Additional specifics on loan/deposit compression

If we considered the ongoing sequence of deposit events and loan events, all in the sandbox, and set to amber. Now, aty any given region of operation, the pit pit organizes the loan eves and deposit events by probability, such that we get two huffman trees, each path through the tree leads to a range of liquidity events, path inverse to probability.

So, in short, let us say that the pit boss can tell us the most common one bit price.  That is, for either L or D, a one bit path leads to set of prices that are most common, and confined to a range. The most common set of prices is the shortest path through the tree.

The pit wants the queue of loan events to equal the queue of deposit events plus bit error events; conserving total probability. (We could probability reverse the position of the bit error events). The strategy is to scale and set price properly for the most common bid/ask pair, then  rinse and repeat.

But, the pit boss need only scale the price axis  until the number of events meets the queue condition for the  most common price, the most common event has a computable queue size at equilibrium. Once I the queue sizes are computed, then my deposit and loan queues have to obey the price ratio rule, based on the ratio of queue sizes so computed.

The price ratio works because in the sand box, shipments slightly mismatched cause a temporary liquidity event at the S&L (when all the assumptions ate met). The liquidity events being accurate representations of shipments, which in fact have to obey queuing law, in the sense that inventory is conserved..

My queuing assumption
In the most common, one bit bin, I have 6 loan events and 4 deposit events.  My conservation of queue says:
6-4 = 2
then I have two bit error events on the hook.  Divide through by 2,  treat the resulting mean and variance of a queue can be treated as a constricted flow, I assume hyperbolic condition holds, and that gives me a relationship on sigma ratios.
In yhe process, the price axis is scaled in the distribution, so the algorithm knows how yhe bit error changed for loans and deposits.  Under the assumptions, the pit extracts an loan interest payment and makes a deposit interes payment