Say we have a standard queue, where entities are waiting to be processed.
- A histogram can be generated which represents the "average length of the queue".
This should be somewhat equivalent to:
- a "continuous distribution" of time-waited for all entities.
Given a bunch of entities and their waiting times, it seems fairly obvious how to generate a plot of their waiting times, and do some simple curve fitting to see a continuous distribution.
However, for some reason it is not obvious to me, how to generate a discrete plot representing the size of the queue. The x-axis would be number of items in the queue, and the y-axis would represent the time spent with the queue at that length?
Is there some algorithm that's used to depict this type of information?
If you have have the actual wait times for the $N$ items and you are looking to analyze the frequency distribution by wait time, you need to bin the wait times into intervals i.e., 0 to 5 seconds, 5 to 10 seconds etc., using a suitable interval width for your data and plot the frequency for each bin.
Also, what would help is if you could calculate the average $\mu$ and standard deviation $\sigma$ of the wait times. Then you could look at the bins in terms of number of standard deviations from the mean.
Wait times in real world generally follow a Poisson distribution. So you are likely to find the distribution to be skewed and following a Poisson model.