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 packetbypacket 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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 Fall '10
 Eugene Ng
 Scheduling algorithm, Roundrobin scheduling, Scheduling algorithms, Ow, Fair queuing, ows

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