Here is a math like Fed rule

The Fed operates with short term view, and gains or loses depending who has the most acurate long term view.

Thus, treat the short term as a fixed width channel, meaning the Fed deposit and loans requested have to fit a transaction limited channel, it will not pay more than 15 basis points per transaction, and that means risk equalized.

In this model, the Fed promises to deliver a white noise market error with less than half point variance. The noise is white relative to any properly defined contract for currency function.

The solution is a queue control.  Adjust the window when loans demanded and deposits offered seem balanced, then grab the queue, lock it up and identify the matched loan/deposit value at linearity. Interest charges are proportional to the skew of the particular transaction, -iLog(i) all within an integer for the matched distribution.  The currency risk, market error, is balancing skew between the two. Equilibrium is when the waits in line for trades are about 2 or 3, when matched by quant.

We are really finding the minimum of the total waits in line across an uncertain market. Solves a basic question, Why is the Damn X so  Damn Y? Because the waits in line are too unstable, the pit boss cannot handle the extreme skew, no risk equalization. Stay balanced, oooooooommmm.