Recitations

Recitation material

Uploaded before the recitation.

Problems for all recitations (pdf)

Solutions for all recitations (pdf)

Recitation 1 material (pdf) (updated 2016-01-22)

Recitation 2 material (pdf) (updated 2016-01-27)

Recitation 3 material (pdf) (updated 2016-01-30)

Recitation 4 material (pdf) (updated 2016-02-06)

Recitation 5 material (pdf) (updated 2016-02-10)

Recitation 6 material¶ Recitation 7 material¶ Detailed solutions Recitations 8¶ Detailed solutions Recitation 9¶ Detailed solution Recitation 10 (Queuing Networks!)¶ Detailed solutions (pdf) (updated 2016-02-18)¶

Recitation 7 material (pdf) (updated 2016-02-18)¶

Recitations 8 (pdf) (updated 2016-02-18)¶

Recitation 9¶

Recitation 10 ¶

Recitation 11

Practice problems, and solutions to be uploaded before the recitation.

Recitation plan - updated continuously

Chapter numbers refer to the problem set chapter. In same cases we also give the set of problems discussed on the recitation. The rest of the problems should be solved at home!

R1 Probability theory - overview

R2 Probability theory - problems (Ch.1, Problems to be considered on the recitation: 3,5,6,7)

R3 Poisson Process (Ch.2, problems 4,7) Markov chains (Ch.3, problem 4 - first part)

R4 Markov Chains (Ch. 3, problems 3,5,6), Queuing systems (Ch. 4),

R5 M/M/1 (Ch. 5, At he recitation: 3.3, 5.1, 5.2, 5.6)

R6 M/M/m/m loss system, (Ch. 6, At the recitation: 6.5, 6.6), M/M/m wait system (Ch 7 7.1, 7.6), suggestion for home exercise: Exam 7.

R7 M/M/m/S and M/M/m//K (remaining 7.6, Ch. 8: 8.4 with additional small questions)

R8 Queuing networks (Ch. 12: 12.2, extra exam problem, 12.3)¶

R9 Method of stages (Ch. 9 : 9.1, 9.2, Exam 4.a. Suggestion for home exercise: Exam 6.)

R9 Queuing networks (Ch. 12: 12.2, extra exam problem, extra closed queuing networks problem, do 12.3 at home! )¶ R10 M/G/1 (Ch. 10: 10.1a,b, 10.2a, 10.4, Exam 9.a. Suggestion for home exercise: 10.3, 10.5a, Exam 5 )

R11 (old R10) M/G/1 with vacation and priorities (Ch.11: exercise 11.3, 11.5)

R12 Course summary, example exam problems

Exam problems solved on the recitations

During the second part of the course we will solve an exam problem on most of the recitations, to prepare for the exam. Try to solve the problem on your own before coming to the recitation, then you will benefit more from the discussion there.

List of typos in the solution manual¶ 2.5: Final result should be divided by (k!)¶ 4.6: Part b does not make sense, neither the problem, nor the solution. Do not solve it...¶ 10.1.c.: a rho is missing in f_W(t)