The Role of Advanced Math in Teaching Performance Modeling

How should we teach performance modeling without assuming a deep mathematical background? One approach is to focus on rigorously studying relatively simple stochastic models that do not require too much math background. But this may leave students underprepared to reason about systems in practice. They have multiple servers, bursty arrivals, heavy tails, and other features that demand more complex stochastic models. Reasoning about these phenomena calls for advanced tools from performance modeling theory, but rigorously learning such tools requires more math background than many computer science and engineering students have.