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What is "Fair" ?

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• Max-Min Fairness
  • A commonly used definition of fairness in computer network is Max-Min fairness

  • Suppose a number of (TCP or UDP) connections share a common bottleneck link

  • The sharing is max-min fair max-min fair when:

    the minimum data rate that a dataflow achieves is maximized; the second lowest data rate that a dataflow achieves is maximized; the third lowest data rate that a dataflow achieves is maximized; and so on.

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• Consequence of Max-Min Fairness
  • When the Max-Min Fairness property is achieve in a sharing of a bottle neck link, then ill-behaved flows that send a large number of packets, will only punish itself and other flows will NOT be affected by ill-bahaved flows .

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• Example of a Max-Min Fair Bandwidth assignment
  • Consider the following 4 flows sharing a common bottle neck link:

  • The bottleneck link has a bandwidth of 10 Mbps

    There are 4 flows sharing the bottleneck link

    Hence, the fair share of each flow is:

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

  • So a first division of the bottleneck bandwidth would be:

    Flow 1:   2 Mbps (because it could not use all of the 2.5 Mbps)   Flow 2:   2.5 Mbps Flow 3:   2.5 Mbps Flow 4:   2.5 Mbps Unused bandwidth = 0.5 Mpbs

    We see that:

    • the minimum data rate that a dataflow achieves (flow 1 with its 2 Mbps) is maximized;

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  • Because there is still unused bandwidth remaining, we divide the Unused bandwidth among the other flows

    Each (of the other) flow will get:

    0.5 Mbps ---------- = 0.1666666 Mbps - extra per flow 3

  • So a second division of the bottleneck bandwidth would be:

    Flow 1:   2 Mbps Flow 2:   2.6 Mbps (because it could not use all of the 2.666666.. Mbps)   Flow 3:   2.666666.. Mbps Flow 4:   2.666666.. Mbps Unused bandwidth = 0.066666.. Mpbs

    We see that this sharing achieves:

    • the minimum data rate that a dataflow achieves (= flow 1 with its 2 Mbps) is maximized;

    • the second lowest data rate that a dataflow achieves (= flow 2 with its 2.6 Mbps) is maximized;

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  • Because there is still unused bandwidth remaining, we divide the unused bandwidth among the other flows

    Each (of the other) flow will get:

    0.0666666 Mbps ---------------- = 0.0333333.. Mbps - extra per flow 2

  • So a third division of the bottleneck bandwidth would be:

    Flow 1:   2 Mbps Flow 2:   2.6 Mbps Flow 3:   2.7 Mbps Flow 4:   2.7 Mbps Unused bandwidth = 0.0 Mpbs

    We see that this sharing achieves:

    • the minimum data rate that a dataflow achieves (= flow 1 with its 2 Mbps) is maximized;

    • the second lowest data rate that a dataflow achieves (= flow 2 with its 2.6 Mbps) is maximized;

    • the third lowest data rate that a dataflow achieves (= flow 3 with its 4 Mbps) is maximized;

    • the fourth lowest data rate that a dataflow achieves (= flow 4 with its 5 Mbps) is maximized;

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  • NOTE:

    The above assignment of bandwidth is the Max-Min fair assignment. If this assignment is enforced, then even if flows 4 and 5 send at a high date rate (4 and 5 Mbps, respectvely), the network will only forward 2.7 Mbps of these flows to the final destination. The excess data will be discarded That is why: When the Max-Min Fairness property is achieved (enforced) in a sharing of a bottle neck link, then ill-behaved flows that send a large number of packets, will only punish itself and other flows will NOT be affected by ill-bahaved flows .

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• Generalization of Max-Min Fairness over multiple links