Syllabus ASRM 597

ASRM 597. Reading Course

Determination of course hours: The number of hours depend on the amount of work required to complete satisfactory work to succeed in the reading course.

Student Learning Outcomes

  1. Students will gain a deep understanding of their chosen topic under the guidance of a faculty instructor.
  2. Practice communicating technical information.

Text: J. Michael Harrison (1985), Brownian Motion and Stochastic Flow Systems. John Wiley & Sons.

Course description: This course will cover the theoretical foundation of Brownian motion and its applications in queuing and inventory theories.


Students will be required to report regularly to the instructor.  The oral or written reports should detail the projects the student worked on and what was learned since last meeting. Assessment will be based on students’ demonstrating understanding of the material.

Chapter 1 Brownian Motion (6 hours)

  • Wiener’s Theorem
  • Quadratic Variation and Local Time
  • Strong Markov Property
  • Brownian Martingale
  • A Joint Distribution
  • Change of Drift as Change of Measure

Chapter 2 Stochastic Models of Buffered Flow (9 hours)

  • A Simple Flow System Model
  • The One-sided Regulator
  • Finite Buffer Capacity
  • The Two-sided Regulator
  • Measuring System Performance
  • Brownian Flow Systems

Chapter 3 Further Analysis of Brownian Motion (6 hours)

  • The Backward and Forward Equation
  • Hitting Time Problems
  • Expected Discounted Costs
  • One Absorbing Barrier
  • Two Absorbing Barriers
  • More on Regulated Brownian Motion

Chapter 4 Stochastic Calculus (9 hours)

  • Ito integrals
  • Ito Formulas
  • Tanaka’s Formula and Local Time
  • Integration by Parts
  • Differential Equations for Brownian Motion

Chapter 5 Regulated Brownian Motion (3 hours)

  • Strong Markov Property
  • Applications of Ito’s formula
  • Expected discounted costs
  • Regenerative structure
  • The Steady-State Distribution
  • The case of a Single Barrier

Chapter 6 Optimal Control of Brownian Motion (6 hours)

  • Barrier Policies
  • Heuristic Derivation of the Optimal Barrier
  • Verification of Optimality
  • Cash Management

Chapter 7 Optimizing Flow System Performance (4 hours)

  • Expected Discount Cost
  • Overtime Production
  • Higher Holding Costs
  • Steady-State Characteristics
  • Average Cost Criterion

Total: 43 hours



100% Weekly reports