Queueing theory is one of my favourite secret superweapons. You can use it to back-of-the-napkin solutions out of feasibility much quicker than it'd take to simulate.

I warmly recommend Harchol-Balter: https://www.amazon.com/Performance-Modeling-Design-Computer-... It is an eminintly practical book which is written in terms of computers, goes beyond the basic M/M/1 but without being overbearing.

(The other secret superpower is statistical process control.)

Performance Modeling and Design of Computer Systems: Queueing Theory in Action https://www.amazon.com/dp/1107027500

To anyone who finds these models interesting and wants to learn a lot more - I’d highly recommend Mor Harchol-Balter’s textbook: https://www.amazon.com/Performance-Modeling-Design-Computer-... (She is currently a professor at Carnegie Mellon).