Classes

1. Tuesday, January 20: Problems from Chapter 1. Probability Review. Chapter 1. First topic: Conditional Probability.

2. Thursday, January 22: A large number of coin tosses. More Probability Review. Section 2.7. The central limit theorem.

3. Tuesday, January 27: Grundlagen (Foundations). Even More Probability Review: Chapters 2 & 3: Random variables.

4. Thursday, January 29: Our friends. Final Probability Review. Section 2.6: Moment generating functions and other transforms.

5. Tuesday, February 3: Markov Mouse. Chapter 4. Introduction to Markov chains.

6. Thursday, February 5: more Markov chains., Still Chapter 4.

7. Tuesday, February 10: even more Markov chains. A Markov chain example in finance.

8. Thursday, February 12: reversibility. Section 4.8.

9. Tuesday, February 17: Review of 2007 first midterm exam. Chapter 4: End of discrete-time Markov chains.

10. Thursday, February 19: FIRST MIDTERM EXAM This covers Chapters 1-4. Open book.

11. Tuesday, February 24: The Magic Distribution. Chapter 5. The exponential Distribution. A concise summary of basic properties of the exponential distribution and the Poisson process.

12. Thursday, February 26: Gone Fishing. Chapter 5. Introduction to the Poisson process. Solutions.

13. Tuesday, March 3: Pooh and the broken copiers. Introduction to continuous-time Markov chains. Chapter 6. Extra Lecture Notes on CTMCs.

14. Thursday, March 5: The DJ Barbershop. Birth-and-death processes, special CTMC's.

15. Tuesday, March 10: Staffing a service system. Nonhomogeneous Poisson process, staffing and the infinite-server queue, Chapter 5.
    • 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. See Figure 1. Look at Section 1 up to Remark 1 (about one full journal page).

    • 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. (Optional: an application of the Mt/G/infty queue to staffing)

16. Thursday, March 12: the infinite-server queue

17. MARCH 16-20: SPRING BREAK

18. Tuesday, March 24: reversibility and networks of queues

19. Thursday, March 26: review of the 2007 midterm

20. Tuesday, March 31: review of the 2005 midterm

21. Thursday, April 2: SECOND MIDTERM EXAM This covers Chapters 5-6. Open book.

22. Tuesday, April 7: The DMV. Problem 2 on the exam.

23. Thursday, April 9: Life as a traffic cop. Chapter 7. renewal theory.

24. Tuesday, April 14: Driving back and forth. Chapter 7. more renewal theory.

25. Thursday, April 16: The inspection paradox. Chapter 7. renewal theory ad nauseam.

26. Tuesday, April 21: Patterns. Chapter 7. renewal theory ad absurdam.

27. Thursday, April 23: BM basics. Chapter 10. Introduction to Brownian motion and martingales.

28. Tuesday, April 28: BM, Gambler's Ruin and Martingales Chapter 10. more BM and MGs. Supplementary notes on MGs.

29. Thursday, April 30: Staggering to the finish line: Chapter 10. even more BM and MGs.