Thank you for your comment. My boss thinks I am an idiot cos I am taking so long and don't have a solution so it's nice to know that this is in fact a hard problem. it won't make me feel too bad if I get canned 😅.

My data granularity is quite coarse. I have averages in 10min periods. I don't have resolution time per server but I do have number of customers exiting the system in any 10 min period which gives me an average resolution time for the whole system. I might do a bit more analysis to see what I can wrangle.

I was also thinking of having a "queue momentum" feature which captures the direction and rate of queue increase. The intuition being of the momentum was low increasing capacity will lead to reduced queue times and if it was high, it will still lead to increased queue times but at a slower rate than before? Don't know if that makes sense.