The realisation of optical network architectures may hold the key to delivering the enormous bandwidth demands of next generation Internet applications and services. Optical Burst Switching (OBS) is a potentially cost-effective switching technique that can satisfy these demands by offering a high bit rate transport service that is bandwidth-efficient under dynamic Internet traffic loads. Although various aspects of OBS performance have been extensively investigated, there remains a need to systematically assess the cost/performance trade-offs involved in dimensioning OBS switch resources in a network. This goal is essential in enabling the future deployment of OBS but poses a significant challenge due to the complexity of obtaining tractable mathematical models applicable to OBS network optimisation. The overall aim of this thesis lies within this challenge. This thesis firstly develops a novel analytic performance model of an OBS node where burst contention is resolved by combined use of Tuneable Wavelength Converters (TWCs) and Fibre Delay Lines (FDLs) connected in an efficient share-per-node configuration. The model uses a two-moment traffic representation that gives a good trade-off between accuracy and complexity, and is suitable for extension to use in network modelling. The OBS node model is then used to derive an approximate analytic model of an OBS network of switches equipped with TWCs and FDLs, again maintaining a two-moment traffic model for each end-to-end traffic path in the network. This allows evaluation of link/route loss rates under different offered traffic characteristics, whereas most OBS network models assume only a single-moment traffic representation. In the last part of this thesis, resource dimensioning of OBS networks is performed by solving single and multi-objective optimisation problems based on the analytic network model. The optimisation objectives relate to equipment cost minimisation and throughput maximisation under end-to-end loss rate constraints. Due to non-convexity of the network performance constraint equations, a search heuristic approach has been taken using a constraint-handling genetic algorithm.