I have an classical service random distribution where customers appear after random period of time. I have a multiple services working in different geo regions. Some very local - one city, some global.
The problem is the night time: there is 10x less activity during nights: (night time in blue)
I can not "hardcode" that fluctuations because they are different from service to service because of time zone shift and different geo area - whole US would be working in 3 TZs and whole Norway would be only one so "wave" function will have a different fall/raise angle and ratio of low/high activity time frame.
My ultimate goal is to calculate probability of "service down" vs "no customers" at the given moment. Example: If no customers completed their purchases from 2 hours ago till now, what are the chances that the service is down vs no one really came to buy in 2 hours? Practically no purchase in 2 hours during day is 99% chance that service is down but not during night and not for services with very low use. You need to wait longer or simply ignore service monitoring during predicted low traffic period.
How can I adjust my distribution to those daily fluctuations?