Distribution¶
-
class
NetworkSim.simulation.tools.distribution.Distribution(seed, model=None)[source]¶ Distribution class to generate interarrival time based on the chosen distribution.
- Parameters
model (Model, optional) – The network model used for simulation, containing network constants.
seed (int, optional) – The randomisation seed. Default is
0.
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get_pareto_parameters()[source]¶ Calculation of Pareto distribution parameters.
Pareto distribution could be described by the pdf 1:
\[f(x) = \frac{ba^b}{x^{b+1}}\]where \(a\) is the position parameter and \(b\) is the shape parameter.
The Hurst parameter is given by 2:
\[H = \frac{3 - b}{2}\]- Parameters
hurst_parameter (float, optional) – The Hurst parameter for the Pareto distribution. Default is
0.82. However, this parameter is not in use currently as the average bit rate is used to calculate the shape parameter.- Returns
position_parameter (float) – The position parameter.
shape_parameter (float) – The shape parameter.
References
-
get_poisson_parameters()[source]¶ Calculation of Poisson distribution parameters,
The interarrival time distribution follows a biased exponential distribution 3:
\[ \begin{align}\begin{aligned}f_T(t) = 0 \quad t<a\\f_T(t) = b \exp(-b(t-a)) \quad t \geq a\end{aligned}\end{align} \]where \(a\geq 0\) is the position parameter and \(b>0\) is the shape parameter.
For a source with average rate \(\lambda_a\) and burst rate \(\sigma\):
\[ \begin{align}\begin{aligned}\frac{1}{\lambda_a} = a + \frac{1}{b}\\b = \frac{\sigma \lambda_a}{\sigma - \lambda_a}\end{aligned}\end{align} \]- Returns
interarrival – A list of interarrival time in ns.
- Return type
list
References
- 3
Gebali, F., 2008. Analysis of computer and communication networks. Springer Science & Business Media.
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pareto()[source]¶ Pareto distribution variate generation.
- Returns
- Return type
A new interarrival time calculated from the Pareto distribution.