Classes

1. Tuesday, September 3: Chapter 1. Start of Probability Review, First topic: Conditional Probability.

2. Thursday, September 5: Chapter 2. Random Variables, Distributions and Expected Values.

3. Tuesday, September 10: central limit theorem and normal approximations.

4. Thursday, September 12: our friends: transforms.

5. Tuesday, September 17: Chapter 4. Markov chains. Introduction to Markov chains.

6. Thursday, September 19: more Markov chains. application in finance.

7. Tuesday, September 24: gambler's ruin problem. Section 4.5.1.

8. Thursday, September 26: time reversible Markov chains. Section 4.8.

9. Tuesday, October 1: Review of first 2012 midterm exam.

10. Thursday, October 3: First Midterm Exam in class. Chapters 1-4 (assigned material)

11. Tuesday, October 8: trip to the post office Chapter 5. solutions Summary of key facts: all you need to know.

12. Thursday, October 10: Gone Fishing: the Poisson process. solutions

13. Tuesday, October 15: Pooh: continuous-time Markov chains Chapter 6. lecture notes on CTMC's

14. Thursday, October 17: the barbershop.

15. Tuesday, October 22: compound Poisson and other Poisson models, Section 5.4

16. Thursday, October 24: The Mt/G/infinity Queue, Section 5.4 (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 Section 1 (about 2-3 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.

17. Tuesday, October 29: reversibility and queueing network models, Sections 6 and 7.1-7.3 of the CTMC notes

18. Thursday, October 31: review of 2012 second midterm exam.

19. Tuesday, November 5. No Class, Election Day.:

20. Thursday, November 7: Second Midterm Exam in class. Chapters 5-6 (assigned material)

21. Tuesday, November 12. introduction to renewal theory, Chapter 7.

22. Thursday, November 14: the inspection paradox

23. Tuesday, November 19. alternating renewal processes and the renewal equation

24. Thursday, November 21: patterns, last topic on renewal theory.

25. Tuesday, November 26. introduction to Brownian motion, Chapter 10.

26. Thursday, November 28: holiday, Thanksgiving.

27. Tuesday, December 3. Brownian motion, Gambler's Ruin and Martingales. Supplementary Notes on Martingales.

28. Thursday, December 5: two old Brownian exam problems, last class.

29. Final Exam, Sunday, December 15. 1-4pm, Rooms 303, 833 Mudd. Covers Chapters 4-7 and 10 (assigned material).