Nyhetsflöde
Logga in till din kurswebb
Du är inte inloggad på KTH så innehållet är inte anpassat efter dina val.
Har du frågor om kursen?
Om du är registrerad på en aktuell kursomgång, se kursrummet i Canvas. Du hittar rätt kursrum under "Kurser" i personliga menyn.
Är du inte registrerad, se Kurs-PM för EP2200 eller kontakta din studentexpedition, studievägledare, eller utbilningskansli.
I Nyhetsflödet hittar du uppdateringar på sidor, schema och inlägg från lärare (när de även behöver nå tidigare registrerade studenter).
Sladana Josilo redigerade 25 januari 2017
Recitation material¶ Updated before recitation.
Problems for all recitations (pdf)
Solutions for all recitations (pdf)
Recitation 1 material (pdf) - updated
Recitation 2 material (pdf)- updated¶
Recitation 2 material (pdf) - will change
Recitation 3 material (pdf) - will change
Recitation 4 material (pdf)
Recitation 5 material (pdf)
Recitation 6 material (pdf) Note, for solution 7.6/d we agreed in i-1 services, instead of the i-2 given in the solution here and in the booklet.
Recitation 7 material (pdf)
Recitations 8 (pdf)
Recitation 9 (pdf)
Recitation 10 (pdf)
Recitation 11 + a missing problem on vacation systems (11.5), solutions
Recitation 12 Practice problems, 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 4,7) 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.)
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 M/G/1 with vacation and priorities (Ch.11: exercise 11.3, 11.5)
R12 Course summary, example exam problems
Sladana Josilo redigerade 26 januari 2017
Updated before recitation.
Problems for all recitations (pdf)
Solutions for all recitations (pdf)
Recitation 1 material (pdf) - updated
Recitation 2 material (pdf)- updated
Recitation 3 material (pdf) - will changeupdated
Recitation 4 material (pdf)
Recitation 5 material (pdf)
Recitation 6 material (pdf) Note, for solution 7.6/d we agreed in i-1 services, instead of the i-2 given in the solution here and in the booklet.
Recitation 7 material (pdf)
Recitations 8 (pdf)
Recitation 9 (pdf)
Recitation 10 (pdf)
Recitation 11 + a missing problem on vacation systems (11.5), solutions
Recitation 12 Practice problems, 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 4,7) 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.)
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 M/G/1 with vacation and priorities (Ch.11: exercise 11.3, 11.5)
R12 Course summary, example exam problems
Sladana Josilo redigerade 31 januari 2017
Updated before recitation.
Problems for all recitations (pdf)
Solutions for all recitations (pdf)
Recitation 1 material (pdf) - updated
Recitation 2 material (pdf)- updated
Recitation 3 material (pdf) - updated
Recitation 4 material (pdf) - updated
Recitation 5 material (pdf)
Recitation 6 material (pdf) Note, for solution 7.6/d we agreed in i-1 services, instead of the i-2 given in the solution here and in the booklet.
Recitation 7 material (pdf)
Recitations 8 (pdf)
Recitation 9 (pdf)
Recitation 10 (pdf)
Recitation 11 + a missing problem on vacation systems (11.5), solutions
Recitation 12 Practice problems, 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 4,7) 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.)
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 M/G/1 with vacation and priorities (Ch.11: exercise 11.3, 11.5)
R12 Course summary, example exam problems
Sladana Josilo redigerade 31 januari 2017
Updated before recitation.
Problems for all recitations (pdf)
Solutions for all recitations (pdf)
Recitation 1 material (pdf) - updated
Recitation 2 material (pdf)- updated
Recitation 3 material (pdf) - updated
Recitation 4 material (pdf) - updated
Recitation 5 material (pdf)
Recitation 6 material (pdf) Note, for solution 7.6/d we agreed in i-1 services, instead of the i-2 given in the solution here and in the booklet.
Recitation 7 material (pdf)
Recitations 8 (pdf)
Recitation 9 (pdf)
Recitation 10 (pdf)
Recitation 11 + a missing problem on vacation systems (11.5), solutions
Recitation 12 Practice problems, 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 4,7) 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.)
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 M/G/1 with vacation and priorities (Ch.11: exercise 11.3, 11.5)
R12 Course summary, example exam problems
Sladana Josilo redigerade 2 februari 2017
Updated before recitation.
