The frame perspective

Banks form a tree as in the original scheme. This defines the transitive superior and inferior relations between banks. For each bank there is a service key rather analogous to the meter service key. An order on the service key produces a bank key.

Every frame is in just one of three states:

A reserved frame is reserved at just one bank.
An allocated frame is allocated at just one bank.
A frame is under a bank B iff it is allocated at B or at some bank that is inferior to B.
Every bank has a non-negative integer, its limit.

To buy a page non promptly from bank B, if the limits of B and of the superior banks are all positive then an available frame is allocated at B and all of those limits are decremented. A page is thereby created and returned to the buyer. If one of the limits is 0 then the bank keeper of the lowest bank with 0 limit is invoked with arguments:

To sell a page non promptly to bank B, the frame of that page must be allocated at B. The limits of B and all of its superior banks are incremented.