max-min fairness

Every flow either receives what they demand, or share equally with all other flows that did not receive what they asked for.

Formally:

• $N$ is the total number of flows
• $x_n$ is the resource demand by flow $n$
• $C$ is the capacity
• $m_n$ is the actual resource allocation to flow $n$

So we have $M_n=\frac{C-\sum _{i=1}^{n-1}{m}_i}{N-n+1}$as the resource available to flow $n$. The way to read this is “an equal share of the capacity that’s left.” Then $m_n=\min (x_n,M_n)$. If you ask for less than what your fair share would be, you get your demands met. Otherwise, you get an equal share of what’s available.

Notably, the flows must be sorted for this algorithm to work (as stated anyway).