MATLAB

• Available on computers in IEOR Computer Lab, 301 Mudd

  an online tutorial

Numerical Transform Inversion

• Papers on inversion

  • Joseph Abate and Ward Whitt, Numerical Inversion of Laplace Transforms of Probability Distributions. ORSA Journal on Computing, vol. 7, 1995, pp. 36-43. [PDF]

  • Joseph Abate, Gagan L. Choudhury and Ward Whitt, An Introduction to Numerical Transform Inversion and its Application to Probability Models, in Computational Probability, W. Grassman (ed.), Kluwer, Boston, 1999, pp. 257-323 (with ). [PDF]

  • Joseph Abate and Ward Whitt, Numerical Inversion of Probability Generating Functions. Operations Research Letters, vol. 12, No. 4, 1992, pp. 245-251. [PDF]

  • Gagan L. Choudhury, David M. Lucantoni and Ward Whitt, Multi-Dimensional Transform Inversion with Applications to the Transient M/G/1 Queue. Annals of Applied Probability vol. 4, 1994, pp. 719-740. [PDF]

  • For more related material, see my papers with Joe Abate and my papers with Gagan Choudhury

• Programs

  Markov Chain Tools

  • Examples of transition matrices constructed in MATLAB:

    • two-state example (in PDF)

    • six-state example (in PDF)

    • magic-square example (in PDF)

      (doubly stochastic example)

    • five-state example (in PDF)

      (classifying states)

    • seven-state example (in PDF)

      (classifying states)

  • Markov Chain Programs and Data for MATLAB:

    • (stationary) Markov Mouse Example (PDF) (See Class Lecture Notes for 7/14.)

      Markov Mouse data (to use as input to MATLAB using load command)

      stationary vector MATLAB programs: stat.m (PDF version) and stationary.m (PDF version)

      Escaping Mouse Example(PDF)

      Escaping Mouse Q data (to use as input to MATLAB)

      Escaping Mouse R data (to use as input to MATLAB)

      absorbing Markov chain MATLAB program: absorbing.m (PDF version)

      six-state periodic chain example (PDF)

      data for six-state periodic example (to use as input to MATLAB)

  MATLAB Programs for the Erlang A model (M/M/s/r+M):

  • MMsrMa.m (main program)

    inversion2.m (function required by MMsrMa.m, does inversion)

    laplace2.m (function required by MMsrMa.m, defines the transform)