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Unformatted text preview: Computer Networks Fairness Saad Mneimneh Computer Science Hunter College of CUNY New York Life is not fair, but we can at least theorize 1 Introduction So far, we analyzed a number of systems in terms of average occupancy, through- put, and delay. However, we did not make any distinction among the customers arriving to the system. For instance, consider the M/M/1 system with a finite queue of packets. If multiple flows are sharing the link, it is possible to achieve high throughput by making one flow generate enough packets, and preventing other flows from sending (their packets will be dropped). Therefore, we need another property to ensure that all flows receive an equal share of the resources. Although not very well defined at this point, we will call this property fairness . To illustrate the basic idea, consider the following figure: 1 2 Figure 1: Fairness with two flows In the above figure, efficiency means that 1 + 2 is close to . However, fairness means that 1 is equal to 2 . We previously showed that a good op- erating point is when 1 + 2 / 2 (at 50% utlization, throughput/delay is high). We also argued that this behavior of M/M/1 is simiar to that of a net- work in general (because each link can be modeled as an M/M/1 system). But a network in general is not just one link; therefore, for fairness, the notion of equal share in not necessarily what we think of equality, in particular, how do we handle flows that use different paths? 1 2 A motivating example Assume there is no explicit demand or reservation of bandwidth, and that all the links have a capacity of 1 (unit of bandwidth in bps). How should we assign rates to the flows in the following figure? 1 4 2 3 Figure 2: An example of fairness If all flows receive an equal share of the resources, we would assign each flow a rate of 1/3. However, while it makes sense to limit the rates of flows 1, 2, and 3 to 1/3, it is pointless to do the same for flow 4. Flow 4 may receive a rate of 2/3 because no other flow will benefit by reducing the rate of flow 4 below 2/3. On the other hand, increasing the rate of flow 4 beyond 2/3 will reduce the rate of at least one other flow among those which receive a rate of 1/3. So the assignment of rates (1 / 3 , 1 / 3 , 1 / 3 , 1 / 4) is fair in some sense. This shows that4) is fair in some sense....
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- Spring '08
- Computer Networks