Dr Małgorzata O'Reilly
School of Mathematics and Physics
Room: 460
Phone: +61 3 6226 2405
Fax: +61 3 6226 2410
Email: Malgorzata.OReilly@utas.edu.au
Teaching duties:
Operations Research 2
Interesting
things that I do (apart from teaching):
Markovian Fluid Models
In a Markovian fluid
model, a container of fluid is filled/emptied
at a rate that depends on the state of an underlying Markov chain. The
state space is two-dimensional and consists of the
level
variable (the fluid level in the buffer) and the
phase
variable (the state of the
underlying Markov chain). This model has attracted a lot of interest
due to its applicability in the analysis of real-world systems such as,
for example, high-speed communication networks. Very interesting
results for this model have been obtained in the recent five years.
Below is a simple example of a two-phase model (models with any finite
number of phases are studied).
Experience:
In my early career, I made contributions to the theory of optimal
design and reliability of linear consecutive systems. This class of
systems is applicable throughout industry, including, for example,
telecommunications, mining, space exploration and medicine.
Specifically, I have developed several necessary conditions for the
optimal design of linear consecutive-k-out-of-n systems and procedures
to improve designs not satisfying these conditions. I have developed
novel results for variant optimal designs, a type of optimal design
that is particularly difficult to treat. Both my Master and PhD theses
were in the area of linear consecutive systems.
In 2001, I gave two presentations on linear consecutive-k-out-of-n
systems at the Optimization Day at the 16th National Conference of the
Australian Society for Operations Research (ASOR). To see the slides
from these presentations, click here, and
then here.
Recently, I have been involved in research in matrix analytic models,
in collaboration with Profs Nigel Bean (The University of Adelaide) and
Peter Taylor (The University of Melbourne). This work resulted in
interesting contributions to the development of fluid flow models, a
class of models which can be used to model high-speed
telecommunications systems. This has led, so far, to:
·
the
development of new
performance
measures and formulae, including their physical interpretations,
·
the
construction of new
algorithms to
evaluate the performance measures,
·
the
comparison of
several known
algorithms and these introduced algorithms with respect to their
physical
interpretations, convergence rates, number of iterations, complexity,
and
suitability for analysis, depending on the nature of the process,
·
the
treatment of bounded
as well as
unbounded level-independent models,
·
the analysis
of fluid
models where an
element of level-dependence has been introduced.
In 2004, I gave av invited talk on Fluid Models at the Tutorial
Workshop on Matrix-Analytic Methods for Stochastic Modelling, organized
by ARC Centre for Excellence for Mathematics and Statistics of Complex
Systems in Melbourne. To see the slides from this talk, click
here.
Book chapters:
- M. O’Reilly. Variant optimal
designs of linear
consecutive-k-out-of-n systems. In: Industrial Mathematics and Statistics, J.C.
Misra , editor, Narosa Publishing House, New Delhi, 486—502, 2003.
- M. O’Reilly. Optimal design of
linear
consecutive-k-out-of-n systems. Presented at the Optimization Day, 27 September 2001, Adelaide, Australia. To appear in: Optimization:
Theory and Application. Springer.
C.E.M. Pearce and E. Hunt,
editors. Accepted 07/02/2003.
- M. O’Reilly. The (k+1)-th
component of linear
consecutive-k-out-of-n systems. Presented at the Optimization Day, 27 September 2001, Adelaide, Australia. To appear in: Optimization:
Theory and Application. Springer.
C.E.M. Pearce and E. Hunt,
editors. Accepted 07/02/2003.
Journal articles:
- N.G.
Bean, M.M.
O'Reilly and P.G. Taylor. Hitting
probabilities and hitting times for stochastic fluid flows. Stochastic
Processes and Their Applications 115(9): 1530-1556, 2005.
- N.G.
Bean, M.M.
O'Reilly and P.G. Taylor. Algorithms for
the first return probabilities for stochastic fluid flows. Stochastic
Models 21(1): 149-184, 2005.
- N.G. Bean
and M.M.
O'Reilly. Hitting
probabilities and hitting times for stochastic fluid flows in the
bounded model. Submitted.
- N.G. Bean
and, M.M.
O'Reilly. N.G. Bean and M.M. O'Reilly. Performance measures of a
multi-layer Markovian fluid model. To appear in Annals of Operations Research.
Accepted 8/08/2007.
- N.G.
Bean, M.M.
O'Reilly and P.G. Taylor. Algorithms for
the Laplace-Stieltjes transforms of the first return probabilities for
stochastic fluid flows. To appear in Methodology & Computing in Applied
Probability.
Accepted 18/10/2007.
- N.G.
Bean, M.M.
O'Reilly and J. Sargison. Stochastic fluid flows for operation and
maintenance of hydro-power generators. In preparation.
- A.E.R.
Helfgott, N.G.
Bean, S. Connolly, A. Baird and M.M. O’Reilly. Modelling the resilience
of coral reefs to global climate change: A stochastic fluid model of
the adaptive bleaching hypothesis on the great barrier reef. In
preparation.
Theses:
- PhD thesis: "Necessary conditions for the optimal
design of
linear consecutive systems", University of Adelaide, October 2001.
- Masters
thesis:
"A hypothesis by Derman, Lieberman and Ross", Wroclaw University, 1987.
