Contents Telektronikk - Telenor

3.1 Measured results
Initial tests showed unacceptable values
for many of the above measurements.
After having made some simple measurements
with an Ohmmeter, insufficient
grounding of the equipment was found to
be the cause. This greatly increased the
performance, but in order to achieve the
results given above the synchronisation
set-up as explained in section 1.5, “The
test set-up” was necessary.
Due to company policy detailed information
about the measured values is not
given in this document. What can be said
is that all of the performance requirements
detailed in the previous chapter
were met.
For many of the measurement intervals
where CLR, CER and CMR were measured,
not a single erroneous event was
recorded.
4 Validity of tests and
test results
All of the tests outlined in the paper were
based on requirements by network operators.
The interfaces used, bandwidth allocated
during test periods, duration of test
period, and the desired results were specified
a priori by network operators. How
to obtain the values for each measurement
were specified by the test group
where the tests were performed.
Much can be said about the validity of
each test, and there is little doubt that
improvements to the tests outlined are
possible. Test equipment is constantly
becoming more advanced, as is the
equipment it is being designed to test.
These tests were made with the equipment
available at the time of testing.
The duration of the measurements is also
a subject for discussion. When attempting
to record rare events such as the
CLR, CER and CMR, months or even
years may be necessary. All we can do in
the time frame available is make a estimate
which will be correct with a certain
probability. This issue and some other
areas which may be subject to improvement
are outlined in the following section.
4.1 Validity of the test set-up
As previously stated, due to several reasons
the tests outlined in this report were
to be kept simple. Firstly, limitations in
both the test equipment and the system
under test (for simplicity only three
switch interfaces were used) presented a
finite number of test configuration possibilities.
It was stated that 80 % Bernoulli background
traffic was to be present in the
switch during the measurement periods.
Bernoulli traffic should have been present
on all switch interfaces simultaneously,
though whether this would have
had any impact on the measurement
results is doubtful.
Secondly, with the short time available
for performing each test and the need to
perform each test a number of times,
simplicity was essential.
4.2 Validity of long measurements
A very important question which has
arisen during the initial stages of these
tests is; “What measurement duration is
necessary in order to be able to estimate
the frequency of rare events, such as the
CLR, with reasonable accuracy”. Though
requirements on the duration of each test
were given by network operators, the following
section outlines some of the
thoughts around this issue.
4.2.1 Rare events and point processes
Let us assume that during some (long)
experiment a number of (rare) events are
observed and counted. The process of
events is described by the mathematical
term point process, and a point process
can be described in two ways; either by
the interval representation or by the
counting representation. In the interval
representation, track is kept of all interarrival
times, and this gives in some
sense a microscopic and very detailed
view of the process. In the counting representation,
a measurement interval is
chosen and the number of events in this
interval is studied. This yields in some
sense a more macroscopic view of the
process.
A basic objective of the experiment is to
estimate the rate (or the probability) of
rare events. The chances of doing this is
very dependent on the a priori knowledge
we have of the process.
If the process is known, more can be
said. If the process under study is a Poisson
process with rate λ, and we take a
measurement interval of length T then
the mean number of events will be λT
and the standard deviation will be √λT.
This implies that with a measurement
period of 100 times the expected time
between events we will be able to say
that the number of events will be between
80 and 120 with approximately
95 % probability. If the measurement
period is only 4 times the expected time
between events there will be no events at
all with 2 % probability and with 95 %
probability there will be between 1 and 8
events, i.e. we have no accurate estimation
of the rate.
If the underlying process is renewal (the
same as Poisson except that the interarrival
time between events is arbitrary
and not exponential), then the more variance
the interarrival time distribution
has, the less can be said. For example, if
the variance is 4 times the case for the
Poisson process the measurement period
of 100 expected interarrival times will
give a 95 % confidence interval of 60 to
140 events.
As this small example shows, the variance
of the underlying process plays a
significant role on the time a measurement
must run before a given accuracy of
the expected rate of rare events can be
given.
If the process is unknown things are even
worse, because it is very unlikely that the
process of the rare events are known in
advance. The cell loss process in ATM
switch buffers is not well understood and
depends very much on the traffic which
is even less understood.
One way to attack the problem is to run a
number M (at least 10) experiments and
try to arrange the experiments such that
they are independent of each other. If we
let Xi denote the number of events in
experiment i, then we have the following
estimates of the mean and variance
X = 1
M
S =
M�
i=1
1
M − 1
Xi
M�
(Xi − X) 2
i=1
Since the Xi ’s are independent we may
approximate their sum by a normal distribution
and obtain quantiles from that.
This method of course has the problem
that the variance is also only an estimate,
and for processes with correlation in time
the uncertainty in the variance estimate
may be significant. The interested reader
is recommended to see [12].
4.2.2 Rare events in the test
measurements
As explained previously, the bandwidth
of the test traffic during the CLR, CER
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