Visa version
Recitations
Recitation material
Recitation order has been changed: 10: Queuing Networks, 11: M/G/1 with vacations and priority
Problems for all recitations (pdf)
Solutions for all recitations (pdf)
Recitation 5 material (Problems in mixed order, worry for that... We have not solved the problem with the z-tranform, and it will not be exam material. However, it shows an interesting numerical method.)
Detailed Solutions to the exercises (to be updated BEFORE each recitation)
Detailed solutions Recitations 8
Detailed solutions Recitation 9
Detailed solution Recitation 10 (Queuing Networks!)
Detailed solutions Recitation 11
Practice problems (updated), and solutions
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 4,6,7) Markov chains (Ch.3, problem 4)
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 Method of stages (Ch. 9 : 9.1, 9.2, Exam 4.a. Suggestion for home exercise: Exam 6.)
R9 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 )
R10 (old R10) Queuing networks (Ch. 12: 12.2, extra exam problem, extra closed queuing networks problem, do 12.3 at home! )
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)