Resource Management within a Bundle

Table 1: OverQoS Notation table

$b$	Maximum sending rate on a virtual link
$c$	CLVL available/ aggregate bandwidth
$q$	CLVL target loss rate / statistical
	bound on the CLVL loss-rate
$r$	CLVL redundancy factor
$c_{min}$	Minimum statistical bandwidth guarantee
$u$	Probability of not meeting the
	bandwidth guarantee $c_{min}$

The CLVL abstraction provides the bundle an available bandwidth, $c$, which varies with time and guarantees the entire bundle a target loss rate, $q$. If the traffic arrival rate of the bundle is larger than $c$, the extra traffic is dropped at the entry overlay node. The overlay node can employ any QoS scheduling discipline to distribute $c$ and the losses across the flows in the bundle. In particular, in a Diffserv-like model, if every packet is associated with a priority, then the overlay node can use these priorities to preferentially drop packets and allocate bandwidth to different flows.

Figure: The cumulative distribution of $c$ across three separate CLVLs is measured on Jan 20, 2003 by transmitting 1,500,000 packets over each virtual link(each with 250 bytes payload). The intersection point between $u=0.01$ and the CDF curves represent the values of $c_{min}$ along the three links.

While in general the available bandwidth, $c$, of a CLVL bundle varies with time, it might be possible to statistically bound the minimum bandwidth of the bundle to offer bandwidth guarantees to a fraction of OverQoS traffic. Given a small probability value, $u$, one can capture the variations of the available bandwidth on a CLVL using a distribution and determine a value $c_{min}$ such that the probability, $P(c<c_{min}) = u$ where $u$ represents the probability of not meeting the bandwidth guarantee, $c_{min}$. If the corresponding $c_{min}$ is a significant fraction of $c$, then OverQoS can provide statistical bandwidth guarantees by allocating bandwidth to flows within a CLVL as long as the total allocated bandwidth is less than $c_{min}$. Table 1 tabulates all the variables we use in expressing the properties of a CLVL.

In practice, we notice that the value of $c_{min}$ across overlay links can be reasonably high implying that OverQoS can indeed be used to provide meaningful statistical bandwidth guarantees to applications. Figure 2 shows the distribution of $c$ for three different overlay links traversing international links and broadband networks: Lulea (Sweden)-Korea, Mazu (Boston)- Cable Modem (SF), Netherlands-Intel (SF). The values of $c_{min}$ across these links to provide a $u=0.01$ guarantee are 160 Kbps, 420 Kbps, and 269 Kbps respectively. Statistical bandwidth guarantees can be provided only to a subset of the OverQoS flows, potentially at the expense of other flows. Flows requiring guarantees should be given a higher priority over other flows at an OverQoS node. The remaining bandwidth $c{-}c_{min}$ is distributed among the other flows.