Value Distributions

To import the TrafPy generator, run:

>>> import trafpy.generator as tpg

The most simple probability distribution for random variable values is the uniform distribution, where each random variable value has an equal probability of occurring:

>>> prob_dist, rand_vars, fig = tpg.gen_uniform_val_dist(min_val=0, max_val=100, round_to_nearest=1, return_data=True, show_fig=True, num_bins=101)

Demand characteristics of real network traffic patterns are rarely uniform. However, they can often be described by certain well-defined named distributions. These named distributions are themselves characterised by just a few parameters, making them easy to reproduce.

Named distributions supported by TrafPy include the exponential distribution

>>> prob_dist, rand_vars, fig = tpg.gen_named_val_dist(dist='exponential', params={'_beta': 1.0}, return_data=True, show_fig=True, xlim=[0,10], num_bins=101)

the log-normal distribution

>>> prob_dist, rand_vars, fig = tpg.gen_named_val_dist(dist='lognormal', params={'_mu': 0, '_sigma': 1.0}, return_data=True, show_fig=True, xlim=[0,5], num_bins=10000)

the Weibull distribution

>>> prob_dist, rand_vars, fig = tpg.gen_named_val_dist(dist='weibull', params={'_alpha': 1.5, '_lambda': 1.0}, return_data=True, show_fig=True, xlim=[0,3.5], num_bins=101)

and the Pareto distribution

>>> prob_dist, rand_vars, fig = tpg.gen_named_val_dist(dist='pareto', params={'_alpha': 3.0, '_mode': 1.0}, return_data=True, show_fig=True, xlim=[0,5], num_bins=101)

However, some demand characteristics cannot be accurately described by these named distributions. Instead, they might be described by arbitrarily skewed distributions which may or may not have some amount of skewness and/or kurtosis

>>> prob_dist, rand_vars, fig = tpg.gen_skewnorm_val_dist(location=50, skew=-5, scale=10, return_data=True, show_fig=True, num_bins=15)

Note that setting skew=0 simply generates a normal distribution with standard deviation scale and mean location

>>> prob_dist, rand_vars, fig = tpg.gen_skewnorm_val_dist(location=50, skew=0, scale=10, return_data=True, show_fig=True, num_bins=15)

You can also use TrafPy to generate multimodal distributions with an arbitrary number of modes

>>> prob_dist, rand_vars, fig = tpg.gen_multimodal_val_dist(min_val=10,max_val=7000,locations=[20,4000],skews=[6,-1],scales=[150,1500],num_skew_samples=[10000,650],bg_factor=0.05,return_data=True,show_fig=True,logscale=True,xlim=[10,10000],num_bins=18)

Later in this tutorial, you will see how to visually shape a multimodal distribution using TrafPy, allowing for almost any distribution to be generated.

Once you have your value distribution, you can use it to generate as many random variable values as you like

>>> rand_vars = tpg.gen_rand_vars_from_discretised_dist(unique_vars=list(prob_dist.keys()),probabilities=list(prob_dist.values()),num_demands=1000)