# CSE 372 Stochastic Modeling (3 credits)

Typically offered during both the fall and spring semesters.

## Catalog description:

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 301/401/501 or concurrent registration or STA 368.

## Miami Plan:

MPT - Second course in thematic sequence, CSE 3 - Mathematical & Computer Modeling .

## 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
- introduction to inventory models: basic EOQ model, single-period decision models, news vendor problems
- introduction to forecasting: moving average, simple exponential smoothing, Holt's method (trend)
- introduction to simulation
- utility theory

- Exams/Review (1)

## Course Outcomes

**1: To be able to apply previous knowledge of probability theory to construct stochastic models of random systems.**

1.1: The student can use probability distributions to represent random components of a system.

1.2: The student can use the probability theory to compute event probabilities, expected values, and variances in random environments.

1.3: The student can use the theoretical distributions Binomial, Poisson, Normal, and Exponential to represent random components of a system.

**2: To be able to model time dependent random phenomena as a Markov chain.**

2.1: The student can explain the fundamental assumptions and terminologies of a Markov chain.

2.2: The student can recognize and compute state probabilities and expected passage times for ergodic Markov chains.

2.3: The student can recognize and compute absorption probabilities and expected time until absorption for absorbing Markov chains.

**3: To be able to model birth-death queuing systems in steady state.**

3.1: The student can explain the fundamental assumptions and terminologies of birth-death queuing systems.

3.2: 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.

3.3: The student can recognize and perform similar computations to those listed in (3b) for a simple non birth-death queuing systems.

3.4: The student can recognize and perform similar computations to those listed in (3b) for a birth-death queuing networks with and without feedback.

**4: To be able to model decisions with uncertain outcomes.**

4.1: The student can represent a decision problem with uncertain outcomes as a decision tree and determine the action with the best expected performance.

4.2: The student can compute the expected performance improvement by obtaining additional information and perfect information.

4.3: The student can apply Bayes’ rule to compute posterior probabilities based on the value of the additional information.

4.4: The student can model a decision maker’s behavior using utility functions.

**5: To be able to deal effectively with stochastic elements in a wide variety of systems.**

5.1: The student can apply the fundamentals developed in Objectives 1-4 to a wide variety of application areas.

5.2: The student understands how to use data to model stochastic elements of a system.