Subventions et des contributions :

Subvention ou bourse octroyée s'appliquant à plus d'un exercice financier. (2017-2018 à 2022-2023)

In today's technologically advanced world, the study of network reliability is very important. Many different reliability models have been developed to represent a variety of desired network properties. These models fall into one of two categories: coherent or non­-coherent reliability systems.

In this proposed research I will investigate specific reliability models from both categories, with the purpose of understanding the properties of general coherent and non-coherent reliability systems. The goals of the proposed research are as follows:

1) To deepen our understanding of the behaviour of the reliability polynomial on [0,1].
2) To analyse the underlying combinatorial structure of reliability systems.
3) To apply the theoretical study of reliability systems to the real world design of networks.

To achieve these goals, I will study specific reliability models by using and expanding on techniques from my previous successful network reliability investigations. I will answer questions regarding the analytic properties and behaviour of the reliability polynomial on [0,1], as well as propose optimal network designs. The anticipated research will advance the knowledge of reliability systems and have direct applications to the design of networks. The introduction of a new non-coherent reliability system, the strongly connected node failure reliability model, will provide new problems to investigate and have applications to directed networks with potential node failures.