We can think of banker bot as solving a queuing problem

Queuing over a finite network, establishing a consistent index sequence, and constrained flow really are just three different views of the same thing, making probabilistic assumptions work with money so it can be used as a numerator.

As a queueing problem, banker bot is really adjusting deposit and loan rates so the member banks are not congested, they therefore have liquidity. If banker bot reached beyond the member banks and buys, say long term assets, all the banker bot is doing is inviting a new member bank to the queue, and re-establishing the index sequence. The key here is that banker bot determines the starting  two sequences in the price index, and making sure they are consistent. Banker bot has no mechanism to look beyond the first two indices in the sequence, the very act of looking beyond the first two creates an arbitrage opportunity, and the numerator is being managed by something else.