As identical conditions are commonly quite dif-
ficult to achieve, continuityis frequently used.
Then a methodology for a given metric exhibits
continuity if, for small variations in conditions
(δ), the variation in the measurements are small
(ε). That is, for every positive ε, there exists a
positive δsuch that if two sets of conditions are
within δof each other, the resulting measure-
ments will be within εof each other. A metric
that has at least one method exhibiting continu-
ity is said itself to exhibit continuity.Some examples of measurement methods are:- Direct measurement of a performance metric
using injected test traffic. Example: measure-
ment of the round-trip delay of an IP packet of
a given size over a given route at a given time. - Projection of a metric from lower-level mea-
surements. Example: given accurate measure-
ments of propagation delay and bandwidth for
each step along a path, projection of the com-
plete delay for the path seen by an IP packet
of a given size. - Estimation of a constituent metric from a set
of more aggregated measurements. Example:
given accurate measurements of delay for
given one-hop path for IP packets of different
sizes, estimation of propagation delay of the
link of that one-hop path. - Estimation of a given metric at one time from
a set of related metric at other times. Example:
given an accurate measurement of flow capac-
ity at a past time, together with a set of accu-
rate delay measurements for that past time and
the current time, and given a model of flow
dynamics, estimate the flow capacity that
would be observed at the current time.
A measurement method is said to be conserva-
tive in case the act of measuring does not mod-ify, or has little impact on the value of the per-
formance metric the method is to measure.When a metric is defined purely in terms of
other metrics, it is called a derived metric.A metric can be composed either in a spatial
sense or in a temporal sense. The former refers
to a case when a metric for a path can be found
by considering metrics for subpaths composing
the path. The temporal sense refers to a case
when a metric for a path at a given time is
related to the metric for the path at other in-
stances in time.Related to measuring, three notions can be used
(see Figure 17):- Singleton metric – a metric that is atomic in a
sense (e.g. a single observation); - Sample metric – metrics derived from a given
singleton metric by taking a number of dis-
tinct instances together; - Statistical metric – metrics defined from a
sample metric by computing some statistics of
the values defined by the singleton metric on
the sample (e.g. mean value of a sample).
A way of collecting samples is to undertake
measurements separated by certain amounts of
time. The time instants can be separated with
intervals that are found by sampling from a func-
tion, say G(t). If G(t) is a deterministic function,
periodic sampling will occur. One major draw-
back of period sampling is that any periodicity
of the traffic flow to be measured may not be
easily detected. Therefore, other distribution
functions are commonly suggested, like Poisson
and geometric.In [ID_temeas] traffic measurements is inter-
preted as characterising a flow of IP packets
from one point to another. Typical characteris-
tics are (see also [Vike01]):- Throughput; being a measure of the amount of
data passed between two end points. This is
commonly given by bits per second or packets
per second. In some cases a 5 minute interval
is used, allowing for a certain averaging effect
at the same time as a so-called active traffic
measurement management can be supported.
Several values can be given, like mean and
95 % percentile. - Loss; the loss ratio gives the amount of data
not arriving at the far end point divided by the
amount of data entering the near end point.
Again, measurement interval and ways of
Figure 17 Notion of metrics statistical
metric
sample
metricsingleton
metric