# IE 515: Stochastic Process Modeling

### Catalog Description:

IE 515 - Stochastic Process Modeling - An introduction to the use of stochastic processes in the modeling of physical and natural systems. Use of generating functions, conditional probability and expectation, Poisson processes, random walk models, Markov chains, branching processes, Markov processes, and queuing processes in an applied setting. Requires an elementary knowledge of calculus-based probability and statistics (e.g., IE 311) as well as knowledge of differential equations (e.g. MATH 392). (3 cr.)

### Expanded Course Description

A stochastic process is a mathematical model that can represent the behavior of complicated systems in very realistic ways. In practice, these models are constructed by putting together simple elements in a systematic way, allowing one to infer the behavior of the whole from that of its parts. Although there are applications of this technique in virtually every form of applied science, from agriculture, to medicine, to all sorts of engineering, this offering focuses primarily on those applications of special interest to engineers. These topics include:

• The distribution of such things as
• errors in communictions systems
• defects in a manufactured product
• insects or weeds in a field
• the arrivals of customers, shipments, ect.
• The reliability of machines and complicated systems
• The availability of machines in a system
• How behavior changes over time
• How to intelligently guess how a system might work
• How to interpret statements from suppliers and vendors.

To effeicently and effectively discuss these topics, I assume that you have had a calculus based course in probability and statistics (IE 311, or equivalent) and engineering mathematics through differential equations (MATH 392). While the approach is advanced and you will have to deal with interesting mathematics, the emphasis is on knowing (rather than mathematically proving) results. To this end, we will use MatLab heavily to:

• Facilitate matrix mathematics and visualizing data. You will use this as a basic tool to reduce the number of hand calculations you will need to do.
• As a simulation tool. You will execute pre-written simulation programs and will not be expected to write any.
• To analize output data and view the stochastic behavior of these systems directly so that you can appreciate better what the numbers are trying to tell you.

No pre-knowledge of either software is presumed, though experience in MatLab, or a similar package, would be helpful. MatLab is available in the IE computer lab.

### Details:

 Instructor: John Mullen, Tel:(505)646-2958, email: jomullen@nmsu.edu Text: Elements of Applied Stochastic Processes, 3rd Ed., by U. N. Bhat and G. K. Miller. 2002. ISBN: 0-471-41442-5 Computer: Web-CT Site: https://salsa.nmsu.edu/ MatLab

Revision Date: December 15, 2005 by jpm.