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min fair alloca7on 16 Recall • We want a good bandwidth alloca7on to be fair and eﬃcient – Now we learn what fair means • Caveat: in prac7ce, eﬃciency is more important than fairness 17 7 11/12/13 Eﬃciency vs. Fairness • Cannot always have both! – Example network with traﬃc AB, BC and AC – How much traﬃc can we carry? A 1 B 1 C 18 Eﬃciency vs. Fairness (2) • If we care about fairness: – Give equal bandwidth to each ﬂow – AB: ½ unit, BC: ½, and AC, ½ – Total traﬃc carried is 1 ½ units A 1 B 1 C 19 8 11/12/13 Eﬃciency vs. Fairness (3) • If we care about eﬃciency: – Maximize total traﬃc in network – AB: 1 unit, BC: 1, and AC, 0 – Total traﬃc rises to 2 units! A 1 B 1 C 20 The Slippery No7on of Fairness • Why is “equal per ﬂow” fair anyway? – AC uses more network resources (two links) than AB or BC – Host A sends two ﬂows, B sends one • Not produc7ve to seek exact fairness – More important to avoid starva7on – “Equal per ﬂow” is good enough 21 9 11/12/13 Generalizing “Equal per Flow” • Bo`leneck for a ﬂow of traﬃc is the link that limits its bandwidth – Where conges7on occurs for the ﬂow – For AC, link A–B is the bo`leneck A 1 B 10 C Bo`leneck 22 Generalizing “Equal per Flow” (2) • Flows may have diﬀerent bo`lenecks – For AC, link A–B is the bo`leneck – For BC, link B–C is the bo`leneck – Can no longer divide links equally … A 1 B 10 C 23 10 11/12/13 Max
Min Fairness • Intui7vely, ﬂows bo`lenecked on a link get an equal share of that link • Max
min fair alloca7on is one that: – Increasing the rate of one ﬂow will decrease the rate of a smaller ﬂow – This “maximizes the minimum” ﬂow 24 Max
Min Fairness (2) • To ﬁnd it given a network, imagine “pouring water into the network” 1. Start with all ﬂows at rate 0 2. Increase the ﬂows un7l there is a new bo`leneck in the network 3. Hold ﬁxed the rate of the ﬂows that are bo`lenecked 4. Go to step 2 for any remaining ﬂows 25 11 11/12/13 Max
Min Example • Example: network with 4 ﬂows, links equal bandwidth – What is the max
min fair alloca7on? 26 Max
Min Example (2) • When rate=1/3, ﬂows B, C, and D bo`leneck R4—R5 – Fix B, C, and D, con7nue to increase A Bo`leneck 27 12 11/12/13 Max
Min Example (3) • When rate=2/3, ﬂow A bo`lenecks R2—R3. Done. Bo`leneck Bo`leneck 28 Max
Min Example (4) • End with A=2/3, B, C, D=1/3, and R2—R3, R4—R5 full – Other links have extra capacity that can’t be used • , linksxample: network with 4 ﬂows, links equal bandwidth – What is the max
min fair alloca7on? 29 13 11/12/13 Adap7ng over Time • Alloca7on changes as ﬂows start and stop Time 30 Adap7ng over Time (2) Flow 1 slows when Flow 2 start...
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