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Małgorzata O'Reilly


Małgorzata O'Reilly's homepage

Associate Professor Małgorzata O'Reilly
Discipline of Mathematics
Room: 455
Phone: +61 3 6226 2405
Fax: +61 3 6226 2410

My Curriculum Vitae

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.

Honours: here     PhD: here  

My research interests: 

stochastic modeling, matrix-analytic methods, applied probability, healthcare modeling, and phylogenetics

Images of some interesting work by my students:

Matrix-analytic methods: kma306 kma306   Operations Research: kma355 kma355    Probability Models: kma305

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.

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.

Selected conference talks:

2020 - AustMS Meeting - 8-11 December 2020, Special session: Probability theory and stochastic processes.      my talk

2020 - Phylomania - The Twelfth Theoretical Phylogenetics Meeting at UTAS, November 25-27.      my talk

2019 - MAM10 - The Tenth International Conference on Matrix-Analytic Methods in Stochastic Models.      my talk

2017 - AP@Rock - An International Workshop To Celebrate Phil Pollett's 60th Birthday, April 17-21, Ayers Rock Resort.      my talk

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

2012 - ANZAPW - Australia and New Zealand Applied Probability Workshop, January 23–27, Auckland, NZ.     my talk    

2011 - MAM 7 - Seventh International on Matrix Analytic Methods in Stochastic Models, June 13–16, New York, USA.     my talk   

Selected publications:

Journal Articles:

  •  Battula, S.K., O'Reilly, M.M., Garg, S., Montgomery, J. A Generic Stochastic Model for Resource Availability in Fog Computing Environments. IEEE Transactions on Parallel and Distributed Systems, 32(4),9253552, pp. 960-974, 2021.
  • Heydar, M., O’Reilly, M.M., Trainer, E., (...), Taylor, P.G., Tirdad, A. A stochastic model for the patient-bed assignment problem with random arrivals and departures. Annals of Operations Research, Article in Press.
  • Abera, A.K., O’Reilly, M.M., Fackrell, M., Holland, B.R., Heydar, M. On the decision support model for the patient admission scheduling problem with random arrivals and departures: A solution approach. Stochastic Models, 36(2), pp. 312-336, 2020.
  • M.M. O'Reilly, W. Scheinhardt. Stationary distributions for a class of Markov-modulated tandem fluid queues. Stochastic Models, 33(4), pp. 524-550, 2017. 
  • A. Samuelson, A. Haigh, M.M. O'Reilly, N.G. Bean. On the generalized reward generator for stochastic fluid models: a new equation for Psi. Stochastic Models, 1-29, 2017.
  • T.L. Stark, D.A. Liberles, B.R. Holland, M.M. O'Reilly. Analysis of a mechanistic Markov model for gene duplicates evolving under subfunctionalization. BMC Evolutionary Biology, 17(38):1-16, 2017.
  • B. Margolius, M.M. O'Reilly. The analysis of cyclic stochastic fluid flows with time-varying transition rates. Queueing Systems, 82(1-2):43-73, 2016.
  • 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.
  • M.M. O'Reilly and Z. Palmowski. Loss rate for stochastic double fluid models. Performance Evaluation, 70 (9):593-606, 2013.
  • N.G. Bean and M.M. O'Reilly. Stochastic Two-Dimensional Fluid Model. Stochastic Models, 29(1): 31-63, 2013.
  • 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.



Personal interests:
music et al.