Algorithmic Methods in Queueing Theory

Meetings:
Instructor:	Ivo Adan
	office:	HG 9.07
	telephone:	247 29 32
	e-mail:	iadan@win.tue.nl
Office Hours:	when I am in
Text:	A class of Markov processes on a semi-infite strip
	A queueing model with locking
	The shortest queue problem
	Analysis of the Ek|Er|c queue
Slides:	A class of Markov processes on a semi-infite strip
	A multi-server queueing model for train maintenance
Computer programs:	C-routine Gaussian elimination
Examination:	Take home assignments

Assignments:

#1

Course outline from week to week

1. Numerical solution of equilibrium equations: direct methods (updated 08-02-2006)
2. Numerical solution of equilibrium equations: iterative methods (updated 08-02-2006)
3. Markov processes
   Transient analysis of Markov processes
4. Examples of M/M/1 type models
5. M/M/1 type models
   G/M/1 type models
6. G/M/1 type models with linear rates
7. M/G/1 type models
8. Single-server models
9. Multi-server models

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.