**CS712/812 Stochastic Modeling**

**Spring 2018**

**Instructor:** Professor Stephan Olariu

Office: E&CS 3202

Phone: 683-3915

**Course Description:**
Stochastic processes are ways of quantifying the dynamic relationships of sequences of random events. Stochastic models play
an important role in elucidating many areas of science and engineering. These models can be used to analyze the variability
inherent in biological processes, in computer science phenomena, and in the complexities of social interactions, to name just
a few. The first main objective of this course is to expose the participants to standard concepts and methods of stochastic
modeling. The second main goal of the course is to illustrate the rich diversity of applications of stochastic modeling.
The approach is hands-on, where the students will learn stochastic modeling by applying theoretical modeling concepts to a
host of problems arising in applications.

**Motivation:**
In undergraduate computer science courses, even in the most advanced ones, computer science phenomena are being looked at
either deterministically or, at best, from a simplistic ``average case'' perspective. This approach flies in the face of the
fact that virtually all phenomena underlying computer science are stochastic in nature. It follows that the student walks
away with an incomplete and often distorted understanding of many fundamental computer science concepts. And yet, the analysis
of a good many of these phenomena is within reach, assuming a reasonable exposure to probability theory, stochastic processes and
queueing theory. To the best of this instructor's knowledge, no undergraduate course in probability theory covers all the topics
above with the needs of a Modeling and Simulation graduate student in mind.
There is a huge body of knowledge concerning probability theory, stochastic processes and queueing theory. The main challenge
and stated goal is to select those topics that will equip the participants with the basic tools necessary for the stochastic
modeling of phenomena arising in computer science, engineering, economics, biology, etc.

**Intended audience:**
In an ideal world, the students taking this class should have been exposed to: advanced calculus at a suitable level and
probability theory at advanced undergraduate level. In a less-than-perfect world, the students often lack proficiency in one
or more of the above areas. With this in mind, the first part of the course (roughly, four weeks) will be devoted to a review
of relevant topics in probability theory.
While the course is intended to be mathematically correct, rigor is occasionally sacrificed on the altar of simplicity: this is
to say, proofs that rely on measure-theoretic concepts will be systematically omitted and/or replaced by intuitively
satisfying arguments.

**Material:** Tentative topical coverage

- Module-I: Review of probability theory and some important probability distributions
- Module-II: Transforms and their applications, generating functions and the Laplace transform
- Module-III: Introduction to basic stochastic processes
- Markov chains
- Poisson processes
- Birth-and-death processes
- Elementary renewal theory
- Markov processes

- Module-IV: Case studies

** Text:** The textbook used in this class is
* Introduction to Stochastic Modeling*,
by Mark A. Pinsky and Samuel Karlin, Fourth Edition, Elsevier, 2011. The material in the text will occasionally be supplemented
by material from the open literature

**Prerequisite:**
Graduate standing in Computer Science, Modeling and Simulation, Mathematics, Computer Engineering, Mechanical Engineering, etc.

**Grading Scheme:**

- Midterm Examination: 30%
- Final Examination: 30%
- Programming Project: 30%
- Class Participation: 10%

**Office Hours:** TBA

Old Dominion University is committed to ensuring equal access to all qualified students with disabilities in accordance with the Americans with Disabilities Act. The Office of Educational Accessibility (OEA) is the campus office that works with students who have disabilities to provide and/or arrange reasonable accommodations.

- If you experience a disability which will impact your ability to access any aspect of my class, please present me with an accommodation letter from OEA so that we can work together to ensure that appropriate accommodations are available to you.
- If you feel that you will experience barriers to your ability to learn and/or testing in my class but do not have an accommodation letter, please consider scheduling an appointment with OEA to determine if academic accommodations are necessary.

The Office of Educational Accessibility is located at 1021 Student Success Center and their phone number is (757)683-4655. Additional information is available at the OEA website: http://www.odu.edu/educationalaccessibility/

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