Classes

1. Tuesday, September 3: Chapter 1. laws of large numbers and random variables.

2. Thursday, September 5: modes of convergence and proof of the SLLN.

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

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

5. Tuesday, September 17: Chapter 2. lecture notes on the exponential distribution. Chapter 2. The exponential distribution. Concise summary of exponential and Poisson.

6. Thursday, September 19: Poisson process viewed as special case of other processes.

7. Thursday, September 24: The Mt/G/infty Queue (nonhomogeneous Poisson processes, Poisson random measures) and engineering applications: staffing service systems in face of time-varying demand. Examples 2.3B and 2.4A in the textbook.

   Main paper to be discussed: The Physics of The Mt/G/infty Queue by Steven G. Eick, William A. Massey and WW, Operations Research, vol. 41, No. 4, 1993, pp. 731-742. (primarily Section 1, 4 pages)

   Supplementary papers:

   • Mt/G/infty Queues with Sinusoidal Arrival Rates by Steven G. Eick, William A. Massey and WW, Management Science, vol. 39, No. 2, 1993, pp. 241-252. (Shows explicit formulas for sinusoidal arrival rates, see Theorem 4.1 and Section 5.)

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

   • Offered Load Analysis for Staffing. by WW, Manufacturing and Service Operations Management, vol. 15, No. 2, Spring 2013, pp. 166-169.

   • Coping with Time-Varying Demand when Setting Staffing Requirements for a Service System. by Linda V. Green (DRO), Peter J. Kolesar (DRO) and WW, Production and Operations Management (POMS), vol. 16, No. 1, January-February 2007, pp. 13-39.

8. Thursday, September 26: more on the infinite-server queue and its application.

9. Thursday, October 1: the compound Poisson process

10. Thursday, October 3: simulating an NHPP and homework 5

    Sunday, October 6. FIRST MIDTERM EXAM, Chapters 1 and 2.

11. Tuesday, October 8: Chapter 3. elementary renewal-reward theory.

12. Thursday, October 10: the renewal function, the renewal equation and renewal theorems.

13. Tuesday, October 15: the inspection paradox, the excess, age and total lifetime.

14. Thursday, October 17: patterns.

15. Tuesday, October 22: proof of Blackwell's renewal theorem via coupling.

16. Tuesday, October 24: Chapter 4. introduction to Markov chains. Study notes: The Big Picture. Chapter 4.

17. Tuesday, October 29: the contraction approach. The associated fixed point theorem.

18. Thursday, October 31: the M/G/1 queue. Notes from Gnedenko and Kovalenko (1968).

19. Tuesday, November 5: NO CLASS. Election Day.

20. Thursday, November 7: reversibility.

21. Tuesday, November 12: regenerative processes and semi-Markov processes. Sections 3.7 and 4.8.

22. Thursday, November 14: review of 2012 second midterm exam

    Sunday, November 17. SECOND MIDTERM EXAM. Chapters 3 and 4.

23. Tuesday, November 19: CTMC's, Chapter 5 in Ross. Sections 1-3 and 5 in lecture notes on CTMC's.

24. Thursday, November 21: birth and death processes, Section 4 of notes (now following notes).

25. Tuesday, November 26: reversibility and queueing networks, Sections 6-8.

26. Thursday, November 28: NO CLASS. Thanksgiving.

27. Tuesday, December 3: regularity and irregularity plus more birth and death processes, Sections 10 and 11.

28. Thursday, December 5: stochastic loss models, Section 9. (LAST CLASS).

29. Sunday, December 15: FINAL EXAM.