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.)