Course outline from week to week:

    1 Numerical solution of equilibrium equations: direct methods link
      Numerical solution of equilibrium equations: iterative methods link
      Lecture 1 slides: link
    2 Markov processes link
      Transient analysis of Markov processes link
      Lecture 2 slides: link
    3 M/M/1 type models link
      Examples of M/M/1 type models link
      Lecture 3 slides: link
    4 G/M/1 type models link
      G/M/1 type models with linear rates link
      Lecture 4 slides: link
    5 Finite level dependent QBDs link TBA
      Examples from spare parts management and traffic link TBA
      Lecture 5 slides: link
    6 Queueing models with multiple waiting lines - Indirect methods link
      The boundary value method link
      The kernel method link link link
      Numerical inversion of probability generating functions link
      Dominant pole approximation link
      Lecture 6 notes: link
    7 Queueing models with multiple waiting lines - Indirect methods cont'd
      The uniformization method, Wiener-Hopf factorization link
      The 2x2 switch link
      Lecture 7 notes: link
    8 Queueing models with multiple waiting lines - Direct methods link
      The compensation approach method link (chapter 2)
      Connection of the matrix geometric approach, the kernel method, and the compensation approach link
      Lecture 8 notes: link
    9 General intro to PSA for 1D MC link
      General intro to PSA for multi-D MC link
      Convergence and variations of the PSA link
      Exact analysis of finite MC with PSA link
      PSA and the SQ model link
      Lecture 9 notes: link


    References:

    1. ◘ J. Van der Wal, P.J. Schweitzer: Iterative bounds on the equilibrium distribution of a finite Markov chain, Probability in the Engineering and Informational Sciences, vol. 1, 1987, pp. 117-131.
    2. ◘ M.F. Neuts: Matrix-geometric solutions in stochastic models: an algorithmic approach, Johns Hopkins University Press, 1981.
    3. ◘ V. Ramaswami: Algorithmic analysis of stochastic models; The changing face of Mathematics. Ramanujan Endowment Lecture at Anna University, Chennai, India, 2000.
    4. ◘ V. Ramaswami, G. Latouche: A general class of Markov processes with explicit matrix-geometric solutions. OR Spektrum, vol. 8, 1986, pp. 209-218.
    5. ◘ G. Latouche, V. Ramaswami: A logarithmic reduction algorithm for quasi-birth-death processes. J. Appl. Prob., vol. 30, 1993, pp. 650-674.
    6. ◘ G. Latouche, V. Ramaswami: Introduction to matrix analytic methods in stochastic modeling, Philadelphia, SIAM, 1999.
    7. ◘ 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.
    8. ◘ 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.
    9. ◘ 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.