Problems for all recitations (pdf)
Solutions for all recitations (pdf)
Recitation 1 material (pdf) - updated
Recitation 2 material (pdf)- updated
Recitation 3 material (pdf) - updated
Recitation 4 material (pdf) - updated
Recitation 5 material (pdf) - updated
Recitation 6 material (pdf) Note, for solution 7.6/d we agreed in i-1 services, instead of the i-2 given in the solution here and in the booklet.
Recitation 7 material (pdf)
Recitations 8 (pdf)
Recitation 9 (pdf)
Recitation 10 (pdf)
Recitation 11 + a missing problem on vacation systems (11.5), solutions
Recitation 12 Practice problems, 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 4,7) 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.)
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 M/G/1 with vacation and priorities (Ch.11: exercise 11.3, 11.5)
R12 Course summary, example exam problems
Sladana Josilo redigerade 7 februari 2017
Updated before recitation.
Problems for all recitations (pdf)
Solutions for all recitations (pdf)
Recitation 1 material (pdf) - updated
Recitation 2 material (pdf)- updated
Recitation 3 material (pdf) - updated
Recitation 4 material (pdf) - updated
Recitation 5 material (pdf) - updated
Recitation 6 material (pdf) Note, for solution 7.6/d we agreed in i-1 services, instead of the i-2 given in the solution here and in the booklet.- updated
Recitation 7 material (pdf)
Recitations 8 (pdf)
Recitation 9 (pdf)
Recitation 10 (pdf)
Recitation 11 + a missing problem on vacation systems (11.5), solutions
Recitation 12 Practice problems, 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 4,7) 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.)
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 M/G/1 with vacation and priorities (Ch.11: exercise 11.3, 11.5)
R12 Course summary, example exam problems
Sladana Josilo redigerade 9 februari 2017
Updated before recitation.
Problems for all recitations (pdf)
Solutions for all recitations (pdf)
Recitation 1 material (pdf) - updated
Recitation 2 material (pdf) - updated
Recitation 3 material (pdf) - updated
Recitation 4 material (pdf) - updated
Recitation 5 material (pdf) - updated
Recitation 6 material (pdf) - updated
Recitation 7 material (pdf) - updated
Recitations 8 (pdf)
Recitation 9 (pdf)
Recitation 10 (pdf)
Recitation 11 + a missing problem on vacation systems (11.5), solutions
Recitation 12 Practice problems, 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 4,7) 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.)
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 M/G/1 with vacation and priorities (Ch.11: exercise 11.3, 11.5)
R12 Course summary, example exam problems
Sladana Josilo redigerade 14 februari 2017
Updated before recitation.
Problems for all recitations (pdf)
Solutions for all recitations (pdf)
Recitation 1 material (pdf) - updated
Recitation 2 material (pdf) - updated
Recitation 3 material (pdf) - updated
Recitation 4 material (pdf) - updated
Recitation 5 material (pdf) - updated
Recitation 6 material (pdf) - updated
Recitation 7 material (pdf) - updated
Recitations 8 (pdf) material (pdf) -updated
Recitation 9 (pdf)
Recitation 10 (pdf)
Recitation 11 + a missing problem on vacation systems (11.5), solutions
Recitation 12 Practice problems, 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 4,7) 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.)
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 M/G/1 with vacation and priorities (Ch.11: exercise 11.3, 11.5)
R12 Course summary, example exam problems
Sladana Josilo redigerade 17 februari 2017
Updated before recitation.
Problems for all recitations (pdf)
Solutions for all recitations (pdf)
Recitation 1 material (pdf) - updated
Recitation 2 material (pdf) - updated
Recitation 3 material (pdf) - updated
Recitation 4 material (pdf) - updated
Recitation 5 material (pdf) - updated
Recitation 6 material (pdf) - updated
Recitation 7 material (pdf) - updated
Recitation 8 material (pdf) - updated
Recitation 9 (pdf (pdf) - updated (Note, I discussed Exm. Collection problem 6/b (the mean time the system remains in blocking state) with Viktoria and we agreed that the provided solution is correct (we can discuss about it next time if you are still interested...)
Recitation 10 (pdf)
Recitation 11 + a missing problem on vacation systems (11.5), solutions
Recitation 12 Practice problems, 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 4,7) 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.)
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 M/G/1 with vacation and priorities (Ch.11: exercise 11.3, 11.5)
R12 Course summary, example exam problems
Sladana Josilo redigerade 21 februari 2017
Updated before recitation.
