A continuous-time Markov chain is a probabilistic model that is successful at describing the
uncertain time evolution of various systems. Since it is also quite simple to make predictions about
its future behaviour, it has become a very popular tool in a large range of applied domains, including
engineering, artificial intelligence, mathematical finance, bio-informatics and queueing. However,
when the dimensions of the model are too large, computations become intractable to perform. This
limits its practical use to applications of a limited scale.
During the last year, it has been discovered that this problem can be solved by using an imprecise
continuous-time Markov chain. Simply put, this is a specific collection of smaller models whose
common conclusions are guaranteed to be compatible with the original large-scale model. By
performing computations for all of these smaller models simultaneously, it becomes feasible to
compute reliable inferences for large-scale models.
Unfortunately, imprecise continuous-time Markov chains are not yet sufficiently developed to be
able to fully exploit this discovery. In particular, performing computations with them is currently
only feasible for a fairly limited class of inferences. This project aims to develop the required
mathematical and algorithmic foundations for dealing with the more advanced inferences that are
typically needed in practical applications, and to apply them to large-scale queueing models.