In this section, we answer the question: What bandwidth guarantees are realizable on a virtual link?
Recall that the statistical bandwidth guarantee achievable along a
virtual link is given by such that
,
where
represents the instantaneous bandwidth along the virtual
link, and
represents the probability with which the guarantee is
not met. The Rate Estimator module updates
once every window of
packets (
(RTT) sec) based on the feedback information received from
the next OverQoS hop.
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Across the pairs of nodes between the 19 end-hosts in our
testbed, we monitored
unique virtual links over a period of 7
working days. Figures 8(a) and (b) show the distribution
of
for
and
. We make two
observations. First, the value of
is greater than
Kbps
for more than
of the links.
of the links are
predominantly connected to broadband hosts. Second, in many cases,
is at least
of the average throughput along the
virtual link. In specific cases,
is as large as
of
the average throughput. The median value of
is
and
for
and
respectively. Figure 9 shows the variation of
as a function of
. As
increases,
we notice that the maximum value of
increases while
the minimum value decreases. The minimum decreases because we notice
self-induced losses across some of the links thereby causing
MulTCP to drastically reduce its sending rate and thereby reducing
.
Stability of : If the underlying distribution of
is
stable, the estimated value of
will roughly be a constant.
However under dynamic conditions, we need to continuously re-estimate
and flows need to renegotiate their bandwidth
reservations. For a given value of
, we estimate
using
samples of
. As an example, given
msec and
, we can calculate
based on the last
samples (representing a history of 200 seconds). In this scenario,
flows renegotiate their bandwidth requirements every few minutes.
Figure 8(c) shows the variation as a function of time
across four separate virtual links from Europe to North America. We
make two observations: First, the value of is very stable
compared to variations in the available bandwidth,
. Across these
links,
does not deviate more than
around its mean
value. Second, an on-line algorithm for estimating
based on
past history is a reasonable approach. While we set
to
be
, the actual value of
is less than the estimated
in no more than
of the cases across all four virtual links.