Classes

1. Tuesday, September 4: Chapter 1. Start of Probability Review, First topic: Conditional Probability.

2. Thursday, September 6: Chapter 2. Random Variables, Distributions and Expected Values.

3. Tuesday, September 11: central limit theorem and normal approximations.

4. Thursday, September 13: our friends: transforms.

5. Tuesday, September 18: Chapter 4. Markov chains. Markov mouse.

6. Thursday, September 20: more Markov chains. An example from finance.

7. Tuesday, September 25: Even more Markov chains. Chapter 4.

8. Thursday, September 27: Section 4.8. time reversible Markov chains.

9. Tuesday, October 2: Review.

   Thursday, October 4: FIRST MIDTERM EXAM, Covers Chapters 1-4 (assigned material). In class, open book, but only the course textbook and one sheet of notes.

10. Tuesday, October 9: Chapter 5. Trip to the Post Office, the exponential distribution. solutions. All you need to know.

11. Thursday, October 11: Gone Fishing. the Poisson process. solutions.

12. Tuesday, October 16: Chapter 6. continuous-time Markov chains. Lecture Notes on CTMC's.

13. Thursday, October 18: birth-and death processes.

14. Tuesday, October 23: Chapter 5 again. compound Poisson process.

15. Thursday, October 25: The Mt/G/infty Queue (nonhomogeneous Poisson processes, Poisson random measures) and engineering applications: staffing service systems in face of time-varying demand. Also see Examples 5.18 and 5.25 in the textbook.

    The class discussion draws on \S 1 (3 pages) of: The Physics of The Mt/G/infty Queue by Steven G. Eick, William A. Massey and Ward Whitt, Operations Research, vol. 41, No. 4, 1993, pp. 731-742.

    Supplementary papers:

    • Mt/G/infty Queues with Sinusoidal Arrival Rates by Steven G. Eick, William A. Massey and Ward Whitt, Management Science, vol. 39, No. 2, 1993, pp. 241-252.

    • Server Staffing to Meet Time-Varying Demand by Otis B. Jennings, Avishai Mandelbaum, William A. Massey and Ward Whitt, Management Science, vol. 42, No. 10, 1996, pp. 1383-1394.

16. Tuesday, October 30: NO CLASS: Hurricane Sandy. Chapter 6 again. The structure of CTMC's. Reading Assignment

17. Thursday, November 1: Reversibility and Networks of Queues. Section 6 of the CTMC lecture notes.

18. Tuesday, November 6: NO CLASS. Election Day.

19. Thursday, November 8: SECOND MIDTERM EXAM: Chapters 5 and 6, Exponential Distribution, Poisson Process and Continuous-Time Markov Chains. In class, closed book. (Change from before.)

20. Tuesday, November 13: introduction to renewal processes and renewal reward processes. Chapter 7.

21. Thursday, November 15: the inspection paradox: the excess and the age..

22. Tuesday, November 20: Review: Discussion of the second midterm exam.

23. Thursday, November 22: NO CLASS. THANKSGIVING.

24. Tuesday, November 27: patterns. Sections 3.6.4 and 7.9. This is the end of our discussion of renewal processes. Here is optional extra material on renewal processes, not to be covered on the final exam.

25. Thursday, November 29: Introduction to Brownian motion. Chapter 10.

26. Tuesday, December 4: Brownian motion and martingales, Chapter 10. Supplementary notes on martingales..

27. Thursday, December 6: Last Class: Oatpower, Inc.. Optional: martingales and gambling.

28. Final Exam, Sunday, December 16. Covers Chapters 4-7 and 10 (assigned material).