A brief review of the concepts of probability, random variables, and parameters; probability distributions; moments; inequalities related to probabilities; the central limit theorem; stochastic processes; the Poisson process; birth-death processes; Markov chains; an introduction to queueing theory and its fundamental concepts; Little’s Law; and M/M/1 queueing systems.

Course Objectives

To develop the ability for stochastic, logical, and mathematical thinking. To build the foundational knowledge necessary for understanding stochastic systems. To equip students with the ability to analyze and interpret simple queueing systems. To foster the ability to understand and interpret certain performance criteria of stochastic systems. To possess knowledge of classical and computationally intensive statistical methods, and to be able to perform probabilistic modeling.

Recommended or Required Reading

Arnold O. Allen.(1990) Probability, Statistics, and Queueing Theory with Computer Science Applications. (2nd Ed.), Academic Press, Boston,Sheldon M. Ross (1996) Stochastic Processes, (2nd Ed.) J. Wiley & Sons. New York

Learning Outcomes

1.The ability to understand and define random variables.

2.Gaining knowledge of stochastic processes and the ability to perform basic analyses.

3.The ability to understand queueing systems and to analyze simple queueing models.

4.The ability to compute and analyze certain performance criteria in queueing systems.

Grading

Midterm: 40%

Final: 60%