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

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