Fractional reserve banking, the semantics

I don't always get it, and so say little about it.
My understanding is the reserves are cash and credit n hand to cover variations in asset yield.  Example, keeping cash on hand to handle the occasional default.  This is different than the deposit to loan ratio, these terms are more like the balance sheet, assets and liabilities.  In the balance, the banking network seeks to spread the  default risk.

Anyway, I am getting closer.   The reserves is the currency risk,  when the results are in, we get more or less if our reserves back, the residual spent on price neutrality.  So, my interpretation says fractional reserve banking is OK.  Loan/deposit is the key variable, even in the balance sheet.  At no time do assets equal liabilities, all balance sheets should have residual currency risk term.  On other words, the units of the balance sheet share the uncertainty.  So the banker risk is simply; are deposits or loans becoming congested relative to the 'float' the currency bot allows.

So, the member banks have two stacks of paper, incoming deposits and outgoing loans.  His banking model says he wants the ratio around some standard number for his type pf banking.  Banker monitors the height of the two stacks,  At some time the banker notices the variance of the queue sizes imply a bulge of deficit in the deal flow, which exceeds the estimated currency float the currency bot uses.  So the banker changes his rates, he alters his location and size on the local baking network.  The banker seeks to always to make loans the currency bot considers typical.   Then his two stacks of paper will have a slightly different typical ratio, the the implied congestion what the currency bot likes.

Currency bot at the short end

Currency bot s a spreadsheet function  It sorts incoming and outgoing stack sizes, and makes a generator for the typical sequence.    The transaction costs are nill, that means currency bot will occupy whatever portion of the yield curve the member banks want, starting at the short end.  Measuring variance is done by assigning the static queue results in a currency bot float of one unit variance.  But that allows no reserve for dynamic changes in he deal flow, it is assumed the typical sequence is unchanging.  That would be the variance of the member banks deposit flow minus loan flow to and from the currency bot.  That published variance should have correspondence with the window size of the typical sequence.

So the currency banker generates uncertainty, on purpose, as no one know yet what happened in  the immediate past.  The uncertainty is minimized when the banking network is high ranked (it has a long tyical sequence.).  In that case, the currency bot is pushed way over to the short end, and occupies a much smaller region of the curve.  Andf when the currency bot occupies he smaller part, the immediate pas is much smaller, mark to market happens quicker.  The smaller the currency uncertainty, the longer the typical sequence.