PhD student Halldora Thorsdottir of CWI has developed new theorems for probabilistic systems which are influenced by a random environment, such as biological cell mechanisms or data transfer over the internet. She defends her thesis ‘Limit theorems for Markov-modulated queues’ on Friday 13 May at the University of Amsterdam (UvA).
In her thesis, Thorsdottir focuses on the performance of such doubly stochastic systems at the system limits. Imagine an ice cream parlour at the beach. Sales are heavily influenced by random events in terms of weather, making it very hard to predict sales on a specific day in the future. However, if you zoom out on a larger time scale of months or even years, you can recognize patterns and make useful approximations. Thorsdottir shows that scaling of systems in a random environment to the extreme will eventually produce known probability distributions such as a normal or exponential distribution.
The results of this research are applicable in various contexts where random events are involved, such as the production of molecules in a biological cell or logistic tasks involving queues. This research is funded by CWI via NWO in 2010, with additional funding from Korteweg-de Vries Institute of the University of Amsterdam.
Image: Thesis cover. Impression of a system influenced by a random environment, based on Turing patterns. Bouwe van der Molen, 2016.