Classes

1. Tuesday, September 4: Chapter 1. laws of large numbers and modes of convergence.

2. Thursday, September 6: continued. normal approximations and the central limit theorem.

3. Tuesday, September 11: our friends: transforms

4. Thursday, September 13: Laplace transform notes

5. Tuesday, September 18: Chapter 2. lecture notes on the exponential distribution. Chapter 2. The exponential distribution. Concise summary of exponential and Poisson.

6. Thursday, September 20: The Mt/G/infty Queue (nonhomogeneous Poisson processes, Poisson random measures) and engineering applications: staffing service systems in face of time-varying demand.

   Main paper to be discussed: 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.

7. Tuesday, September 25: more on the Mt/G/infty Queue. Poisson process viewed as special case of other processes.

8. Thursday, September 27: compound Poisson process. Supplement on simulating a nonhomogeneous Poisson process.

9. Tuesday, October 2: counting processes: the inverse relation and its application.

10. Thursday, October 4: renewal reward processes.

    Sunday, October 7. FIRST MIDTERM EXAM, Chapters 1 and 2.

11. Tuesday, October 9: Chapter 3. the renewal function, the renewal equation and renewal theorems.

12. Thursday, October 11: the excess and the age Chapter 3.

13. Tuesday, October 16: patterns. Chapter 3.

14. Thursday, October 18: proof of Blackwell's renewal theorem.

15. Tuesday, October 23: Chapter 4. introduction to Markov chains. Study notes: The Big Picture. Chapter 4.

16. Thursday, October 25: the contraction approach. The associated fixed point theorem.

17. Tuesday, October 30: NO CLASS. Hurricane Sandy.

18. Thursday, November 1: the M/G/1 queue. Notes from Gnedenko and Kovalenko (1968).

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

20. Thursday, November 8: reversibility.

21. Tuesday, November 13: regenerative processes and semi-Markov processes. Sections 3.7 and 4.8.

22. Thursday, November 15: Introduction to continuous-time Markov chains. Chapter 5. Sections 1-3 of Lecture Notes on CTMC's.

    Sunday, November 18. SECOND MIDTERM EXAM. Chapters 3 and 4.

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

24. Thursday, November 22: NO CLASS. Thanksgiving.

25. Tuesday, November 27: birth and death processes. Section 5 of the CTMC notes. Chapter 5 in the textbook.

26. Thursday, November 29: additional results for birth-and-death processes. Section 6 of CTMC notes.

27. Tuesday, December 4: reversibility and Markovian queueing networks. extra notes on stochastic networks. Section 6 of the CTMC notes. Chapter 5 in the textbook.

28. Thursday, December 6: LAST CLASS. loss models.

29. Sunday, December 16: FINAL EXAM.