Traffic Management for the Available Bit Rate (ABR) Service in ...

For example, suppose the overload is measured in successive intervals as: 2, 1,
In nity, 3, In nity, 0.5. The method previously described forgets the history in the
fourth interval, and restarts at the new value 3. Similarly in the sixth interval,
it restarts at the value 0.5. Note that this introduces dependencies between the
boundary cases and the average value of the load factor.
The second problem with this method is that the exponential average does not
give a good indication of the average value of quantities which are not additive. In
our case, the load factor is not an additive quantity. However, the number of ABR
cells received or output is additive.
The load factor is a ratio of the input rate and the ABR capacity. The correct way
to average a ratio is to nd the ratio of the average (or the sum) of the numerators
and divide it by the average (or the sum) of the denominators. That is, the average
of x 1=y 1�x 2=y 2�:::�xn=yn is (x 1 + x 2 + :::+ xn)=(y 1 + y 2 + :::+ yn).
Toaverage load factor, we need to average the input rate (numerator) and the ABR
capacity (denominator) separately. However, the input rate and the ABR capacity
are themselves ratios of cells over time. The input rate is the ratio of number of cells
input and the averaging interval. If the input rates are x 1=T 1�x 2=T 2�:::�xn=Tn, the
average input rate is ((x 1 + x 2 + :::+ xn)=n)=((T 1 + T 2 + :::+ Tn)=n). Here, xi's
are the number of ABR cells input in averaging interval i of length Ti. Similarly the
average ABR capacity is((y 1 + y 2 + :::+ yn)=n)=((T 1 + T 2 + :::+ Tn)=n), where yi's
are the maximum number of ABR cells that can be output in averaging interval i of
length Ti.
The load factor is the ratio of these two averages. Observe that each of the
quantities added is not a ratio, but a number. Exponential averaging is an extension
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