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Unformatted text preview: time and length of the k packet of ow i. The
estimated rate of ow i, ri , is updated every time a new
packet is received:
k
3
rinew = 1 , e,Tik =K lik + e,Tik =K riold ; Ti
where Tik = tk , tk,1 and K is a constant. We discuss
i
i
the rationale for using the form e,Tik =K for the exponential weight in Section 2.7. In the longer version of this paper
22 we show that, under a wide range of conditions, this
estimation algorithm converges. 2.2.2 Link Fair Rate Estimation
In this section, we present an estimation algorithm for t.
To give intuition, consider again the uid model in Section 2.1 where the arrival rates are known exactly, and assume the system performs the probabilistic dropping algorithm according to Eq. 2. Then, the rate with which the
algorithm accepts packets is a function of the current estimate of the fair share rate, which we denote by bt. Letting
F bt denote this acceptance rate, we have F bt = n
X
i=1 min ri t; bt : 4 Note that F is a continuous, nondecreasing, concave, and
piecewiselinear function of b. If the link is congested At
C we choose bt to be the unique solution to F x = C .
If the link is not congested At C we take bt to be
the largest rate among the ows that traverse the link, i.e.,
bt = max1in ri t. From Eq 4 note that if we knew
the arrival rates ri t we could then compute t directly.
To avoid having to keep such per ow state, we seek instead
to implicitly compute bt by using only aggregate measurements of F and A.
We use the following heuristic algorithm with three aggregate state variables: b, the estimate for the fair share
b
b
rate; A, the estimated aggregate arrival rate; F , the estimated rate of the accepted tra c. The last two variables
b
are updated upon the arrival of each packet. For A we use
exponential averaging with a parameter e,T=K where T is
the interarrival time between the current and the previous
packet:
l
b
b
5
Anew = 1 , e,T=K T + e,T=K Aold
b
b
where Aold is the value of A be...
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This document was uploaded on 03/04/2014 for the course ENG 531 at Rice.
 Fall '10
 Eugene Ng

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