Model Calibration based on Queue Length Distribution in AnyLogic

Question

I have come across a quite complex scenario. I have actual data of the following:

1. Queue length distribution
2. Queue waiting time distribution
3. Distribution of the number of agents arriving every day (but not their pattern of arrival throughout the day)

The process can be assumed as a simple "source > queue > delay > sink"

Is there a way to find an arrival rate and a delay time distribution to match the available actual data? I understand that mathematically there might be many solutions to such a problem. But is there a way at all to approach this situation in AnyLogic?

I managed to meet the average queue length and average waiting time but as a distributions, the queue length and queue waiting time are not close to the actual data set.

Answer 1

This is a parameter calibration problem, in which your parameters are the lambdas of your poisson arrival rate for each hour of the day or so, and the parameters of a triangular distribution for your waiting times (delay).

The arrival rates are always poisson, so no need to have a debate on that. When you develop a model, when you don't know what your distribution is or you don't have data, you always use a triangular distribution.

With the parameter calibration you want to minimize the error between your data and your model. The function you want to minimize depends on the distribution you have on your data.

To know what is the distribution of your data, you can use a distribution fitting technique such as cullen and frey graph... but it seems that you already have the distribution