Suppose that we have n time slots, and these are divided randomly between multiple users, with each user drawing a different number of time slots as it needs.
How would I measure the distribution of time slots, so that no user starves, or draws all its time slots as one bulk?
I had a method but the problem is that I only get results by simulation, I cannot derive a mathematical formula for it, so I am searching for mathematical form to measure the distribution.
Update: First: I only want a metric that can measure the fairness of the division, as I said before I found a metric but with no mathematical formula.
Second: there are two ways to divide the time slots between users:
- Completely random.
- Using rounds, example for that if u1 needs 2 time slots, u2 needs 4, and u3 needs 6, then there will be 2 rounds each one has 1+2+3=6 time slots, inside the round the u1 may chose any time slots, u2 may choose any 2 slots and so on.