Survey of methods of stochastic operations research including reliability, Markov processes, queuing theory, and decision theory. Computer used for modeling and solving problems.
Prerequisites:
STA 301, 368, or 401, or concurrent registration in STA 401
Required topics (approximate weeks allocated):
Review of probability (1)
Markov chain models (3)
stochastic processes, Markov chains
classification of states of a Markov chain
steady-state probabilities and first passage times
absorbing states
Decision analysis (2)
decision making under uncertainty
decision making under risk: with and without experimentation
decision trees and Baye's rule
Queuing models (5)
pure birth, pure death and birth-death processes
queuing models based on birth-death processes
models involving non-exponential distributions
Optional topics (3.5)
reliability
introduction to game theory: two-person zero-sum games
To be able to apply previous knowledge of probability theory to construct stochastic models of random systems
The student can use probability distributions to represent random components of a system
The student can use the probability theory to compute event probabilities, expected values, and variances in random environments
The student can use the theoretical distributions Binomial, Poisson, Normal, and Exponential to represent random components of a system
To be able to model time dependent random phenomena as a Markov chain
The student can explain the fundamental assumptions and terminologies of a Markov chain
The student can recognize and compute state probabilities and expected passage times for ergodic Markov chains
The student can recognize and compute absorption probabilities and expected time until absorption for absorbing Markov chains
To be able to model birth-death queuing systems in steady state
The student can explain the fundamental assumptions and terminologies of birth-death queuing systems
The student can recognize and compute state probabilities, expected utilizations, expected time in the system, and expected number in the system for birth-death queuing systems with various numbers of servers, various amounts of queuing space, and various size populations
The student can recognize and perform similar computations to those listed in (3b) for a simple non birth-death queuing systems
The student can recognize and perform similar computations to those listed in (3b) for a birth-death queuing networks with and without feedback
To be able to model decisions with uncertain outcomes
The student can represent a decision problem with uncertain outcomes as a decision tree and determine the action with the best expected performance
The student can compute the expected performance improvement by obtaining additional information and perfect information
The student can apply Bayes' rule to compute posterior probabilities based on the value of the additional information
The student can model a decision maker's behavior using utility functions
To be able to deal effectively with stochastic elements in a wide variety of systems
The student can apply the fundamentals developed in Objectives 1-4 to a wide variety of application areas
The student understands how to use data to model stochastic elements of a system
Department of Computer Science and Software Engineering
