Prospective
students:
If you are interested in post-graduate study
under my supervision, feel welcome to contact me
to discuss possibilities. Please refer to the
examples of topics below.

Operations Research 2 (KMA255) and Operations
Research 3 (KMA355) – these Operations Research
(OR) units develop skills in the analysis,
evaluation and optimization of real-life systems
using deterministic or probabilistic methods,
which are essential for careers in Engineering,
Management, Finance, and Economics. The applied,
meaningful context of these units means that
they are also highly advantageous for careers in
Teaching.

KMA305 – this (Probabilistic) OR unit develops
skills that are essential in constructing models
for the analysis and performance assessment of
real-life systems with element of uncertainty,
which, since unpredictability is the common
feature of many real-life systems of great
significance, are essential for careers in the
Physical and Biological Sciences, Engineering,
Computer Science, Finance, and Economics.

KMA306 – this (Probabilistic) OR
unit is an introduction to modern methods of
stochastic modeling with the focus on
applications in real-life systems, essential for
careers in the Physical and
Biological Sciences, Engineering, Computer
Science, Finance, and Economics.

Operations
research is an interdisciplinary
mathematical science that focuses on the
application of advanced analytical methods to
help make better decisions. Operations Research
methods are used in modelling a wide range of
industrial, environmental, and biological
systems of significance. Its latest technologies
use methods drawn from Probability, Optimization
and Simulation. Operations Research
is a highly
sought-after field of expertise by
industry, which contributes millions of dollars
in benefits and savings each year.

Stochastic Modeling is a research area
within Operations Research that focuses on
developing probabilistic models for real-life
systems having an element of uncertainty. The
work involves constructing useful models,
analyzing them analytically, deriving
mathematical expressions for various important
performance measures, and building efficient
algorithms for their numerical evaluations. Markov
Chains is the most important class of
stochastic models due to their powerful modeling
features, numerical tractability, and
applicability to a wide range of real-life
systems of great engineering or environmental
significance. A Markov Chain, named for Andrey
Markov, is a mathematical system that undergoes
transitions from one state to another, between a
finite or countable number of possible states.
It is a random process characterized as
memoryless, as the next state depends only on
the current state and not on the sequence of
events that preceded it. This specific kind of
"memorylessness" is referred to as the Markov
property.

My current fun:
Markovian-modulated Stochastic 2-Dimensional
Models

Markovian-modulated
models are built on the concept of
Markov Chains. Their state space is
two-dimensional and consists of the phase
variable i(t) and the level
variable X(t). Phase is used to model the
state of some real-life environment, while
level is used to model its performance measure
at time t. The phase changes according to some
underlying Markov Chain. The rate at which the
level changes at time t depends on the current
phase i(t). For example, in modelling of a
telecommunications buffer, the phase may
represent the operating switch, while the
level may be the amount of data in the buffer.
The rate at which the buffer empties of fills
in, depends on which switch is on.

Markovian-modulated models have attracted a
lot of interest due to their applicability to
a wide range of real-life systems of great
engineering or environmental significance,
well beyond applications in high-speed
telecommunications systems, from which
they were originally derived. Very
interesting results for this class of models
have been obtained in recent years. My recent
interest is in 2-dimensional models. The
applications of these include ad-hoc mobile
networks, the process of coral bleaching,
operation of hydro-power generation, amongst
other examples. I am interested in
constructing useful models, analyzing them
analytically, deriving mathematical
expressions for various important transient
and stationary performance measures and
building efficient algorithms for their
numerical evaluations.

Experience:

During my Masters and PhD research, 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, as well as 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.

In recent years, I have been involved in
research in matrix-analytic models. This work
resulted in interesting contributions to the
development of fluid flow models, which is a
class of Markov-driven stochastic models. My
contributions include:

·development
of
expressions for various performance measures
and their physical interpretations,

·construction
of
several fast algorithms to evaluate these
performance measures,

·comparison
of
algorithms
with respect to their physical
interpretations, convergence rates, number of
iterations, complexity, and suitability for
analysis,

·treatment
of bounded and unbounded level-independent
models,

·analysis
of
fluid models with an element of
level-dependence,

·some
work on multi-dimensional fluid models.

I gave an 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 in 2004. To see the
slides from this talk, click here.

Apart from my research interests in
matrix-analytic methods, I am currently involved
also in collaborations in healthcare modeling,
change detection using MODIS satellite data
analysis, and phylogenetics.

