Stochastic Processes

IE 521 is about modeling systems that evolve randomly over time — the mathematical machinery (Poisson, Markov, renewal, semi-Markov processes) you need when "what happens next" depends on chance and history rather than a deterministic rule. Expect weekly problem sets that are heavy on derivations: setting up Kolmogorov equations, computing limiting distributions, applying Wald's identity, and working out steady-state behavior of birth-death and queueing models. It assumes a solid probability background and serves as the analytical foundation for later work in queueing, inventory, reliability, and simulation, which is why it's a near-universal first-year requirement for IE graduate students.