freq * log(freq). Log frequency being a component of the basket size, it is a link going down the decompression tree.

But, the point is, your gold company has a very accurate set of fixed baskets (trucks, cars and planes), with accurate schedules of arrival.  So, your pit  has the direct logistics challenge, not the indirect; or your pit is promising a set of very fixed basket sizes meaning a severely bound bit error function.  In this case, your price compression is easier done with rapid in/out matching.  Find all the requests to move in one direction, map them to specific requests to move in the other.Each map requires you do a bubble sort. When you have about "1.5" days of the stuff, split the price and set the order.  Each  opposing sign is a canceled shipment, you can meet most of the requirements by canceling matching, but opposite signed, baskets.

You are still engaging in lossy compression and your baskets can never be completely full, you do suffer some jitter. If to goof up, and have to much on the dock, hen it is a very expensive effort to protect the loot.  So your inventory nevere quite matches your in and outs, exactly, that is why youhave inventory.

So, your gold company runs the defacto S&L for gold coins that circulate in the sandbox.  Using the associated tokenization scheme your company controls, anyone can trade their gold certificate for gold.You have a physical ledge system.  The denominations of the gold certificates will resemble the basket sizes your company uses to move gold. The certificates can be  subtracted from and added up normally, the endpoints guarantee to meet your monetary rules, such as three day delivery.

Popular? Yes, very, the idea that I can go to the local depot and get the gold.  Risky? You company will carry gold risk, on the margin your delivery system ends up owning gold, temporarily,. then selling it, by market choice.  But you tell people, and define yourself; are you a precious metal delivery system or a bank.