Grants:

ARC LP140100152
2014-2017
Modeling Healthcare Systems
with Dr Mark Fackrell, Prof Peter G Taylor, Prof
Donald A Campbell; Mr Keith A. Stockman; Mr Simon
P. Foster
$410,000 plus industry contributions

ARC Discovery Project DP110101663
2011-2013
Advanced matrix analytic methods with applications
with Prof Peter G Taylor, Prof Nigel G Bean, Dr
Sophie M Hautphenne, Dr Mark W Fackrell, Prof Guy
G Latouche
$600,000

Australian Research Council (ARC) Discovery
Project DP0770388
2007-2009
The Use of stochastic fluid models for the
evaluation of applications-driven sample path
integrals
with Prof Nigel Bean
$198,000

Conferences:

2015 - ANZAPW
- Australia and New Zealand Applied Probability
Workshop, July 8-11, Adelaide.

2013 - ANZAPW
- Australia and New Zealand Applied Probability
Workshop, July 8-11,
Brisbane. my talk

2008-2010 - Dr Ren Yong (currently a Professor in
the Department of Mathematics at the Anhui Normal
University)

Publications:

Journal Articles:

B.
Margolius, M.M. O'Reilly. The analysis of
cyclic stochastic fluid flows with
time-varying transition rates. Queueing
Systems, in print, 2015.

A.
Anees, J. Aryaj, M.M. O'Reilly, T. Gale. A
Relative Density Ratio-Based Framework for
Detection of Land Cover Changes in MODIS
NDVI Time Series. IEEE Journal of
Selected Topics in Applied Earth
Observations and Remote Sensing,
vol.99, pp. 1-13, 2015.

Ashley
Teufel, Jing Zhao, Malgorzata O'Reilly,
Liang Liu, David Liberles. On Mechanistic
Modeling of Gene Content Evolution:
Birth-Death Models and Mechanisms of Gene
Birth and Gene Retention. Computation,
Computational Biology section,
special issue ``Genomes
and Evolution: Computational Approaches'',
2:112-130, 2014.

M.M.
O'Reilly.
Multi-stage
stochastic fluid models for congestion
control. European Journal of Operational
Research, 238 (2) pp. 514-526, 2014.

N.G.
Bean
and M.M. O'Reilly. The Stochastic
Fluid-Fluid Model: A Stochastic Fluid Model
driven by an uncountable-state process,
which is a Stochastic Fluid Model itself. Stochastic
Processes and Their Applications, 124
(5) pp. 1741–1772, 2014.

N.G.
Bean
and M.M. O'Reilly. Spatially-coherent
Uniformization of a Stochastic Fluid Model
to a Quasi-Birth-and-Death Process. Performance
Evaluation, 70 (9):578-592, 2013.

M.M.
O'Reilly and Z. Palmowski. Loss rate for
stochastic double fluid models. Performance
Evaluation, 70 (9):593-606, 2013.

N.G.
Bean,
M.M. O'Reilly and Yong Ren. Second-order
Markov Reward Models driven by QBD
Processes. Performance
Evaluation 69(9): 440-445, 2012.

N.G.
Bean,
M.M. O'Reilly and J. Sargison. Stochastic
fluid flow model of the operations and
maintenance of power generation systems. IEEE
Transactions on Power Systems, 25
(3): 1361-1374, 2010.

N.G.
Bean,
M.M. O'Reilly and P.G. Taylor. Hitting
probabilities and hitting times for
stochastic fluid flows: the Bounded Model. Probability in
the Engineering and Informational Sciences,
23 (1): 121-147, 2009.

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. Annals of
Operations Research, 160 (1):
99-120, 2008.

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. Methodology and Computing in
Applied Probablility, 10 (3):
381-408, 2008.

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.

Research
Book Chapters:

M.
O’Reilly. Optimal design of linear
consecutive k-out-of-n systems. Springer
Optimization and Its Applications, Springer,
C Pearce and E Hunt (ed), New York, pp.
307-326, 2009.

M.
O’Reilly. The (k+1)-th component of linear
consecutive-k-out-of-n systems. Springer
Optimization and Its Applications, Springer,
C Pearce and E Hunt (ed), New York, pp.
327-342, 2009.

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.

Refereed
Conference Articles:

Anees,
A and Olivier, JC and O'Reilly, MM and
Aryal, J, “Detecting beetle infestations
in pine forest using MODIS NDVI
time-series data”, IEEE International
Geoscience and Remote Sensing Symposium
Proceedings (IGARSS 2013), 21-26 July
2013, Melbourne, Australia, pp. 3329-3332,
2013.

Theses:

PhD
thesis: "Necessary conditions for the
optimal design of linear consecutive
systems", University of Adelaide, October
2002. Supervisor: Prof
Charles E.M. Pearce. Also, see Adelaidean
2002.