Stochastic fluid flow models and their applications in industrial and environmental systems
Stochastic fluid models are a class of models with a two-dimensional state-space consisting of a phase and a level. The phase variable is often used to describe the state of some physical environment that we want to model. Simple two-phase examples are on/off mode of a switch in a telecommunications buffer, peak/off-peak period in a telephone network, or wet/dry season in reservoir modeling. The model assumes that the transitions between phases occur according to some underlying continuous-time Markov Chain. Furthermore, the rate of increase of the fluid level at time t depends on the phase at time t, and so the Markov Chain is the process that drives the fluid level at time t. For example, in reservoir modeling, when the phase is dry, the fluid level in the reservoir is decreasing at some rate, due to the consumption of the water. Alternatively, when the phase is wet, the fluid level in the reservoir is increasing.
Although a rapid development of the area has been observed in recent years, the transfer of the theoretical results to applications still needs work. The models have tremendous application potential in many areas, well beyond telecommunications, from which they emerged. These encompass all areas of industry, including insurance and manufacturing/management systems, as well as environmental problems, such as coral modeling and water management, as examples. The aim of the project is to explore this potential and originate some application ideas. Work will involve modeling, analysis of the models, construction of numerical methods and programming.
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