Better uncertainty models that more accurately predict, for example, spread of infectious diseases

(06-10-2021) In his PhD, Alexander Erreygers brings solutions for making uncertainty models better.

"In engineering applications, we often model things -- systems -- whose state evolves over time in an uncertain way. One popular type of models are Markovian jump processes, which can serve as models for a wide range of systems: from the checkout line at a supermarket to the spread of an infectious disease in a population. We use these models to calculate relevant performance measures, such as the expected time until no one is infected," Alexander explains.

However, despite their popularity, Markovian jump process models suffer from three problems: first, it is often not possible to precisely determine the characterizing parameters of these models, second, the systems we want to model often do not actually satisfy the underlying (mathematical) assumptions, and third, the number of states of these models is so large that we cannot calculate the relevant performance measures within an acceptable time.

"In my dissertation, I reach a solution to these three problems," Alexander explains.

The first two problems are solved by generalizing Markovian jump processes to Markovian imprecise jump processes. The generalization consists of no longer requiring that the characterizing parameters be given exactly - but, for example, by bounds — and by weakening the underlying mathematical assumptions.

"In the first part of my dissertation, I sensitively extend the existing theory of Markovian imprecise jump processes. Previously, this theory was limited to performance measures that depend on the state of the system in a finite number of time points — for example, the expected number of infected people tomorrow afternoon at four o'clock— but I have extended this theory to more general performance measures — for example, the expected time average of the number of infected people over a week or the expected time until no one is infected anymore."

"In the second part of my dissertation, I solve the third problem of Markovian jump processes: I show that, in a Markovian jump process model whose number of states is too large, we can accumulate states to arrive at a Markovian imprecise jump process model with many fewer states, and that with this smaller model we can compute bounds on the relevant performance measures that we could not otherwise compute within an acceptable time. In particular, I use this technique to look at spectrum fragmentation in an optical cable," Alexander concludes.

PhD Title: Markovian Imprecise Jump Processes: Foundations, Algorithms and Applications

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Read the entire PhD

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Contact:  Alexander ErreygersJasper De Bock (promotor), Gert De Cooman (promotor), Herwig Bruneel (promotor)

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Editor: Jeroen Ongenae - Illustrators: Roger Van Hecke and Paulien Verheyen