AlQT: Algorithmic Methods in Queueing Theory
Fall 2014

Meetings:	Monday from 13.00 to 14.45 Room 611AB, Mathematical Building, Uithof
Instructors:	Ivo Adan
	office:	Gemini-Zuid 0.125, TU/e
	telephone:	247 2932
	e-mail:	iadan@tue.nl
	Johan van Leeuwaarden
	office:	MetaForum 4.096, TU/e
	telephone:	247 2813
	e-mail:	j.s.h.v.leeuwaarden@tue.nl
Text:
Slides:
Examination:	Take home assignments

Assignments:

#1 Algorithms for inverting transforms

#2 Performance evaluation of a production system

#3 Combining make-to-order and make-to-stock

Course outline from week to week

1. Numerical solution of equilibrium equations: direct methods
   Numerical solution of equilibrium equations: iterative methods
   
2. Kernel method for discrete queues (only sects. 1-5, 10-11 of lecture notes are required for assignment 1)
3. Kernel method for discrete queues (continued)
4. Kernel method for discrete queues (continued)
   Queues in the Halfin-Whitt or QED regime
   Abate, J., W. Whitt (1992). Numerical inversion of probability generating functions. Operations Research Letters 12: 245-251.
5. Kernel method for (reflected) 2-D random walks
   Dominant pole approximation
   Prodinger, H. (2004). The Kernel Method: Collection of Examples. Séminaire Lotharingien de Combinatoire 50.
   Queueing models with multiple waiting lines: Direct methods
   Examples of M/M/1 type models
6. Markov processes
   Transient analysis of Markov processes
7. M/M/1 type models
8. G/M/1 type models
   G/M/1 type models with linear rates
   Additional notes
   Single-server models
   some SMART BOARD notes

References

• J. Van der Wal, P.J. Schweitzer:
  Iterative bounds on the equilibrium distribution of a finite Markov chain, Probability in the Engineering and Infromational Sciences, vol. 1, 1987, pp. 117-131.
• M.F. Neuts:
  Matrix-geometric solutions in stochastic models: an algorithmic approach, Johns Hopkins University Press, 1981.
• V. Ramaswami:
  Algorithmic analysis of stochastic models; The changing face of Mathematics.
  Ramanujan Endowment Lecture at Anna University, Chennai, India, 2000.
• V. Ramaswami, G. Latouche:
  A general class of Markov processes with explicit matrix-geometric solutions.
  OR Spektrum, vol. 8, 1986, pp. 209-218.
• G. Latouche, V. Ramaswami:
  A logarithmic reduction algorithm for quasi-birth-death processes.
  J. Appl. Prob., vol. 30, 1993, pp. 650-674.
• G. Latouche, V. Ramaswami:
  Introduction to matrix analytic methods in stochastic modeling, Philadelphia, SIAM, 1999.
• I. Mitrani:
  The spectral expansion solution method for Markov processes on lattice strips.
  In: Advances in queueing : theory, methods, and open problems, J.H. Dshalalow (ed.), CRC Press, 1995.
• A.G. De Kok:
  A moment-iteration method for approximating the waiting-time characteristics of the GI/G/1 queue.
  Probability in the Engineering and Informational Sciences, vol. 3, 1989, pp. 273-287.
• I.J.B.F. Adan, M.J.A. van Eenige, J.A.C. Resing:
  Fitting discrete distributions on the first two moments.
  Probability in the Engineering and Informational Sciences, Vol. 9, 1995, pp. 623-632.