Dr Małgorzata O'Reilly, University of Tasmania, Australia
Continuous-time Markov Chains (CTMCs) are the key class of stochastic models used to analyse the evolution of industrial, environmental and biological systems. We use CTMCs to model the transitions between the various states of an underlying physical environment of interest.
Stochastic Fluid Models (SFMs) extend this modelling potential by including an extra variable in the model, referred to as the level, which is used to model some continuous performance measure of the system. The literature on the standard SFMs, which are one-dimensional in level (i.e. have one level variable), is well-developed and includes theoretical results and algorithms for the stationary (long-run) as well as transient (time-dependent) analysis.
My recent interest has been in extending the modelling potential of the SFMs even further, by considering possibilities such as having more than one level variable, or letting the parameters of the SFMs vary in time.
In this talk, I will describe the recent advances in the area of two-dimensional SFMs, and SFMs with cyclic parameters, which offer powerful modelling ability for a wide range of real-life systems of significance.