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.
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.