Contents Telektronikk - Telenor

The internal blocking mechanism is illustrated
in Figure 30. A call generated in
stage A searches an outlet in direction x
in group C over an available set of links
in stage B. If all free links in B are opposite
busy circuits in C and vice versa, the
call is blocked, even though there are
free servers in both stages. The calling
individual (traffic source) in A competes
with a limited number in the same column
for the B-link, and the binomial distribution
is normally the natural choice.
That means that the number n of sources
in an A-column is less than or equal to
the number m of links in the B-column.
We will assume n = m. In stage C, however,
all A-stage sources contribute to the
load, and the Engset distribution would
be feasible. For simplicity Erlang will be
preferred, leading to a more conservative
dimensioning. Also the assumed independence
between stages leads to an
overestimation of blocking.
The analysis of a link system is primarily
attributed to C. Jacobæus, and a key formula
is the Palm-Jacobæus formula
H(k) =
(65)
where H(k) = P {k particular out of m circuits
are busy, irrespective of the states of
the remaining m - k circuits}. In the binomial
case (with n = m) H(k) = ak .
Internal blocking E between an A-column
and a B-column occurs when exactly k
circuits in the C-stage and the remaining
m – k (and possibly others) in the B-stage
are busy. Any value of k, 0 ≤ k ≤ m, may
occur:
E =
m�
p(i) ·
i=k
�i � k
m
k
�
�
m�
E(k) · H(m − k)
k=0
(66)
If we use H(k) and introduce the selected
distributions above in stages B and C, we
obtain the remarkably simple expression
for internal blocking (time congestion):
E = E (m,A) / E (m,A/a) (67)
where A is the offered traffic in the Ccolumn
and a is the carried traffic per
link in the B-column. Clearly we must
have a < 1, so that A/a > A, and with
m ≤ n the denominator should normally
be substantially greater than the numerator,
thus keeping E much less than 1, as it
ought to be.
m
n
Source
If the number of sources in the A-stage is
less than the number of accessible links
in the B-stage (n < m), the formula is
simply modified to
E = E (m,A) / E (n,A/a)
14. 7 Traffic shaping
B C
While the previous effects of traffic disturbance
or shaping are unintentional
results of source group or system properties,
traffic smoothing may be used intentionally
to obtain better efficiency and/or
better service quality. An unintentional
smoothing happens implicitly by means
of system limitations that lead to call
loss. Loss occurs around traffic peaks to
the effect that peaks are cut off. The
resulting smoothing leads to better utilisation
of following stages.
The most obvious smoothing mechanism
is queuing. The simplest way of queuing
happens at the traffic source, where the
traffic demands may be lined up to give
near to 100 % utilisation even on a single
server. For comparison, with random
calls and no queuing a requirement of
1 % loss will only give 1 % utilisation,
and 90 % utilisation will give 90 % loss.
If random calls arrive at a queue, the
server utilisation can be increased arbitrarily,
but only at the expense of increasing
waiting time.
Priorities can be used to even out the system
load. An early example was introduced
in the No. 1Ess computer controlled
switching system, where detection
of new calls were delayed by low priority
in order to avoid overload while calls already
in the system were being processed.
In state-of-the-art systems like ATMbased
B-ISDN various traffic shaping
A
Direction x
Figure 30 Illustration of internal blocking in a link system
k
B C
m-k m
mechanisms are employed. There are
several control levels. Traffic demand
may be held back by connection admission
control with the objectives of obtaining
the intended fairness, quality of
service and utilisation. Further shaping is
carried out within established connections
by means of service related priorities,
queuing and discarding of cells. A
major distinction has to be done between
constant bit rate (CBR) and variable bit
rate (VBR) services. Critical CBR services
are immediate dialogue services
like speech conversation. One-way entertainment
services like video and speech
transmission are not so delay-critical,
whereas delay variations have to be contained
by buffering. Less delay-critical
are most data services, even interactive
services. These often have a bursty character,
and there is much to be gained by
smoothing through buffering.
A trade-off between delay and cell loss is
common, as a CBR service may accept
high cell loss and only small delay,
whereas the opposite may apply to a
VBR service.
14.8 Repeated calls
The traffic shaping effects as discussed
so far are due to random fluctuations in
combination with system properties and
deliberate control functions. A particular
type of effects stems from system feedback
to users.
One feedback level is that which reduces
a traffic intent to a lower traffic demand,
because of low service quality expectations.
An abrupt upward change in service
quality will demonstrate an upward
swing of demand, closer to the intent
(which can never be measured).
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