Assoc. Professor Malgorzata O'Reilly

Małgorzata received her MSc degree in Mathematics and Education from Wroclaw University in 1987. She completed her MSc thesis in the area of reliability of linear consecutive systems under the supervision of the esteemed Prof Tomasz Rolski, which has sparked her long-term interest in the probability theory. She then received her PhD degree in applied probability from the University of Adelaide in 2002. Her PhD thesis supervisor was the esteemed Prof Charles Pearce. Later, she completed her postdoc at the Teletraffic Research Centre at Adelaide University, working as a Research Associate on an ARC Discovery project, with Profs Peter Taylor and Nigel Bean in the area of matrix-analytic methods (MAMs). She has been a lecturer in probability, operations research, stochastic modelling and discrete mathematics at the University of Tasmania since 2005.

She is the member of the Steering Committee of the MAMs Conferences and has chaired and organised the MAM10 conference Hobart in 2019. She has been an Editor of the MAM10 conference proceedings, and on the Editorial Board of the Special Issue devoted to MAM10 in Stochastic Models.

Małgorzata is one of the key contributors to MAMs, in particular to the theory of stochastic fluid models (SFMs), a class of Markovian modulated models with a state consisting of a discrete phase variable driven by a Markov chain and a continuous level variable with rates of change modulated by this chain. She has constructed direct methods (which do not require mapping to other models such as QBDs) of the analysis of the SFMs [1], and algorithms for the computation of transient/stationary/quasi-stationary quantities in the context of various classes of SFMs (multi-layer, bounded, multi-stage, cyclic, and so on) [2, 3]. She has introduced her idea of two-dimensional SFMs [4-6] which further extend the modelling potential of SFMs and has recently derived matrix-analytic methods that enabled their numerical analysis with ease for the first time [6-8].

Małgorzata has keen interest in developing theory as well as applications of applied probability to modelling and analysis of complex systems (e.g. evolution of species, evolution of gene families, smart traffic, healthcare systems, mobile networks).

She is leading a multidisciplinary team in modelling and optimisation of healthcare systems, in collaboration with the Tasmanian Department of Health.

Selected references:

[1] N. G. Bean, M. M. O'Reilly, and P. G. Taylor. Hitting probabilities and hitting times for stochastic fluid flows. Stochastic Process. Appl., 115(9):1530-1556, 2005.

[2] N. G. Bean, M. M. O'Reilly, and P. G. Taylor. Algorithms for the Laplace-Stieltjes transforms of first return times for stochastic fluid flows. Methodol. Comput. Appl. Probab., 10(3):381-408, 2008.

[3] B. Margolius and M. M. O'Reilly. The analysis of cyclic stochastic fluid flows with time-varying transition rates. Queueing Systems, 82(1-2):43-73, 2016.

[4] N. G. Bean and M. M. O'Reilly. A stochastic two-dimensional fluid model. Stochastic Models,29(1):31-63, 2013.

[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 Process. Appl., 124(5):1741-1772, 2014.

[6] M. M. O'Reilly and W. Scheinhardt. Stationary distributions for a class of markov-modulated tandem fluid queues. Stochastic Models, 33(4):524-550, 2017.

[7] N. G. Bean, M. M. O'Reilly, and Z. Palmowski. Matrix-analytic methods for the analysis of stochastic fluid-fluid models. arXiv:2010.13077.

[8] M. M. O'Reilly, Z. Palmowski, and A. Aksamit. Random walk on a quadrant: Mapping to a one-dimensional level-dependent Quasi-Birth-and-Death process. Close to submission.