# CSCE 317 (Spring 2015): Lecture Log

January 13 (Tue), 2015 Administrative information: textbook, syllabus, grading policy. Examples of queueing systems (from ch.1 of Adan and Resing; see full reference under "Some useful links" on the course website). Ch.1 [H] ("Motivational Examples of the Power of Analytical Modeling").

January 15 (Thu), 2015 Ch.2 through the beginning of p.20 (throughput for open single-server network).

January 20 (Tue), 2015 HW1 assigned: exercises 3.2, 3.4, 3.5 in Section 3.16 [H], due Tuesday 2015-01-27. Q1. Ch.2 completed. Exercise 2.1 done in class.

January 22 (Thu), 2015 HW1 due date postponed to Thursday 2015-01-29. Q2. Kolmogorov's axioms of probability. Classical, limiting frequency, and subjective (Bayesian) interpretations of probability. We show that the classical and subjective interpretations are models of the axioms. Beginning of ch.3 ("Probability Review") [H].

January 27 (Tue), 2015 HW1 due date postponed to Tuesday 2015-02-03. Q3. Chapter 3 continued through Bayes's Law.

January 29 (Thu), 2015 HW1 (exercises 3.2, 3.4, 3.5 in section 3.16 [H]) is due on Tuesday 2015-02-03. Ch.3 continued through section 3.7.1 [H].

February 3 (Tue), 2015 HW1 collected and corrected in class. Q4. The Poisson distribution. Continuous distribution: pdf and cdf. Simple examples of functions that are or are not pdfs.

February 5 (Tue), 2015 Class canceled. All late afternoon CSCE classes were canceled: ******* [2:13pm] CSE Students and Faculty, I was not emphatic enough in my earlier email all CSCE classes are cancelled for the rest of the afternoon. Manton M. Matthews Chair Department of Computer Science and Engineering ******

February 10 (Tue), 2015 HW2 assigned: exercises 3.6, 3.7, 3.11, 3.15, 3.16, 3.19, 3.20, 3.24(parts a and b only), due Tuesday, 2015-02-17. Further discussion of HW1. Proof of the memoryless property of the exponential distribution and of the fact that no other continuous distribution has this property (notes from Kishor Trivedi). Ch.3 [H] through section 3.10.

February 12 (Thu), 2015 HW2 due date changed to Thursday, 2015-02-19. Ch.3 [H] through section 3.13 ("Linearity of Expectation"), but with much of 3.12 ("Probabilities and Expectations via Conditioning") still to do. Several examples from Trivedi's notes.

February 17 (Tue), 2015 Midterm will be on Thursday, February 26. 3.12 ("Probabilities and Expectations via Conditioning"). The normal (Gaussian) distribution from Trivedi's notes. Ch.3 [H] completed. Start of ch.4 [H] ("Generating Random Variables for Simulation").

February 19 (Thu), 2015 HW3 assigned: Exercises 3.21, 3.22, 3.23 [H]. HW2 collected and corrected. Students have the opportunity to resubmit this homework for additional credit.

February 24 (Tue), 2015 Reminder: Midterm exam will be on Thursday (2015-02-26). It will be closed book. Use of calculators is permitted, but only for numeric calculation, and it is not recommended. HW2 resubmission collected. HW3 collected. HW3 discussed in detail. Exercise 3.17 (Normal Approximation) discussed in detail.

February 26 (Thu), 2015 MT1.

March 3 (Tue), 2015 MT1, HW2, and HW3 returned. MT1 discussed in detail. Chapter 4 [H]: Generating Random Variables for Simulation: the Inverse-Transform Method (section 4.1). Difficulties in the application of the Inverse-Transform Method (first part of exercise 4.1). The Accept-Reject Method (section 4.2): discrete case completed; continuous case almost completed.

March 5 (Thu), 2015 HW4 assigned: exercises 4.1, 4.2, and 5.1 [H], due 2015-03-19. Chapter 4 [H] (Generating Random Variables for Simulation) completed.

