Dynamic and Stochastic Models

SA402 ■ Fall 2016 ■ Sections 3002 and 4001
Assoc. Prof. Nelson Uhan


6 Dec

Final Exam on Friday 16 December, 7:55 - 10:55.

  • Section 3002: CH157      Section 4001: CH160
  • Calculators allowed.
  • No other outside materials allowed.
  • You will be given the same formulas that you have been given in past assessments.
  • The following course standards will not appear on the final exam:
    A1, B1, B2, B3, B4, B5, C1, E1, F1, G1, G2, G3
  • For each letter grade, you need to meet certain benchmarks on your final exam scores. Please see the course policy statement for details.


  • Your scores on the final exam will count as re-assessments.
  • You may re-assess 1 course standard that will not appear on the final exam anytime between now and the final exam. Submit your requests as usual.

EI. I'm around — if you need extra instruction, just e-mail me and we can set up a time to meet.

5 Dec Please include a copy of your previous drafts and score sheets when you submit a revision of your project.
1 Dec

A few adjustments to the re-assessment schedule:

No re-assessments for F3 - F7 on Fri 2 Dec. I plan to go over some parts of Wednesday's quiz on Friday. Some of you will want to re-assess these standards; I want to make sure you have time to properly review the material. To compensate...

2 re-assessments per class next week. You may re-assess 2 standards per class (instead of 1) next week (Mon 5 Dec, Wed 7 Dec).

23 Nov Plan for the end of the semester:
M28 NovReview — birth-death processes, standard queueing models
W30 NovLong quiz (30 minutes) on standards F3-F7
Office hours, re-assessments
F2 DecOffice hours, re-assessments
M5 DecOffice hours, re-assessments
W7 DecRe-assessments, wrap-up
  • Re-assessments:
    • For the rest of the semester, re-assessments will take place in class on 30 Nov, 2 Dec, 5 Dec and 7 Dec
    • You may request 1 re-assessment per class — please make sure to submit your request by COB the day before
  • Projects: you may revise and resubmit your project twice, any time before 16 Dec
17 Nov Because of my absence this week and the short week next week:
  • You may schedule 1 re-assessment for this week and 1 re-assessment for next week
    OR you may schedule 2 re-assessments (taken at the same time) for next week.
There will also be opportunities for extra re-assessments after Thanksgiving break — details TBA.
7 Nov There will be no quiz this week. Instead, there will be a quiz on Monday 14 Nov.

First drafts of projects are due on Wednesday 23 November. If you are finding your own article, you must get my approval by this Thursday 10 November.

2 Nov I will be in my office this evening (19:00 - 20:00) for re-assessments.

For this week only: you may use this evening re-assessment session to schedule a second re-assessment for this week.

31 Oct I updated course standard F1 and the relevant homework for standard F2. Please make sure you take a look.
26 Oct Upcoming schedule:
F28 OctPlease bring your laptops to class
M31 OctLesson 15 (not covered on Exam 2, but somewhat related)
W2 NovReview in class
I will be available for re-assessments in the evening, 19:00 - 20:00.
Th3 NovEI 19:00 - 20:00 in my office or nearby
F4 NovExam 2 in class

Exam 2.

  • Covers lessons 8-14, standards D1-D6 and E1-E6
  • Calculators allowed
  • No other outside materials allowed

12-week grades. Your 12-week grade will be based on standards A1, B1-B5, C1-C2, D1-D6 and E1-E4 (not E5-E6).

21 Oct Next week's quiz on Wednesday 26 Oct will assess standard E2 again, among other things TBD.
7 Oct Next week's quiz will take place on Friday 14 Oct, instead of Wednesday.
29 Sep

Next week's quiz (Wed) will cover D1, D2 and D3.

I will be available on Monday (3 Oct) evening, 19:00 - 20:00, for re-assessments.

23 Sep There is interest! I will hold a review session and re-assessment for standards B1 and B2 on Wednesday 28 Sep, 19:30 - 20:30. If you are interested but have not taken this poll, please do so that I can get an idea of how many midshipmen to expect.
22 Sep

Re-assessments for this week and next week.

  • Next week’s quiz (Wed) will include a re-assessment for standard C2.
  • You may schedule 1 re-assessment for this week and 1 re-assessment for next week
    OR you may schedule 2 re-assessments (taken at the same time) for next week.
  • If there is interest, I will hold a review session and re-assessment for standards B1 and B2 next Wednesday evening (19:30 - 20:30). Please take the poll here.

6-week grades. Your 6-week grade will be based on standards A1, B1-B5, and C1-C2.

12 Sep Upcoming schedule:
W14 SepLesson 7
F16 SepQuiz (standards B1, B2, C1, C2), worksheet with review problems
M19 SepReview in class
T20 SepEI 19:30 - 20:30 in my office
W21 SepExam 1

Exam 1

  • Covers lessons 1-7, standards A1, B1-B5, C1-C2
  • Calculators allowed
  • No other outside materials allowed
22 Aug Welcome!

