New characterisations of spatial linear networks for geographical accessibility

Abstract

Target 9.1 of the United Nations Sustainable Development Goals specifies the need for affordable, equitable access for all. In South Africa, where most travel occurs via the road network, apartheid policies designed the historical road network to segregate rather than integrate. Since the end of apartheid, there has been an increased need for integrated urban accessibility. Since government initiatives are typically enacted at a regional level, it is relevant to model accessibility between regions. Very few methods exist in the literature that model road-based inter-regional accessibility, and none account for structural characteristics of the road network. The aim of this thesis is to develop a novel stochastic model that estimates road-based inter-regional accessibility, and that is able to take the homogeneity of road networks into account. The accessibility model utilises Markov chain theory. Each region represents a state, and the average inverse distances between regions act as transition probabilities. Transition probabilities between adjacent regions are stored in a 1-step transition probability matrix (TPM). Assuming the Markov property holds, raising the TPM to the power n gives transition probabilities between regions up to n steps away. Letting n→∞ gives the prominence index, which quantifies the accessibility of a region regardless of the journey’s starting point. Road network homogeneity is tested by extending a test for the homogeneity of spatial point patterns to spatial linear networks. An unsupervised clustering method is then developed which subdivides a road network into regions that are as homogeneous as possible. Finally, road-based accessibility is calculated between these regions. The accessibility model was first applied to electoral wards in the City of Tshwane. Based on the wards, the central business district (CBD) was most accessible, but there was poor accessibility to the CBD from outlying townships. The homogeneity test showed that distinct residential neighbourhoods were internally homogeneous, and was thus able to identify neighbourhoods within a road network. The unsupervised clustering method was then used to identify two new regionalisations of the road network within the City of Tshwane at different spatial scales, and the accessibility model was applied to these regionalisations. For one regionalisation, an emerging economic area was most accessible, while for the other, a central educational area was most accessible. Although accessibility was not correlated with road network homogeneity, different spatial scales and regionalisations had a great impact on the accessibility results. This thesis develops a new characterisation of spatial linear networks based on their homogeneity, and uses this to investigate the state of inter-regional road-based accessibility in the City of Tshwane. This is a crucial area of research in the move towards a more equitable and sustainable future.