# Academics  /  Courses  /  DescriptionsIEMS 315: Stochastic Models

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### Prerequisites

IEMS 302 and Gen Eng 205-1; Co-requisite: IEMS 303

### Description

Fundamental concepts of probability theory; modeling and analysis of systems having random dynamics, and in particular, queueing systems. Homework, exams and problem-solving sessions.

• This course is a major requirement for Industrial Engineering.

LEARNING OBJECTIVES

• Students will understand why the relative-frequency view of probability cannot serve as the basis of a successful theory, and the reasons for the definition of probability via the three axioms
• Students will understand that “variance matters,” namely, the need to account for stochasticity in the analysis of systems
• Students will understand the practical need to model systems’ dynamics using the Markov property
• Students will be able to model systems as Markov chains (in discrete and continuous time)
• Students will understand the concept of steady state, and how to compute it for Markov chains in discrete and continuous time
• Students will study the basic principles of queueing theory, in particular, Little’s law, PASTA, and the tradeoffs between efficiency (in terms of servers’ utilization) and quality of service (in terms of waiting times in queue)

TOPICS

• Review of probability theory and fundamental limit theorems for sequences of random variables
• General stochastic processes (definition and in practice)
• Discrete-time Markov chains
• The Poisson process
• Continuous-time Markov chains
• Introduction to queueing theory

MATERIALS

Class notes are distributed