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Bandwidth for High Speed Networks

4 performance bounds return b figure 2 the pseudocode

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Unformatted text preview: els. 2.3 Weighted CSFQ The CSFQ algorithm can be extended to support ows with di erent weights. Let wi denote the weight of ow i. Returning to our uid model, the meaning of these weights is that we say a fair allocation is one in which all bottler necked ows have the same value for wii . Then, if At C , the normalized fair rate t is the unique value such that ,r Pn i i=1 wi min ; wi = C . The expression for the drop,  ping probabilities in the weighted case is max 0; 1 , wii . r The only other major change is that the label is now ri =wi , instead simply ri . Finally, without going into details we note that the weighted packet-by-packet version is virtually identical to the corresponding version of the plain CSFQ algorithm. It is important to note that with weighted CSFQ we can only approximate islands in which each ow has the same weight at all routers in an island. That is, our algorithm cannot accommodate situations where the relative weights of ows di er from router to router within an island. However, even with this limitation, weighted CSFQ may prove a valuable mechanism in implementing di erential services, such as the one proposed in 24 . 2.4 Performance Bounds We now present the main theoretical result of the paper. For generality, this result is given for weighted CSFQ. The proof is given in 22 . Our algorithm is built around several estimation procedures, and thus is inherently inexact. One natural concern is whether a ow can purposely exploit" these inaccuracies to get more than its fair share of bandwidth. We cannot answer this question in full generality, but we can analyze a simpli ed situation where the normalized fair share rate is held xed and there is no bu ering, so the drop probabilities are precisely given by Eq. 2. In addition, we assume that when a packet arrives a fraction of that packet equal to the ow's forwarding probability is transmitted. Note that during any time interval t1 ; t2  a ow with weight w is entitled to receive at most w t2 , t1  s...
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