What is "Fair" ?

Fairness

Humans have a "built-in" sense of fairness for certain things...
(Morality ???)
Example 1:

Example 2:

4 children sharing a cake but:
- Child 1 can only eat 1/10 of the cake.
Fact: it is stupid to give child 1 more than 1/10 of the cake because the extra cake (resource) is wasted
In this case, the "fair" sharing is:

This sense of "fairness" is called max-min fair:

Max-Min Fairness

A sharing of a network resource is "max-min fair" when:

The lowest demand on data rate is maximized;
After the lowest demand on the network resource has been satisfied, only then the second lowest demand on the network resource will be maximized;
After the second lowest demand on the network resource has been satisfied, only then the third lowest demand on the network resource will be maximized;
and so on.

The Max-Min Fairness Assignment Algorithm

The max-min fair resource assignment algorithm progresses in rounds

Steps performed in each round:

Compute the fair share of each unsatisfied flow
Assign the fair share to each unsatisfied flow

Some flows may have received more than its request

If there are over-assignments:

Take back the over-assigned shares
The sum of the over-assigned shares is the residual amount
Assign the residual amount to the remaining unsatisfied flows

Example of a Max-Min Fair Bandwidth assignment

Consider the following 4 flows sharing a common bottle neck link:

Notes:

The bottleneck link has a bandwidth of 10 Mbps
There are 4 flows sharing the bottleneck link
The demands of each flow is given in the figure

Iteration 1:

compute the fair share of each unsaisfied flow:

10 Mbps --------- = 2.5 Mbps (per flow) 4

Assignment:
Residual:

Notice that:

The flow with minimum demand (i.e., flow 1 with 2 Mbps demand) has been maximized

Iteration 2:

compute the fair share of each unsatisfied flow:

0.5 Mbps --------- = 0.16666 Mbps (per flow) 3

Assignment:

Flow 2: 2.5 + 0.1 Mbps = 2.6 Mbps (because demand = 2.6 Mbps)
Flow 3: 2.5 + 0.16666 Mbps = 2.66666 Mbps
Flow 4: 2.5 + 0.16666 Mbps = 2.66666 Mbps

Residual:

Note:

After the minimum demand (i.e., flow 1 with 2 Mbps) has been maximized, the second lowest demand (i.e., flow 2 with 2.6 Mbps) is now maximized;

Iteration 3:

compute the fair share of each unsatisfied flow:

0.06666 Mbps ---------- = 0.03333 Mbps (per flow) 2

Assignment:
Residual:

Max-min fair assignment:

Flow 1: 2 Mbps
Flow 2: 2.6 Mbps
Flow 3: 2.7 Mbps
Flow 4: 2.7 Mbps

Notice that:

the lowest demand (= flow 1 with its 2 Mbps) is maximized;
the second lowest demand (= flow 2 with its 2.6 Mbps) is maximized;
the third lowest demand (= flow 3 with its 4 Mbps) is maximized;
(Note that maximized is not the same as satisfied. We gave flow 3 the highest possible assignment that is fair)
the fourth lowest demand (= flow 4 with its 5 Mbps) is maximized;
(Note that maximized is not the same as satisfied. We gave flow 4 the highest possible assignment that is fair)

NOTE:

If a max-min assignment is enforced by the network, then flows that transmits more than their fair share, will have their packets dropped

Example:

Suppose flows 4 and 5 are UDP (un-responsive) flow
Suppose flows 4 and 5 transmit 4 Mbps and 5 Mbps, respectively
If the network enforces the max-min assignment, then the network will:

Bottle line:

When the network enforces Max-Min Fair Sharing, then ill-behaved flows (that send a large number of packets) will not be able to affect the performance of other (well-behaved) flows

Weighted Max-Min Fairness

The max-min fair assignment can be generalized by adding weights to each demand.

Weighted demand:

Suppose demand requests x units of network resources
The demand has been given a weight = w

Then this weighted demand can be viewed as:

There are w individual demands
Each individual demand requests an amount of w/x units of network resources
(Even though you view the demand as w individual demands, all assigned network resources will be given to the same request

Weighted fairness:

Suppose demand 1 = x₁ units and has weight = w₁
Suppose demand 2 = x₂ units and has weight = w₂
And so on...
An assignment is max-min fair if the assignment is a max-min fair assignment for the weighted demands

Weighted max-min fair assignment algorithm

The max-min fair is similar to the max-min fair algorithm and again progresses in rounds

Steps in one round of weighted max-min fair assignment algorithm:

Compute the fair share unit:

unallocated resources Fair share unit = ------------------------ total weight

Allocate a fair share unit to each weight unit
Take back any over-assigned resource (residual)
The residual amount is assigned in a new iteration to the (remaining) unsatisfied flows

Example: Weighted max-min fair assignment algorithm

Example: how to divide 10 Mbps of bandwidth among these 4 flows with given weights ?
Note:

Iteration 1:

Compute the fair share unit:

Weights of unsaturated flows: 1, 2, 1, 1 10 Mbps Fair share unit = --------- = 2 Mbps 5

Attempted allocation:
Actual allocation:
Residual: 1 Mbps

Iteration 2:

Compute the fair share unit:

Weights of unsaturated flows: 1, 1, 1 1 Mbps Fair share unit = -------- = 0.33333 Mbps 3

Attempted allocation:
Actual allocation:
Residual: 0 Mbps