How to interpret following max-min optimization criterion

Question

I am reading a paper in which the author says the following about the maximization problem. Now before reading that, please note that I understand that max-min fairness is. But I cannot understand the following equation and how it represents a max-min fairness algorithm. The following is what is written in the paper.

For..., the for computational efficiency ($\eta$ below) is formulated under the max-min fairness criterion as

where, $\eta = \frac{\text{rate of data processing}}{\text{energy harvested by the circuit}}$, $k$ is any user etc...

Answer 1

I'll try to verbalize my understanding of this equation.

It says that,

1. For all $k \in K$, minimize the efficiency ($\eta$).
2. Now, given the parameters $\tau_0, ...$, maximize the value of $\eta$ for all $k$

Further Explanation

Assume that you have $k$ buckets which can store any item $\eta$, lets say water. Each $k$ has its own capacity $c_k$, and without loss of generality, $c_1 < c_2<...c_K$. Now you will start filling buckets with the available item, such that first $c_1$ is filled, followed by $c_2$, and so on. This will ensure that the filling is maximized and no resource is wasted, or any buckets does not get more than what it ask for. Of course, there are some buckets which will remain slightly empty, but this is what we can achieve given that available resources are less than demands.

Hope this helps.