Fairness 3 if we care about eciency maximize total

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Unformatted text preview: x ­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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This document was uploaded on 04/04/2014.

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