There are electrical circuits which behave similarly to the C-14 model. In the circuit below there is a battery which is a large source of electrons that can be used to represent the supply of nitrogen in the air. The production of C-14 is represented by a current flowing through the first conductance which is I = GV = αA approximately. The amount of C-14 in the air is represented by the charge stored in the capacitor which is proportional to the voltage across it, B. The removal of C-14 is represented by the currents through the two remaining resistors. If α is much smaller than the other conductances then the combination α-A acts like a current source which determines the flow through the circuit. If the voltage B is initially zero it will rise to reach an equilibrium value and no current will flow to the capacitor. Again letting λ = γ + β the equilibrium condition is that for which the flow through this equivalent conductance is equal to that of the source. But then one also has I = GV = λB and the equilibrium condition is αA = λB.
In the water bucket model the air gaps and "waterfalls" are necessary to isolate the buckets so that the flow from them is proportional to the amount of water in the bucket. In the electrical circuit is isolation isn't as good but if the other voltage drops are negligible compared to A the model will be a reasonably good analog for the C-14 system.