Grünbaum, Alberto F.
QBD processes and matrix orthogonal polynomilas: somw new explicit examples
Abstract
In the case of birthanddeath processes
there are a few exactly solvable
situations where the nstep transition
matrix can be written down using the
KarlinMcGregor formula. A few of these
come from group representation theory.
I plan to show how this can be extended
to some instances of QBD processes with an
arbitrary finite number of phases. The group
involved is the set of all unitary
matrices of size N. For a fixed N one gets
examples where the number of phases is
a free parameter, and there are a few extra
parameters to play with. By tunning
these parameters
one can exhibit examples where states
are recurrent or transient.
The rather surprising fact that for these
examples one can compute everything
explicitly raises the issue of finding
a possible network application
for this piece of
mathematics that involves matrix
valued orthogonal polynomials.
I will give an abinitio discussion of
the examples starting with the case of one phase.
BibTeX  Entry
@InProceedings{grnbaum:DSP:2008:1392,
author = {Alberto F. Gr{\"u}nbaum},
title = {QBD processes and matrix orthogonal polynomilas: somw new explicit examples},
booktitle = {Numerical Methods for Structured Markov Chains},
year = {2008},
editor = {Dario Bini and Beatrice Meini and Vaidyanathan Ramaswami and MarieAnge Remiche and Peter Taylor},
number = {07461},
series = {Dagstuhl Seminar Proceedings},
ISSN = {18624405},
publisher = {Internationales Begegnungs und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2008/1392},
annote = {Keywords: QBD, orthogonal polynomials, KarlinMcGregor formula, representation theory}
}
Keywords: 

QBD, orthogonal polynomials, KarlinMcGregor formula, representation theory 
Seminar: 

07461  Numerical Methods for Structured Markov Chains

Issue date: 

2008 
Date of publication: 

07.04.2008 