To provide an in-depth examination of the theory,
methods and approaches to the analysis and design of stochastic systems
as they occur throughout physical, engineering, and human systems. The
empahsis in this graduate course is on the theoretical and
computational aspects of stochastic processes and their eventual
applications in Industrial Engineering and Operations Research.
Some of the topic to be covered include but are not limited to the
following:
- Probability Review, Moment Generating Functions, Laplace
Transforms
- Discrete Time Markov Chains (DTMC)
- Branching Processes (BP)
- First Passage and Absorbing Markov Chains (AMC)
- Markov Decision Processes (MDP)
- Exponential Distribution
- Poisson Processes (PP)
- Continuous Time Markov Chains (CTMC)
- Transient and Steady State Markov Processes
- Single-Channel Exponential Queueing Models (M/M/1)
- Birth-Death Models (BD)
- Models with General Arrival and Service Patterns
- Open and Closed Queueing Network Models
- Renewal Procceses (RP)