**January 12 (Tue), 2016**
Administrative information:
textbook, syllabus, grading policy. Roll called.
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") started.

**January 15 (Thu), 2016**
Ch.1 [H] concluded.
Ch.2 [H] ("Queueing Theory Terminology") through section 2 ("The
Single Server Network").

**January 19 (Tue), 2016**
Ch.2 [H] continued: Open Networks (2.4). Exercise 2.1 done in class.

**January 21 (Thu), 2016**
Q1.
Ch.2 [H] completed. Exercise 2.2 partly done in class.

**January 26 (Tue), 2016**
HW1 assigned: exercises 3.2, 3.3, 3.4, 3.5 [H],
due on Tuesday, February 2, 2016.
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].
Examples of section 3.4 started.

**January 28 (Thu), 2016**
HW1 due date changed to February 4, 2016.
Chapter 3 continued through Bayes's Law and the definition of random variable.

**February 2 (Tue), 2016**
HW1 due date changed to February 9, 2016.
Q2 and Q3.
Examples of random variables, including a couple from the experiment of
tossing a fair coin three times in sequence.
Definition 3.14 (pmf, cdf).
The Bernoulli(p) discrete distribution.

**February 2 (Thu), 2016**
HW1 due date changed to February 11, 2016.
(Note: the students are encouraged to work on three of the four exercises
now: 3.2, 3.4, and 3.5.)
Common discrete distributions: Bernoulli(p), Binomial(n,p),
Geometric(p), Poisson(lambda).
Continuous distributions. Definition of probability density function
and cumulative distribution function (pdf, cmf).

**February 9 (Tue), 2016**
Q4.
HW1 due date changed to February 16, 2016.
(Note: the students are encouraged to work on three of the four exercises
now: 3.2, 3.4, and 3.5.)
Some common continuous distributions: Uniform(a,b), Exponential(lambda),
Pareto (alpha). Expectation, with examples from Trivedi.

**February 11 (Thu), 2016**
HW1 is due on February 16, 2016.
More on expectation.
Moments. Expectation of a function of a random variable.
Variance defined. Variance of some common distributions.
Joint probability and independece. An example from Trivedi (disk seek time),
to be concluded.

**February 16 (Tue), 2016**
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, 2016-02-23.
HW1 collected and discussed in detail.
Linearity of expectation. Expectation and variance from Trivedi's notes,
which are available in the blackboard site for this course.

**February 18 (Thu), 2016**
HW2 delayed to Thursday, 2016-02-25.
Computation of the expected value of the Geometric(p) r.v. using conditioning.
Same for the Binomial(n,p) using indicator variables and the
linearity of expectation. The Hats example (p.55-56 [H]).
Reliability (based on Trivedi's notes).
The memoryless (Markov) property of the exponential distribution, using
Trivedi's notes, which are available in the blackboard site for this course.

**February 23 (Tue), 2016**
HW1 returned.
Midterm will be on Tuesday, March 1, 2016. It will be closed book, except
for one letter-size or A4 sheet of formulas, written in blue ink
on one side only.
More on reliability, including (instantaneous) failure rate (aka hazard rate,
force of mortality, intensity rate, conditional failure rate).
The normal distribution, through p.59 [H].

**February 25 (Thu), 2016**
HW2 collected.
Normal distribution completed (using notes from Trivedi, posted on blackboard,
as well as the textbook).
Midterm from last year, in detail.
HW2 correction, briefly.

**March 1 (Tue), 2016**
MT1.

**March 3 (Thu), 2016**
HW3 assigned: exercises 3.21, 3.22, 3.23 [H], due on Thursday, 3/17.
(These are difficult exercises: start now!)
MT1 returned and discussed.
Review of some exercises from HW2, especially 3.11.
A few additional examples on Ch.3[H] material.

**March 15 (Tue), 2016**
Exercises 3.25 [H] and 3.17 [H] done in class as review.
Example 3.10 from Trivedi's notes (file normal-Trivedi.pdf in blackboard) on
random deviates. From the same notes: Theorem 3.1 on Random Deviates;
example 3.11 and Figure 3.18 with a presentation of the
reason why which the Inverse Transform Method works.
Chapter 4 ("Generating Random Variables for Simulation") [H], almost
completed.

