Contents Telektronikk - Telenor

cess a cell is arriving (being generated) in
a cell slot with constant probability p.
Cell arrivals/generations are independent
of previous cell arrivals/generations. This
corresponds to geometrically, identical
and independently distributed cell interarrivals
with mean of 1/p cell periods.
This model is popular due to its mathematical
tractability and is widely used.
There is, however, no physically based
motivation for why a cell stream should
have this characteristic. A somewhat
more sophisticated model is shown in
Figure 2.5. It generates geometrically,
identically and independently distributed
burst of consecutive cells with mean 1/q
and similar gaps with mean 1/p. Also this
model is rather vaguely motivated and
cannot be used to properly characterise
ATM source types. It is seen that it degenerates
to the Bernoulli process when
1-q = p.
A class of processes with far better capabilities
to model the characteristics of
ATM traffic is the DMAP (Discrete-Time
Markovian Arrival Process), introduced
by Blondia [11]. However, since both cell
and burst level behaviour of the source
(see Section 2.3) is captured in a single
level model, the number of states will
become immensely large for source with
a non-trivial behaviour at both layers.
A special class of source models which
also should be mentioned is the deterministic
source models, i.e. the cell from
a source has always the same interarrival
distance. See Figure 2.3.b. This class is
used to model constant bitrate (CBR)
sources, and it is the phases between the
cell arrivals from the different sources
which determine buffering delays and
possible cell losses in the system. See for
instance [12].
2.1.2 Time series
Models based on time series have been
given most attention in the modelling of
variable bitrate coded video sources. The
information flow [bits/time unit] from a
source may be modelled as a time series,
where, for instance, the expected number
of bits in a video frame is determined by
the number of bits in the previous
frames. As an example regard the following
VBR video model from [13] where
Tn is the number of bits per frame in the
n’th frame and
Tn = Max(0, Xn + Yn + Zn ) (1)
where
Xn = c1Xn-1 + An (Long term correlation)
Yn = c2Yn-1 + Bn (Short term correlation)
Zn = KnCn (Scene changes)
The quantities An , Bn and Cn are independently
and normally distributed random
variables with different mean and
variances, c1 and c2 are constants determining
the long and short term correlation
of the video signal and Kn is a random
variable modelling the occurrence
of scene changes which results in a temporarily
very large bitrate. Another simple
video frame oriented model, bridging
the gap between the state oriented models
outlined in Section 2.1.1 and the time
series models, is the discrete autoregressive
(DAR) model [14].
The above mentioned models assume
that the cells generated from one frame
are evenly distributed over the frame
period and that all frames are coded similarly.
Time series models including lineand
frame-recorrelation from an immediate
transmission of cells are proposed
[15], as well as a model taking into
account the lower information rate of the
intermediate frames in MPEG encoded
video [16].
2.1.3 Self similar stochastic
processes
Rather recently, analyses of measurements
of data traffic indicate that this
type of traffic has self similar stochastic
properties. By this is meant that the
statistics of the process, e.g. the variance
and autocorrelation, are the same, irrespective
of the time scale regarded. The
traffic process (packets per time unit)
looks similar whether it is regarded per
second, minute, hour, or day as illustrated
in Figure 2.6. For details see [17, 18]
or [19.]
Our current hypothesis is that this effect
may also be captured by the multilevel
activity modelling outlined in Section
2.3. Simulation and analytical studies
carried out seem to confirm this hypothesis.
2.2 Three approaches to ATM
load generation
Three conceptually very different approaches
to the generation of ATM traffic
for measurement and simulation may be
identified. These are dealt with in the following
subsections.
Packets/hour
Packets/second
Hours
Seconds
Figure 2.6 Illustration of a self similar
stochastic process
2.2.1 Replay of a cell sequence
This is a storage based generation, where
a pre-recorded or predefined cell sequence
is (repeatedly) reproduced during
a measurement. Due to its determinism
and simplicity, this approach is suited for
initial functional testing. It is, however,
unsuitable for validation of traffic handling
capabilities since limited length cell
sequences will be available with a
reasonable memory. (A complete
155 Mbit/s ATM cell stream requires
19 Mbytes/s.)
2.2.2 Generation according to
a class of stochastic
processes
This may be regarded as a black box
approach. A cell stream is generated
according to “some” class of stochastic
process, for instance a renewal process or
(multiple) on-off sources. The parameters
of the stochastic process are chosen to fit
some of the statistics of a source or a
multiplex of sources.
In this case it is possible to generate long
independent sequences, but it still
remains open how well real traffic is represented.
The quality of the traffic generated
will depend on how well the chosen
class of statistics fit the actual process. If
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