Older announcements

General information


Date Problems
21 Nov 8.5ab, 8.8abc, 8.10bcd
18 Nov Finish 8.4abc, 8.6bcd, 8.10f, 8.11bcd.
16 Nov Compute the steady-state probabilities for the processes in 8.4abc, 8.6bcd, 8.10f, 8.11bcd.
9 Nov 8.10e. Write the model for 8.4, 8.8d.
7 Nov 8.6a, 8.11a. Finish the homework for 31 Oct.
31 Oct 7.10
26 Oct Finish the homework for 24 Oct.
24 Oct 6.17a, 6.20a, 6.21a. Justify why the properties of a Markov chain might be satisfied for these problems.
21 Oct 6.8, 6.11, 6.20b, 6.21bc
19 Oct 6.5, 6.6, 6.17c
17 Oct 6.4b, 6.17ab, 6.18 (start by finding the probabilities of preferred beer brands in 1979 and 2016)
14 Oct Finish the homework for 12 Oct.
12 Oct 6.2, 6.4ac, 6.5 (transition diagram only)
3 Oct 5.20. Finish Example 2 in Lesson 10.
30 Sep Finish the homework for 28 Sep.
28 Sep 5.3ef, 5.10, 5.12, 5.13, 5.15, 5.17
26 Sep 5.1bcd, 5.3abcd, 5.6, 5.8, 5.14
23 Sep 5.1a, 5.5
14 Sep 4.4. Finish the homework for 12 Sep.
12 Sep 4.6, 4.8
Hint. For 4.6, you'll need to keep track of the number of jobs waiting to be processed by CPU A and CPU B. Let B be a random variable that takes value 0 with probability 1/2 and 1 with probability 1/2. Map B = 0 to CPU A and B = 1 to CPU B.
9 Sep 3.17ab, 3.18ab, 3.19ab, 3.20ab
7 Sep 3.17c, 3.18c, 3.19c, 3.20c
6 Sep Finish the homework for 31 Aug and 2 Sep.
2 Sep 3.9, 3.31
31 Aug 3.6, 3.8
29 Aug Finish the homework for 26 Aug.
26 Aug 3.1, 3.2, 3.3, 3.5
24 Aug 2.1.  Also: finish the simulation of the self-service system we started in class.
Template for self-service system   Template for full-service system
22 Aug Familiarize yourself with the course policy statement. Read the section on grading carefully!


Dates Lesson
21 Nov 18 Standard queueing models notes
solutions to Problem 1
16 Nov
18 Nov
17 The birth-death process — performance measures notes
solutions to Problems 1 and 2
7 Nov
9 Nov
16 Introduction to queueing processes — the birth-death process notes
solutions to Problem 1
31 Oct
7 Nov
15 A quick start guide to Markov processes notes
solutions to Problem 1
28 Oct How to win at Monopoly notebook
24 Oct
26 Oct
14 Markov chains — modeling and assumptions notes
solutions to Problems 1 and 2
19 Oct
21 Oct
13 Markov chains — time-independent performance measures notes
solutions to Problem 1
14 Oct
17 Oct
12 Markov chains — time-dependent performance measures notes
solutions to Problem 1
12 Oct 11 Introduction to Markov chains notes
7 Oct Poisson processes for fun and profit notebook
3 Oct 10 Nonstationary Poisson processes notes
28 Sep
30 Sep
9 Poisson arrival processes, cont. notes
23 Sep
26 Sep
8 Arrival counting processes and the Poisson arrival process notes
notes on the memoryless property
16 Sep
19 Sep
Review problems
14 Sep 7 A general stochastic process model notes
9 Sep
12 Sep
6 Introduction to stochastic processes notes
7 Sep
9 Sep
5 Random variate generation notes
6 Sep 4 Conditional probability review, cont. notes
solutions to problems
31 Aug
2 Sep
3 Conditional probability review notes
solutions to Example 6
24 Aug
26 Aug
29 Aug
2 Probability review notes
solutions to exercises
22 Aug
24 Aug
1 Sample paths notes


Date Standards
30 Nov F3, F4, F5, F6, F7 quiz    formulas
14 Nov E5, E6, F1, F2 quiz
26 Oct E2, E3, E4 quiz
19 Oct E1, E2 quiz
14 Oct D4, D5, D6 quiz
5 Oct D1, D2, D3 quiz
28 Sep C2, D1, D2 quiz
16 Sep B1, B2, C1, C2 quiz
7 Sep B3, B4, B5 quiz
31 Aug A1, B1, B2 quiz


Date Exam
4 Nov Exam 2 exam
21 Sep Exam 1 exam