Contents Telektronikk - Telenor

cell level is encompassed in the Composite
Source Model by a repetitive cell pattern
associated with each state. See Section
2.4.2.
2.4 The composite source
model
As indicated in the section above, the
activities of a source type are modelled
by state diagrams and generation patterns.
A more thorough presentation and
discussion of the model is found in [21].
The properties of this model is studied
in [22].
In the first subsection the source types
are modelled. A source type may be
regarded as the application of a specific
service, e.g. voice telephony or file transfer.
In Section 2.4.4 it is shown how a
number of individual and independent
sources with a behaviour defined by each
of the source types may be included in a
composite source model.
Before proceeding to the description of
the composite source model, note that the
above discussion may be summarised by
the requirements for the model listed in
the box High level requirements for an
ATM traffic load generator.
2.4.1 State models
The activities on the dialogue- and burst
levels are mostly driven by human activity,
events in the environment of the system,
composition of a number of events
influencing the communication, etc. This
forms a stochastic process. Hence, the
dialogue and burst levels of a source type
are modelled by a finite state machine
(state model). Its behaviour is that of a
finite state continuous time Markov process
[23]. In its simplest form, each
activity is represented by a single state,
giving a negative exponentially distributed
sojourn time of this activity.
However, the sojourn time of an activity
cannot always be properly modelled by a
negative exponential distribution.
Furthermore, it cannot always be modelled
as independent of the previous
state/activity. To handle non-negative
a) b)
λi Figure 2.10 Examples of cell generation patterns
a) Equidistant cell interarrivals
b) Periodic bursts
L
exponential distributions, such activities
are modelled by groups of states, which
may have Coxian, Erlang, hyper-exponential
or general phase type distributed
sojourn times [2]. Dependencies may be
introduced by letting the entry probabilities
of a group be dependent on the previous
state. See Figure 2.9 for an example.
In the figure the “large task” has a nonexponential
sojourn time when it starts
after the source has been idle. Entered
from above, it has a negative exponential
sojourn time distribution.
Formally, the activity on the burst and
dialogue level of source type k is modelled
by a Markov process with transition
matrix Ω (k) . Since it is more descriptive
we have used the transition probabilities
p (k)
ij and the state sojourn times Ti (k) in
the model definitions, i.e.
T j
Finish
j
T p
1 j1
Small
task
p
1
01
λ j
L
p 10
T 0
Idle
0
p ij
p 01
p 0i+1
λ j
λ 1
λ 0
Large
task
T i
i
T i+1
i+1
Figure 2.9 Generalized example of a
source type model
Ω
(2)
a repetitive behaviour. In the generator
we have two kinds of patterns:
- ordinary, with a length 1024 LB 4096 cells with a default value 2048. A
2.4.2 Patterns
pattern of the default length with one
cell roughly corresponds to a payload
Cell generation patterns model the cell transfer rate of 64 kbit/s on a
stream resulting from the information 155 Mbit/s link. Most source types and
transfer associated with each state. This states may be modelled with ordinary
stream is formed by the terminal and/or patterns
end system. Note that the parts of the
system performing these tasks are rather
deterministic “machinery”. Hence, deterministic
models of this activity suffice.
Each state has a pattern λ associated with
- long patterns, with a length n ⋅ LB n =
2, 3, ..., 32. These are used to model
longer cycles, for instance video
frames.
it, see Figure 2.9. The pattern is a binary 2.4.3 A simple source type model
vector where 1 corresponds to the gener-
example
ation of a cell and 0 a cell length gap. As
a trade off between modelling power and
implementation we let this pattern be of
constant length L and cells are generated
cyclically according to this pattern as
long as the source is in the corresponding
state. Figure 2.13 gives an illustration of
two patterns.
To illustrate the model elements introduced
above, a simple example is regarded.
In Figure 2.11 a human user interacts
with a high performance computer via an
ATM network. For every user action, the
computer transfers in average 40.8 kilobytes.
For simplicity assume that the
number of bytes in each transfer is nega-
Constant length patterns give a reasontive exponentially distributed. The link
able model of the behaviour of the termi- rate is 150 Mbit/s and the effective rate
nal and end system since this usually has out of the computer during a burst is
(k) �
= ω (k)
�
ij
ω (k)
p(k) ij
ij =
T (k)
i ≤ ≤
λ i
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