March 17 (Tue), 2015 Chapter 5 [H]: Sample Paths, Convergences, and Averages, through section 5.2.

March 19 (Thu), 2015 HW5 assigned: exercise 6.1 [H]. HW4 collected and discussed. Chapter 5 [H] (Sample Paths, Convergences, and Averages) completed. Chapter 6 [H] (Little's Law and Other Operational Laws) started: statement of Little's Law for Open Systems (Theorem 6.1) and Intuition (Section 6.2).

March 24 (Tue), 2015 HW6 assigned: exercises 6.2, 6.3, 6.4 [H], due 2015-03-31. HW5 collected. Chapter 6 [H] (Little's Law and Other Operational Laws) through Section 6.8 ("More Operational Laws: The Forced Flow Law").

March 27 (Thu), 2015 HW5 returned and discussed. Hints for Exercise 6.4 [H]. Chapter 6 [H] completed. Chapter 7 [H] (Modification Analysis: "What-If" for Closed Systems") through Section 7.3.

March 31 (Tue), 2015 HW7 assigned: exercise 7.4[H], due on Tuesday, April 7. HW6 returned and discussed. Chapter 7 [H] (Modification Analysis: "What-If" for Closed Systems") completed. Chapter 8 [H] (Discrete-Time Markov Chains) started: sections 8.1 and 8.2.

April 2 (Thu), 2015 HW8 assigned: exercises 8.1, 8.2, 8.7 [H], due 2015-04-09. Please use 1024 as the exponent for the matrix exponentiation to be computed for exercise 8.7. HW6 (modified) collected. Exercise 7.3 [H] done and discussed in class. Chapter 8 [H] (Discrete-Time Markov Chains) through section 8.4. 1024th power of the transition matrix for the repair problem computed using R, the matrixcalc package, and the matrix.power function.

April 7 (Tue), 2015 HW7 and HW 8 due dates changed as follows: HW7 is due on 2015-04-09; HW8 is due on 2015-04-14. Discussion of some fine points of HW7. Chapter 8 [H] (Discrete-Time Markov Chains) through section 8.7, without section 8.6. Setting up the linear system for Exercise 8.1. Solving the linear system for Exercise 8.1 using the solve function of R.

April 9 (Thu), 2015 HW7 collected. Chapter 8 completed. Exercise 8.4 almost completed.

April 14 (Tue), 2015 HW8 due date is changed to Thursday, April 16. Exercises 8.7 (hints given), 8.2 (hints given), 8.4, and 8.6 discussed in class. Chapter 9 ("Ergodicity Theory") started.

April 16 (Thu), 2015 HW9 assigned: exercises 9.2 and 9.3 [H] due on Thursday, April 23. HW8 collected. Chapter 9 continued; coverage through the end of Section 9.4[H].

April 21 (Tue), 2015 HW8 returned and discussed. Hints given for HW9. Exercise 9.1 [H] done in class with review of definitions from Ch.9 [H].

April 23 (Thu), 2015 Late and incorrect homework may be turned in for partial credit until noon before the exam for partial (extra) credit. If you are resubmitting homework, please attach your improved work to the original graded paper(s). There will be a review session on Tuesday at class time. HW9 collected and discussed. Chapter 10 [H] ("Real-World Examples: Google, Aloha, and Harder Chains"): the Google PageRank algorithm and Aloha Slotted protocols as examples of DTMCs (finite state and infinite-state, respectively). Discussion of format of final exam. No conclusion! Student Evaluation. End of Course. Post-lecture addition: the final will be closed book and notes (calculators are allowed) and will be based on examples from the book and homework assignments. Only material from chapters 4 (all), 6 (all), 7 (all), 8 (all), 9 (no proofs), 10 (sections 10.1 and 10.2 only).

April 28 (Tue), 2015 Review session (and unofficial makeup of class lost the day of shooting incident in the College of Public Health). Exercise 7.5, Section 10.2, Sections 13.1 1nd 13.2 on M/M/1 queues.