This project aims at developing provably efficient techniques for the simulation of rare events in non-Markovian queueing networks, motivated by the need to accurately estimate failure probabilities in practical systems. This project will move into an unexplored area of stochastic discrete-event simulation, and is challenging as it is a novel combination of three aspects: the non-Markovian nature of the systems, the study of networks of queues rather than single queues, and the aim of achieving provably efficient results. These three aspects have been studied separately before, but not in combination. This project follows the importance sampling approach, in which a so-called change of measure is applied to make the event of interest less rare, and aims for three major advances:
(i) establishment of relations between non-Markovian queueing networks and other problems;
(ii) strategies to decide when and how the change of measure needs to be state-dependent;
(iii) construction of good changes of measure with efficiency proofs.
The proposed research is highly relevant - because most realistic models are non-Markovian - and timely in the sense that comparable advances for the Markovian-network case have been obtained only recently, and study of the non-Markovian case constitutes a natural, yet highly challenging, next step.