To complete this research-methods topic, a student is required to take both of the following IE courses or both of the following MATH courses. Note that the IE courses have IE 53600 (Stochastic Models in Operations Research I) or equivalent as a prerequisite. Note that the MATH courses have MATH 53800/STAT 53800 (Probability Theory I) and MATH 53900/STAT 53900 (Probability Theory II) or equivalent as prerequisites.

IE 53900 Stochastic Service Systems
Theory and application of models of stochastic service systems. Stationary Markov models, nonstationary Markov models, and general models. Numerical algorithms and approximation methods are emphasized.

IE 63600 Stochastic Models in Operations Research II
The continued development of mathematical models of discrete valued stochastic phenomena, with applications to queuing processes, machine repair problems and inventory policy. Poisson processes, renewal processes, semi-Markov and Markov renewal processes. Regenerative processes and renewal reward processes. Multi-dimensional birth and death queuing models.

or

MATH 63800 Stochastic Processes I (STAT 63800 is the same course)
Advanced topics in probability theory which may include stationary processes, independent increment processes, Gaussian processes; martingales, Markov processes, ergodic theory.

MATH 63900 Stochastic Processes II (STAT 63900 is the same course)
Continuation of MA 63800