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Bandwidth for High Speed Networks

The bound does depend crucially on the maximal rate r

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Unformatted text preview: ervice time; we call any amount above this the excess service. We can bound this excess service, and the bounds are independent of both the arrival process and the length of the time interval during which the ow is active. The bound does depend crucially on the maximal rate R at which a ows packets can arrive at a router limited, for example, by the speed of the ow's access link; the smaller this rate R the tighter the bound. Theorem 1 Consider a link with a constant normalized fair rate , and a ow with weight w. Then, the excess service received by a ow with weight w, that sends at a rate no larger than R is bounded above by R r K 1 + ln r + lmax ; 2.7 Miscellaneous Details 8 where r = w, and lmax represents the maximum length of a packet. By bounding the excess service, we have shown that in this idealized setting the asymptotic throughput cannot exceed the fair share rate. Thus, ows can only exploit the system over short time scales; they are limited to their fair share over long time scales. 2.5 Implementation Complexity At core routers, both the time and space complexity of our algorithm are constant with respect to the number of competing ows, and thus we think CSFQ could be implemented in very high speed core routers. At each edge router CSFQ needs to maintain per ow state. Upon each arrival of each packet, the edge router needs to 1 classify the packet to a ow, 2 update the fair share rate estimation for the corresponding outgoing link, 3 update the ow rate estimation, and 4 label the packet. All these operations with the exception of packet classi cation can be e ciently implemented today. E cient and general-purpose packet classi cation algorithms are still under active research. We expect to leverage these results. We also note that packet classi cation at ingress nodes is needed for a number of other purposes, such as in the context of Multiprotocol Label Switching MPLS 4 or for accounting purposes; therefore, the classication required for CSFQ may not be an extra cost. In addition, if the edge rou...
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