**March 17 (Thu), 2016**
HW4 assigned: Exercises 4.1 and 4.2 [H], due on Thursday, 3/24.
HW5 assigned: Exercises 5.1 [H], due on Tuesday, 3/29.
(If you use the notes by Prof. Trivedi on blackboard for exercise 5.1,
make sure to reference them properly.)
Chapter 4 ("Generating Random Variables for Simulation") [H], almost
completed.
Chapter 5 ("Sample Paths, Convergence, and Averages") started:
Markov's inequality, Chebyshev's inequality, and
the Weak Law of Large Numbers. Examples from Trivedi's notes (on
blackboard).

**March 22 (Tue), 2016**
HW3 corrected in class.
Review of Markov's inequality, Chebyshev's inequality, and
the Weak Law of Large Numbers, with a more careful explanation of the Weak
Law of Large Numbers.
Chapter 5 ("Sample Paths, Convergence, and Averages") completed. Sample
average vs. ensemble average (Tim vs. Enzo), very briefly.

**March 24 (Thu), 2016**
HW4 collected and corrected in class.
Sample average vs. ensemble average in detail. Ergodicity.
Simulation. Time in system.
Chapter 6 ("Little's Law and Other Operational Laws") started. Statement
of Little Law. Intuitions behind Little's Law.

**March 29 (Tue), 2016**
HW6 assigned: exercise 6.1 [H], due on Tuesday, April 5.
HW4 returned.
HW5 collected and discussed.
Chapter 6 ("Little's Law and Other Operational Laws") up to the statement of
the forced flow law.

**March 31 (Thu), 2016**
HW7 assigned: exercises 6.2, 6.3, and 6.4 [H], due on Thursday, April 7.
HW4 collected again; I had forgotten to record grades!
HW3 returned.
Chapter 6 ("Little's Law and Other Operational Laws") completed.

**April 5 (Tue), 2016**
HW8 assigned: exercises 7.3 and 7.4 [H], due on Thursday, April 14,
HW7 due date delayed to Tuesday, April 12.
HW6 collected.
HW5 returned.
Chapter 7 [H] (Modification Analysis: "What-If" for Closed Systems")
through Section 7.3.

**April 7 (Thu), 2016**
HW4 returned.
Chapter 7 [H] ("Modification Analysis: 'What-If' for Closed Systems")
completed.
Exercise 7.3 [H] done in class.
Ch. 8 [H] ("Discrete-Time Markov Chains") started: definition of stochastio
process, Markov chain, Markovian (memoryless property), and
transition probability matrix.

**April 12 (Tue), 2016**
HW9 assigned: exercises 8.1, 8.2, 8.7 [H] due April 17, 2016.
HW6 returned.
HW7 collected.
Ch. 8 [H] ("Discrete-Time Markov Chains") continued through parts of
section 8.7.

**April 14 (Thu), 2016**
HW9 (exercises 8.1, 8.2, 8.7 [H]) due date changed to April 19, 2016.
HW8 collected.
HW7 corrected in class.
Exercise 8.1 [H] done in class using R; solution with stationarity equations
(as requested by the exercise) and with high powers of the transition
probability matrix, using the matrixcalc package.
Discussion of Exercise 8.7 [H].

**April 19 (Tue), 2016**
More comments on Exercise 8.7[H].
Exercises 8.4 and 8.6 done in class.
Chapter 9 [H] ("Ergodicity Theory"): highlights only.
Chapter 10 [H] ("Real-World Examples: Google, Aloha, and Harder Chains"):
the Google PageRank algorithm protocol as example of finite DTMC.

**April 21 (Thu), 2016**
HW7 returned.
HW9 collected.
Final will be closed book and notes, except
for one letter-size or A4 sheet (both sides acceptable)
of formulas, written in blue ink.
Exercise 8.2, 9.1, 9.2, 9.3 [H] done in class.
Aloha Protocol Analysis (Section 10.2 [H]).
Exam will not include Ch.9[H], but it will include sections 10.1 and 10.2 [H].
Exam will be based on materials from Ch.4 [H] on. However, note that the
definitions in Ch.2 and the probability review of Ch.3 are heavily used in
examples and exercises for the later chapters.
End of course survey.