Contents Telektronikk - Telenor

As already indicated, continuous space is
not very interesting in teletraffic, but it is
sometimes used in mathematical analysis,
when traffic is considered as a diffusion
process, often with rediscretisation
as a final step. Also in intermediate analysis
stages, calculation of fictitious continuous
server groups may be used to
obtain improved accuracy. Time is most
often considered to be continuous, as the
processes studied are often defined by
random events. However, in modern digital
systems synchronous operation may
be better described in discrete time. If
nothing particular is indicated, discrete
space and continuous time is assumed.
This means that at any instant an integer
number of servers are occupied, and that
the number may change at any instant in
continuous time. In a so-called orderly
process (to be discussed later), any
change is by ±1 only.
6 Traffic variations
6.1 Telephone traffic
The traffic load on a traffic carrying system
is subject to more or less regular
variations on different time scales. In
order to understand the causes behind
such variations one has to study the natural
activity patterns of the set of traffic
sources and the resulting behaviour in
relation to the system. This behaviour is
not independent of the system response.
One can imagine a basic traffic potential
under given conditions of a well dimensioned
system and reasonable tariffs. The
system carries that potential, and it can
be said that the system feedback is weak.
If for some reason a narrow bottleneck
occurs, many call attempts fail. The
result is double: 1) some failed attempts
are repeated, thus increasing the call rate
and giving a further rise in the lost call
rate, and 2) some failed attempts lead to
abandonment, thus leading to less carried
useful traffic. (These effects will be discussed
later under repeated calls.) In general
an improved system, as sensed by
the users, and cheaper tariffs are also
feedback that tend to increase the traffic.
In this section we will assume well
dimensioned system and stable tariffs.
We assume a set (N) of traffic sources
that operate independently. This is a realistic
assumption under normal circumstances.
The service system consists of a
set of servers (n), where n is large enough
to carry the traffic demand at any time. A
time function of the number of busy
servers depicts the stochastic variation of
the carried traffic. It is a discontinuous
curve with steps of ±1 occurring at irregular
intervals, as shown in Figure 3.
An observation period T is indicated, and
it is possible to define an average traffic
Am (T). At this point it is convenient to
define a traffic volume, being the integral
under the traffic curve
� T
V (T )= r(t)dt
(1)
r(t)
t 0
o
where r(t) is the number of busy servers
(the instantaneous traffic value) at time t.
The mean traffic value is given by
V (T )
Am(T )= (2)
T
A 24-hour integration gives the total traffic
volume of that period, and hence
A mom -Poisson traffic σ 2 =m
A mid
Observation period T
Figure 3 Stochastic traffic variations over an observation period T
Busy hour
t 0 +T
n 1 +n 2
Overflow
traffic
σ 2 >m
n 1
Smoothed
traffic
σ 2