Digital Signal Processing Reference
In-Depth Information
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bytes/10 ms (logscale)
FIGURE 6.3
Empirical complementary distribution function for the traffic data (logarithmic scale on both
axes). (From O. Cappe et al.,
Signal Process. Mag.,
19(3), 14-27, May 2002.
c
2002 IEEE. With
permission.)
Figure 6.2 shows traffic measured every 10 ms. The overall length of the
record is about 3 h. The three other plots in Figure 6.2 correspond, from top to
bottom, to the “aggregated” data obtained by accumulating the data counts on
increasing intervals of 100 ms, 1 s, and finally 10 s (bottom plot in Figure 6.2).
After being rescaled in time, each figure corresponds to the segment marked
with a black line in the immediately following figure. The striking feature in
Figure 6.2 is that the aggregation is not successful in smoothing out the data,
which still appears bursty in the bottom plot despite the fact that each point is
obtained as the sum of a thousand successive values of the series displayed in
the top plot of the same figure. Similar characteristics have been observed in
many different experimental setups, including both local area network (LAN)
and wide area network (WAN) data (e.g., References 9 through 11, and the
references therein). Such behavior hints at self-similarity.
The other important characteristic of the data shown in Figure 6.2 is its ex-
treme impulsiveness. Figure 6.3 illustrates this point by plotting the empirical
complementary distribution function (fraction of the data larger than a given
value) estimated from the data shown in the top plot of Figure 6.2 (that is, from
1 million 10-ms byte counts). Looking at the right end of Figure 6.3, it is clear
that the highest bit-rate one actually observes corresponds to the full capacity
of the network link, which is 1 Mbits/10 ms (which corresponds in Figure 6.3
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