Contents Telektronikk - Telenor

74
Si:
extreme
high
n s
n s
normal
s n
0
0 20 40 60 80 100
% of circuit-groups
Figure 11 Distribution (s) of the observed skewness indices (Si)
compared with the skewness of the normal distribution function
(n) [7]
then compared with the basic variations
D. D = (2tmY/T) 1/2 , where tm = average
holding time, Y = measured intensity in
the peak-hour, T = integration period, or
the read-out period.
The peak-hour’s internal skewness was
studied by comparing its half-hour intensities.
It was seen that only in 20 % of the
circuit-groups the skewness was normal,
i.e. in measures of the basic variation
(Figure 11). The skewness was remarkably
higher in 58 % and very remarkably
higher in 22 % of the circuit-groups,
when according to the Poisson-process,
the corresponding percentages were 83.8,
15.7 and 0.5. The variations are thus
clearly higher than ideal. This can be
understood so that the offered intensity is
not constant but changing during the
peak-hour. Thus, the congestions are not
divided evenly over the full hour, but
concentrated to one of the half-hours.
Why dimension during the full hour
when the process, relevant to the quality,
happens during one half-hour only? –
This alone is a reason for reconsidering
the modelling.
In lack of more detailed data, the peakhour’s
internal distribution was studied
as the quarterhours’
relative
range W, i.e. the
difference of the
highest and lowest
quarter-hour
intensity in relation
to the basic
variation. The
observable range
W depends both
on the offered
traffic’s variations,
and the
number of circuits
if it is
dimensioned to limit the variations. In
order to distinguish these two reasons,
the circuit-groups were classified according
to their loading. The Christensen formula’s
goodness factor h is here used for
load classification:
h = (n - Y) / Y 1/2 ,
where h = the load index, n = number of
circuits, Y = average of the round’s days’
peak-hour intensities.
Here the dimensioning is called tight,
when h ≤ 1.5, but normal or loose when
h ≥ 2. Tight dimensioning is used typically
in overflowing high-congestion
first-choice circuit-groups, whereas loose
dimensioning is used in low-congestion
last-choice, and in single circuit-groups.
According to the mathematical tables of
Poissonian distribution, probabilities
10 %, 40 %, 40 %, 10 % are reached by
the range of four samples in corresponding
classes having W = < 1.0, 1.0 to 1.9,
2.0 to 3.2, and > 3.2. The numbers of circuit-groups
in the same classes are given
in Table 1.
It indicates that the circuit-groups in all
are rather well in line with the ideal
Table 1 The range in measured circuit-groups and in the Poissonian distribution,
depending on the dimensioning
Classes of range 3.2 total
Circuit-groups 19 50 26 25 120
% 6 42 22 21 100
Of them tight 19 11 0 0 30
% 63 37 0 0 100
loose 0 39 26 25 90
% 0 43 29 28 100
Poissonian % 10 40 40 10 100
ranges. However, this is only partly a
consequence of ideal offered traffic, but
caused by the combined effect of tight
dimensioning and peaky traffic, namely
- tight dimensioning limits the variations
to narrower than the Poissonian
- loose dimensioning allows the unlimited
variations of the offered traffic,
being generally larger than the Poissonian
- role of the circuit-group – first-choice
or individual or last-choice – has
minor influence on the range, as was
seen separately.
The explanation of the large range in
offered traffic is that the intensity is not
constant during a period of one hour, but
changes by more than the normal variation.
One hour is thus too long a period
for the assumption of equilibrium. – This
result is thus reverse to the English
school which has favoured the smooth
models.
When the distributions in reality differ so
much from the model in common use,
there are two choices:
- to develop the non-Poissonian models
which better describe the large variations
of the hour. The overflow dimensioning
methods give some experiences
in this way, or
- to diminish the dependability of the
model by shortening the read-out
period so far that the assumption of
constant intensity is valid, from one
hour to e.g. a quarter-hour.
A similar phenomenon was observed in
Helsinki at an early stage [1] when the
observed and the calculated congestions
were compared. The calculated congestions
were too few when the read-out
period was half-hour, less differing in
1/8, and well fitting by 1/24 hour. The
only one analysed circuit-group does not
give basis for wide conclusions, but
offers an interesting view for the modellers.
7 The day’s peaks’
concentration to the
peak-hour
The ElCo about the peak-hour concentration
is that the day’s peaks are concentrated
into the peak-hour or to its
vicinity. If the ElCo about peak-hour concentration
is valid, special attention must
be paid to the perfect peak-hour timing.