Courses
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Descriptions
IEMS 460-1: Stochastic Processes I

Quarter Offered

Winter : MW 11:00-12:20 ; Perry

Prerequisites

Permission of instructor

Description

This course is a core PhD course for Industrial Engineering and Operations Management 

LEARNING OBJECTIVES

  •  Students will understand the problems that can arise with measuring sets (e.g., area or volume), and the connection to the axioms of probability
  • Students will understand the need for Lebesgue integration and the connection to expectation of random variables
  • 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

  • Foundations of modern probability
  • Stochastic Processes as random elements: finite-dimensional distributions, existence of processes with a given distribution and non-uniqueness
  • The Poisson process and the Poisson random measure
  • The infinite-server queue with applications to staffing many-server systems
  • Discrete-time Markov chains
  • Continuous-time Markov chains
  • Introduction to queueing theory; in particular, Little’s law and PASTA
  • The tradeoffs between service efficiency (in terms of servers’ utilization) and quality (in terms of waiting times in queue) in single-server systems in contrast to many-server systems 

MATERIALS

Stochastic Processes, 2nd ed. by Sheldon M. Ross.

In addition, class notes are distributed