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Małgorzata O'Reilly


Małgorzata O'Reilly's homepage



Dr Małgorzata O'Reilly
Discipline of Mathematics
Room: 455
Phone: +61 3 6226 2405
Fax: +61 3 6226 2410
Email: Malgorzata.OReilly@utas.edu.au

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  


Summer Research/Honours/PhD: Stochastic Models for the Conservation of Endangered Species project

  



My research interests: 

stochastic modeling, matrix-analytic methods, applied probability, healthcare modeling, MODIS satellite data analysis, and phylogenetics.


SMMP 2015
Stochastic Modelling meets Phylogenetics
collaborative workshop 16-18 Nov 2015



Teaching duties:


Discrete Mathematics with Applications 1 (KMA155)  (semester 2)


Operations Research 2 (KMA255)      (semester 1)     Operations Research 3 (KMA355)    (semester 2)

 

Probability Models 3 (KMA305)    (semester 1)    Stochastic Modelling and Applications 3 (KMA306)   (semester 1)



Images of some interesting work by students:


KMA306: kma306 kma306   KMA355: kma355 kma355    KMA305: kma305
         

 

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.

OR skills are applied in a wide range of areas, including Accounting, Actuarial Work, Computer Services, Corporate Planning, Economic Analysis, Financial Modelling, Industrial Engineering, Investment Analysis, Logistics, Manufacturing Services, Management Services, Management Training, Market Research, Operations Research, Planning, Production Engineering, Quantitative Methods, Strategic Planning, Systems Analysis, Transport Economics. For more information about OR and career opportunities see  
About Operations Research (INFORMS)     Career in Operations Research (ASOR) 
OR classifieds - international (INFORMS)
    Job opportunities in Mathematical Sciences (AMS)    
Mathematics in Industry Study Group (MISG)
     ANZIAM Journal               



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

2013 - Charles Pearce Memorial Symposium    

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    Postcards from NY  

2007 - 14-th INFORMS/APS Conference July 9-11, Eindhoven, Netherlands.

2005 - MAM 5 - Fifth International Conference on Matrix Analytic Methods in Stochastic Models, June 21–24, Pisa, Italy.

2004 - 12-th INFORMS/APS Conference June 23-25, Beijing, China.


Postdoctoral Research Supervision:


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





Publications:


Journal Articles:

  1. B. Margolius, M.M. O'Reilly. The analysis of cyclic stochastic fluid flows with time-varying transition rates. Queueing Systems, in print, 2015.
  2. 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.
  3. 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.
  4. M.M. O'Reilly. Multi-stage stochastic fluid models for congestion control. European Journal of Operational Research, 238 (2) pp. 514-526, 2014.
  5. 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.
  6. 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.
  7. M.M. O'Reilly and Z. Palmowski. Loss rate for stochastic double fluid models. Performance Evaluation, 70 (9):593-606, 2013.
  8. N.G. Bean and M.M. O'Reilly. Stochastic Two-Dimensional Fluid Model. Stochastic Models, 29(1): 31-63, 2013.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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:

  1. 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.
  2. 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.
  3. 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:

  1. 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:

  1. 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.
  2. Masters thesis:  "A hypothesis by Derman, Lieberman and Ross", Wroclaw University, 1987. Supervisor: Prof Tomasz Rolski.

 

Personal interests:
music et al.