Contents Telektronikk - Telenor

186
Level duration
The state sojourn time corresponds to the
time the source stays within one level.
See Figure 3.4.a for an example of one
observation of a sojourn time, TB . Hence,
from the sample output of the source, the
distribution of the state sojourn times
may be estimated, i.e.
P {TB ≤ t} = #(TB ≤ t)
#(TB)
If the sojourn time distribution is sufficiently
close to a negative exponential
distribution, i.e.
t − E(T P {TB ≤ t} ≈1 − e B )
the level may be modelled by a single
phase state. What is accepted as “sufficiently
close”, depends on modelling
accuracy and the constraints put by the
STG hardware, for instance the number
states available in a scenario discussed in
Section 4.2.2. If the sojourn time distribution
differs significantly from a negative
exponential distribution, we may
split the state into a number of phases
similar to the examples in Section 3.1.1
above.
Following this procedure, a Markov
model representing the burst level of the
source without distinct states is established.
It should also be checked for dependencies
between the sojourn times on the
various levels and the next level/state. If,
for instance, there is a positive correlation
between long sojourn times in state
C and transitions into state D (and between
shorter sojourn times and transitions
into B and A), we may include this
A B
C
D
into the phase type model. See Figure 3.5
for an example. In this case, transitions to
A and B will take place after the sojourn
time of the first phase (negative exponentially
distributed) and transition into D
after the sojourn times of both phases
(generalised Erlang-two distributed).
Other combinations of sojourn times –
transition dependencies may of course
also be constructed.
Validation
A check of whether reasonable sojourn
times and transition probabilities are
obtained or not, may be obtained by
- computing the steady state probabilities
- dividing them by the width of the
respective levels, cf. Figure 3.4.b, and
- comparing the result to the level frequency
plots.
In the above procedure, it is implicitly
assumed that the level/state changing
procedure of the source type has a
(semi-) Markov property. This may be
validated by a direct testing of the properties
of the embedded discrete time
chain [30].
The long term dependencies may also be
validated by a comparison between the
autocorrelation of samples from a source
of this type, and the autocorrelation of
the source type model. (Note that the cell
level should be smoothed.) See [22] for a
computational procedure.
3.2 Cell level modelling
The most important factors determining
the cell level behaviour of a source are:
- the processing, data retrieval and transfer
speed of the end user equipment
- the lower layer protocols, their mechanisms
and implementation
- contention in user equipment and customer
premises network, e.g. a CSMA/
CD based LAN, and
L p - length of cell pattern
IB - miniburst
interdistance
- possible traffic forming mechanisms,
see [31] for a discussion.
Based on the experiences from the cell
level modelling so far, a framework for
building cell patterns will be outlined in
this section. Focus will be on the major
influences from the various protocols in
the protocol hierarchy as well as the
other facts mentioned above. For some
source types, not utilising all protocol
levels only parts of the discussion apply.
An example is variable bitrate video
transfer presented directly to the AAL.
However, the basic approach should
apply. The parameters may be obtained
by deduction from system and protocol
descriptions, from measurements of systems
and protocols if these are available,
or by a combination of these approaches.
A cell pattern consists of a set of
minibursts, or subpatterns. These are
usually, but not necessarily, regular.
Minibursts arise from higher level protocol
data units which propagate down
through the protocol levels and result in a
short burst of cells. Figure 3.6 shows a
generic regular cell pattern with its
descriptive parameters, a 4-tuple {IC , IB ,
LB , LP }. In the following we focus on the
different parameters in the tuple, except
for the length of the pattern, LP , which is
chosen to fit the regularity described by
the other parameters as well as the design
of the STG, cf, Section 4.2.3.
3.2.1 Peak cell rate
The peak cell rate is the inverse of the
minimum inter-cell distance, i.e.
1/Min(IC ). The inter-cell distance or cell
spacing depends primarily on the implementation
of AAL (ATM Adaption
Layer). Two extremes may be identified:
- Maximum stretching, as described in
[31]. This implies that cells are spaced
as evenly as possible. The allowable
spacing will depend on the real time
requirement of the source/user. Usually,
these are so slack that cells may be
evenly spaced over an entire pattern,
L B - length of miniburst
V B - volume of miniburst
Figure 3.5 State C is split into two
phases to include sojourn time transition
IC - cell interdistance
dependencies Figure 3.6 Parameterized framework for building cell level models based on patterns