Problems for all recitations (pdf)
Solutions for all recitations (pdf)
Recitation 1 material (pdf) - updated
Recitation 2 material (pdf) - updated
Recitation 3 material (pdf) - updated
Recitation 4 material (pdf) - updated
Recitation 5 material (pdf) - updated
Recitation 6 material (pdf) - updated
Recitation 7 material (pdf) - updated
Recitation 8 material (pdf) - updated
Recitation 9 material (pdf) - updated (Note, I discussed Exm. Collection problem 6/b (the mean time the system remains in blocking state) with Viktoria and we agreed that the provided solution is correct (we can discuss about it next time if you are still interested...)
Recitation 10 (pdf) - updated
Recitation 11 + a missing problem on vacation systems (11.5), solutions
Recitation 12 Practice problems, 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 4,7) 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.)
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 M/G/1 with vacation and priorities (Ch.11: exercise 11.3, 11.5)
R12 Course summary, example exam problems
Sladana Josilo redigerade 23 februari 2017
Updated before recitation.
Problems for all recitations (pdf)
Solutions for all recitations (pdf)
Recitation 1 material (pdf) - updated
Recitation 2 material (pdf) - updated
Recitation 3 material (pdf) - updated
Recitation 4 material (pdf) - updated
Recitation 5 material (pdf) - updated
Recitation 6 material (pdf) - updated
Recitation 7 material (pdf) - updated
Recitation 8 material (pdf) - updated
Recitation 9 material (pdf) - updated (Note, I discussed Exm. Collection problem 6/b (the mean time the system remains in blocking state) with Viktoria and we agreed that the provided solution is correct (we can discuss about it next time if you are still interested...)
Recitation 10 material (pdf) - updated
Recitation 11 + a missing problem on vacation systems (11.5), solutions material (pdf) - updated
Recitation 12 Practice problems, 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 4,7) 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.)
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 M/G/1 with vacation and priorities (Ch.11: exercise 11.3, 11.5)
R12 Course summary, example exam problems
Sladana Josilo redigerade 28 februari 2017
Updated before recitation.
Problems for all recitations (pdf)
Solutions for all recitations (pdf)
Recitation 1 material (pdf) - updated
Recitation 2 material (pdf) - updated
Recitation 3 material (pdf) - updated
Recitation 4 material (pdf) - updated
Recitation 5 material (pdf) - updated
Recitation 6 material (pdf) - updated
Recitation 7 material (pdf) - updated
Recitation 8 material (pdf) - updated
Recitation 9 material (pdf) - updated (Note, I discussed Exm. Collection problem 6/b (the mean time the system remains in blocking state) with Viktoria and we agreed that the provided solution is correct (we can discuss about it next time if you are still interested...)
Recitation 10 material (pdf) - updated
Recitation 11 material (pdf) - updated
Recitation 12 Practice problems, and solutions material (pdf) - updated
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.)
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 M/G/1 with vacation and priorities (Ch.11: exercise 11.3, 11.5)
R12 Course summary, example exam problems
Hi all!
Here are the answers to some of the questions from the consultations:
*Collection of the exam problems (problem 8):
- Question: Why system B is modeled as a system with a finite population and system A is not?
Answer: When should we consider a system as finite population system? Rule of tumb: C < 10m, where m is the number of servers (lecture 7, slide 6).
*Exam March, 2015 (problem 4 (d)):
-Arrivals still happen according to a Poisson distribution, but samples (the moments when the jobs arrive) are uniformly at random distributed over the fixed garbage collection time.
-Regarding the formula for the remaining garbage collection time, please check slide 6 , lecture 11, the first formula from which we started the derivation. In our problem vi is always the same and equal to v, and we consider these jobs that arrive during the garbage collection period, so T in our problem is n*v (total length of the garbage collection period).
*Exam March, 2016 (4 (a)):
-The average length of the idle periods (the solution is correct!).
-Explanation: The resulting process is a Poisson(lambda1 + lambda2). We are interested in the periods when a server is idle. Hence, let us look at the moment when a server becomes idle. The server remains in the idle state until the next arrival happens and the next arrival will happen according to a Poisson(lambda1 + lambda2) distribution. Therefore, the idle periods are exponentially distributed with a mean of 1/(lambda1 + lambda2) . Note that the type of the service time does not affect the distribution of the idle periods! This is because the interarrival time is exponential(lambda1 + lambda2) , and therefore the memoryless property holds (we do not care which type of the service was going on before the server became idle).
*Exam March, 2016 (problem 3(d)) and Exam June, 2016 (problem 2(e)):
Both solutions are correct and acceptable.