How to prove arrival rate follows Exponential Distributions?

Question

I'm studying Anylogic. I'm curious about something. Some people explain that arrival rate follows Exponential Distribution. I wanna know 'How can prove that?'

Any kind guidance from you would be very helpful and much appreciated. Thank you so much.

Answer 1

The arrival rate doesn't follow an exponential distribution, it follows a poisson distribution, so there's nothing to prove on that regard.

What follows an exponential distribution is the inter-arrival time between agents.

To prove that this thing actually follows a particular distribution, you can use one of the many distribution fitting techniques out there, my favorite and the one is the Cullen and Frey Graph. You can see an answer about it here:

https://stats.stackexchange.com/questions/333495/fitting-a-probability-distribution-and-understanding-the-cullen-and-frey-graph

You can also check the wikipedia page on distribution fitting: https://en.wikipedia.org/wiki/Probability_distribution_fitting

Have in mind that distribution fitting is kinda an art, and no technique gives you the correct distribution, but maybe a good enough approximation of a distribution. But in this case it should be quite easy.

You can't really prove that a distribution fits the data though, you can just have maybe an error estimation when you compare the distribution function with the actual data, and you can have a confidence interval for that... I'm not sure if that's what you want.

Answer 2

not exactly sure what you mean by "prove" that it is exponential... But anyway, it is not "some people" that explain that, it is actually mentioned in AnyLogic help under the "Source" topic as follows:

Rate - agents are generated at the specified arrival rate (which is equivalent to exponentially distributed interarrival time with mean = 1/rate).

What you can do is collect the interval time between arrivals and plot that distribution to see that it actually looks like an exponential distribution.

To do that:

• Create a typical DES process (e.g. source, queue, delay, sink)
• Set the arrival type to rate and specify for example 1 per hour
• Create a variable in main called "prevTime"
• Create a histogram data element called "data"
• In the "On exit" of the source write the following code:

data.add(time() - prevTime);
prevTime = time();

Look at the plot of the histogram and its mean.