This is supplemental course information, designed to give you a fuller picture of the course and an expanded look at the topics covered. This is an unofficial document. The USC Course Catalog is the binding description of all university courses. Information such as books, materials covered, and the order of topics is subject to change. Please consult instructor for this semseter to get more upto date course information.
Catalog Data:
465 Probabilistic Methods in Computer Systems Modeling (3, Fa) Review of probability; random variables; stochastic processes; Markov chains; and simple queueing theory. Applications to program and algorithm analysis; computer systems performance and reliability modeling. Prerequisite: MATH 407 or EE 364.
Text Book:
Introduction to Probability Models, 8th edition, Seldon Ross, Academic Press.
Course Coordinator:
Konstantinos Psounis, Department of Electrical Engineering-Systems
Topics:
Basic Probability: random variables, independence, expectation
Conditioning: conditional probability and expectation
Markov Chains: discrete and continuous time
Stochastic Processes: Poisson
Queueing Theory: single and multi server M/M/. queues, networks of queues, the M/G/1 queue
Simulation: generating random variables, implementing a simulator
Course Objectives:
Probabilistic tools are among the most useful for modelling real systems and doing performance analysis.
This course is designed to provide students with the ability to understand and conduct computer systems
modelling and performance analysis. To establish the necessary background, the course starts with an
introduction to basic probability tools and concepts. It then builds up to more advance topics that
are particularly useful in modelling, such as Markov models and queueing theory. Further, the course
covers basic methods for conducting simulations.
Course Outcomes:
The students will be able to:
1. Understand random variables, moments and expectation.
2. Understand conditional probabilities and conditional expectation.
3. Understand the dynamics of discrete time Markov chains.
4. Use discrete time Markov chains to model computer systems.
5. Understand the properties and modelling usefulness of the exponential distribution and the Poisson process.
6. Learn about continuous time Markov chains.
7. Use continuous time Markov chains to model real systems.
8. Learn the fundamentals of queueing theory.
9. Learn about single and multi server queues with Poisson arrivals and exponential service requirements.
10. Learn how to analyze a network of queues with Poisson external arrivals, exponential service requirements
and independent routing. (Jackson networks)
11. Learn the basics of the M/G/1 queue.
12. Understand how to conduct simulations.
13. Apply basic probability techniques and models to analyze the performance of computer systems, and, in
particular, of networks.
Prepared by: Konstantinos Psounis Date: December 2003
