M/M/1 queue theory thoughts in monitoring with integration on statusdroid.
Naive idea is to parse your nginx/apache access logs, presume Poisson distribution (it is very strong assumption) and count basic values from M/M/1 queue thoery.
Example of output:
python3 mmone.py -c config.yml
Description Value
------------------------------------------- ---------------------
Mu - intensity of serve per minute: 233.05968175906384
Lambda - insensity of messages per minute: 13.383333333333333
Rho expected occupacy per minute: 0.057424489865943305
System is: stable
Expected count of tasks in the queue: 0.0035100445094311218
Expected count of tasks in system: 0.060934534375374425
Expected time to serve the task: 0.004290746440792775
Expected time to the task to wait in queue: 0.0002622698263584898
Expected time of task in whole system: 0.0045530162671512655
Math related stuff:
You can get some stats from api by calling it with page guid. That is stated on status page, e.g.:
curl 'https://www.statusdroid.com/api/statistics/response-time/?range_hours=24&user_website_guid=551bf0d2-88aa-430b-a35a-589ecf9409c0®ion=europe'