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 536 (Stochastic Models in Operations Research I) or equivalent as a prerequisite. Note that the MATH courses have MATH 538/STAT 538 (Probability Theory I) and MATH 539/STAT 539 (Probability Theory II) or equivalent as prerequisites.

IE 539 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 636 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 638 Stochastic Processes I (STAT 638 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 639 Stochastic Processes II (STAT 639 is the same course) Continuation of MA 638