Queueing Theory (QT) 2011

The results of the exam of May 16 are ready and are published here. These are the grades for the course as a wole, including the homework assignments.

For those who failed the exam or did not participate, there will be a resit (herexamen) as follows:

Resit Queueing Theory
Date: Monday, June 27, 2011
Time: 13.00-16.00
Place: Minnaert building, room MIN 208 (this is where also the classes were held).

Homework results will again be 20% of the total grade. Afterwards, homework results will be invalid, as this resit will be the last opportunity to finish the course in this academic year. Next year the course will be taught by colleagues from TU Eindhoven.

Please send me an email if you intend to participate in the resit, or if you have any questions.

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See ‘News’ and ‘Agenda’ below

This is an LNMB master course. It is also included in the Mastermath program. Please register for the course at the mastermath website if you have not done so yet.

In 2011, classes are on 12 Mondays in spring.

Dates: January 31 till April 18
Time: From 15.15 till 17.00 hours.
Venue: Minnaert Building at the Uithof in Utrecht, room MIN 208.

The course material consists of the lecture notes ('dictaat') on Queueing Theory, written by Ivo Adan and Jacques Resing of the dept. of Mathematics and Computer Science, TUE. This is available here or here in pdf. Note that you may not want to print out pages 123-180 on paper, as these only contain the solutions to the exercises.

A written exam will be held afterwards, on May 16, from 13.00 till 16.00 hours, in building Aardwetenschappen, grote zaal.

A short tutuorial on Markov chains (in Dutch) has been added here. Here is an old exam, to indicate the level and type of questions you can expect. You can use this formula sheet during the exam (will be handed out with the exam).

News:

- (110124) Note that the first lecture will be January 31, in week 5 (even though other mastermath courses start in week 6)

- (110207) The exam will take place on May 16 (13.00 till 16.00 hours, place t.b.a.).

- (110214) There will be three homework assignments, to be handed in on February 21, March 7 and April 4, respectively. These have to be written in English! The assignments can be found in the Agenda below. The average assignment score determines 20% of the final grade for the course: final grade = (assignment score + 4 * exam score)/5.

- (110301) The second homework assignment has been added, to be handed in on March 7; see below.

-(110328) The third and final homework assignment has been added, to be handed in on April 4 or April 11 (at the latest); see below.

- (110328) Time and place of the exam are known, see above (or below).

- (110523) For news on resit (herexamen), see top of page.

Agenda (indicative; will be updated regularly):

January 31 Topics: Material: Exercises:	Introduction, some concepts from probability theory (Generating functions, Laplace-Stieltjes transforms) Chapters 1 and 2. 1, 2, 4, 5, 6, 11
February  7 Topics: Material: Exercises:	Basic queueing concepts Chapter 3; see also this sheet about the single server queue. 12
February  14 Topics: Material: Exercises: Assignment:	M/M/1 queue: L, S, W, L_q, priorities, E(BP) Chapter 4 except 4.6.2 13 through 20 To be handed in - in English (!)- on February 21, (if this is not feasible for some reason, send an email asking for a one-week delay): 1. Apply Mean Value Analysis (MVA) to the queue (!) of an M/M/1 system to find EL_q and EW. 2. Consider an M/M/1 system with 3 priority classes having different Poisson arrival rates lambda_i (i= 1, 2, 3) and common service rate mu. Class 1 jobs have preemptive priority over jobs of classes 2 and 3, while class 2 jobs have preemptive priority over class 3 jobs. Apply MVA to find EL_i and ES_i, i= 1, 2, 3.
February  21 Topics: Material: Exercises:	Distribution of Busy Period in M/M/1. M/M/infty queue, M/M/c queue 4.6.2 + Chapter 5 21 through 24
February  28 Topics: Material: Exercises: Assignment:	Phase type distributions, M/E_r/1 queue Sections 2.4.4 - 2.4.6, Chapter 6 3, 7-10, 26-36 To be handed in on March 7 (if this is not feasible for some reason, send an email asking for a one-week delay): 1. Exercise 27 from the book; also(!) find p_n explicitly for the case r = 2. (NB: in part iii, the word ‘numerator’ should be replaced by ‘denominator’) 2. Use LST's to prove that any 'mixture of Erlangs' with same scale parameter (as in section 2.4.6) is a special case of the Coxian distribution.
March 7 Topics: Material: Exercises:	M/G/1 queue: MVA, Residual service time, Lindley's equation Sections 7.6, 7.7, 7.5 39 through 42
March 14 Topics: Material: Exercises:	Pollaczek-Khinchine formula for L, finding distr. of L and W from PK-formulas. Sections 7.1, 7.2. 37(except vi), 38, 43 through 48; use formulas (7.8) and (7.9) if needed.
March 21 Topics: Material: Exercises:	Poll.-Khin formulas for W and S, moments, BP, exceptional first customer Sections 7.3, 7.4, 7.8, 10.3 through 49
March 28 Topics: Material: Exercises: Assignment:	G/M/1 queue Chapter 8 50 through 55 To be handed in on April 4 or 11 (at the latest) Let F(t)=1 - 1/2 exp(-2t) - 1/2 exp(-2t/3) Find EW, P(W>0) and P(W>1) in a queue with load rho=1/2 if: (i)  interarrival times iid ~ Exp and service times iid ~ F(t); (ii) interarrival times iid ~ F(t) and service times iid ~ Exp. NB: above 'exp' stands for the exponential function; 'Exp' stands for an exponential distribution.
April 4 Topics: Material: Exercises:	M/G/1 priority models Chapter 9 56 through 62
April 11 Topics: Material: Exercises:	Variations of M/G/1 queue: setup times, up- and down-times. Chapter 10 63 through 73
April 18 Topics: Material: Exercises:	M/G/1 with batch arrivals; Insensitive systems: M/G/inf, M/G/c/c, M/G/1 LCFS, (PS) Section 10.4, Chapter 11. 74 through 79
May 16	Written Exam (13.00 till 16.00 hours, in building Aardwetenschappen, grote zaal)
June 27	Written Resit exam (herexamen): 13.00 till 16.00 hours, in Minnaert building, room MIN 208 (this is where also the classes were held).