Custom Discrete PDFs for Service Times¶

ASQ allows users to define their own discrete service time distributions. An example distribution may look like this:

P(X) 0.1 0.1 0.3 0.2 0.2 0.1

X 9.5 10.2 10.6 10.9 11.7 12.1

In order to define this probability density function, it must be given a name. Let’s call it my_special_distribution_01.

In order to implement this in the parameters dictionary, simply state that that class and node’s service distribution is Custom, and the name the distribution as a parameter:

'Service_rates':{'Class 0':[['Custom', 'my_special_distribution_01'], ['Exponential', 0.1]], 'Class 1':[['Exponential', 0.3], ['Exponential', 0.1]]}

In the parameters.yml file, under Serivce_rates, for the given class and node enter Custom and the name of the distribution below it. An example is shown:

Service_rates:
  Class 0:
  - - Custom
    - my_special_distribution_01
  - - Exponential
    - 0.1
  Class 1:
  - - Exponential
    - 0.3
  - - Exponential
    - 0.1

This tells ASQ that at Node 1 all Class 0 customers will have their service time drawn from the custom distribution my_special_distribution_01. This distribution hasn’t been defined yet.

To define the distribution, add the following to your parameters dictionary:

'my_special_distribution':[[0.1, 9.5], [0.1, 10.2], [0.3, 10.6], [0.2, 10.9], [0.2, 11.7], [0.2, 12.1]]

To define the distribution in the parameters.yml file, add the following lines to the end:

my_special_distribution_01:
  - - 0.1
    - 9.5
  - - 0.1
    - 10.2
  - - 0.3
    - 10.6
  - - 0.2
    - 10.9
  - - 0.2
    - 11.7
  - - 0.1
    - 12.1

Here we are saying that the value 9.5 will be sampled with probability 0.1, the value 10.2 will be samples with probability 0.1, etc. This fully defines the custom discrete PDF.

Note:

For each distribution, probabilities must sum to 1.
You may add as many custom probability distributions as you like.
Service times are sampled from the custom probability distribution, even though they are placed under the heading Service_rates.