Grant: Discovery Grants Program - Individual

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. **