A predictive continuum dynamic user-optimal model for a polycentric urban city

A predictive continuum dynamic user-optimal model is extended to investigate the traffic equilibrium problem for a polycentric urban city with multiple central business districts (CBDs). The road network within the city is assumed to be dense and can be viewed as a continuum in which travellers can choose their routes in a two-dimensional space. Travellers are assumed to choose their route to minimise the actual total cost to the destination (i.e. the CBD). The model consists of two parts: the conservation law part and the Hamilton–Jacobi part. The finite volume method is used to solve each part on unstructured meshes. Because the two parts are closely interconnected and have different initial times, solving the model can be treated as a fixed-point problem, which is solved using a self-adaptive method of successive averages. Numerical experiments for an urban city with two CBDs are presented to demonstrate the effectiveness of the model and the numerical algorithm.postprin

Revisiting Jiang's dynamic continuum model for urban cities

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Dynamic Continuum Model with Elastic Demand for a Polycentric Urban City

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Reformulating the Hoogendoorn-Bovy predictive dynamic user-optimal model in continuum space with anisotropic condition

Hoogendoorn and Bovy (2004) developed an approach for a pedestrian user-optimal dynamic assignment in continuous time and space. Although their model was proposed for pedestrian traffic, it can also be applied to urban cities. The model is very general, and consists of a conservation law (CL) and a Hamilton–Jacobi–Bellman (HJB) equation that contains a minimum value problem. However, only an isotropic application example was given in their paper. We claim that the HJB equation is difficult to compute numerically in an anisotropic case. To overcome this, we reformulate their model for a dense urban city that is arbitrary in shape and has multiple central business districts (CBDs). In our model, the minimum value problem is only used in the CL portion, and the HJB equation reduces to a Hamilton–Jacobi (HJ) equation for easier computation. The dynamic path equilibrium of our model is proven in a different way from theirs, and a numerical algorithm is also provided to solve the model. Finally, we show two numerical examples under the anisotropic case and compare the results with those of the isotropic case.postprin

Network Centralities in Polycentric Urban Regions: Methods for the Measurement of Spatial Metrics

The primary aim of this thesis is to explain the complex spatial organisations of polycentric urban regions (PURs). PURs are a form of regional morphology that often evolves from post-industrial structures and describe a subnational area featuring a plurality of urban centres. As of today, the analysis of the spatial organisation of PURs constitutes a hitherto uncharted territory. This is due to PURs’ inherent complexity that poses challenges for their conceptualisation. In this context, this thesis reviews theories on the spatial organisation of regions and cities and seeks to make a foundational methodological contribution by joining space syntax and central place theory in the conceptualisation of polycentric urban regions. It takes into account human agency embedded in the physical space, as well as the reciprocal effect of the spatial organisation for the emergence of centralities and demonstrates how these concepts can give insights into the fundamental regional functioning. The thesis scrutinises the role that the spatial organisation plays in such regions, in terms of organising flows of goods and people, ordering locational occupation and fostering centres of commercial activity. It proposes a series of novel measurements and techniques to analyse large and messy datasets. This includes a method for the application of large-scale volunteered geographic information in street network analysis. This is done, in the context of two post-industrial regions: the German Ruhr Valley and the British Nottinghamshire, Derbyshire and Yorkshire region. The thesis’ contribution to the understanding of regional spatial organisation and the study of regional morphology lies in the identification of spatial structural features of socio-economic potentials of regions and particular areas within them. It constitutes the first comparative study of comprehensive large-scale regional spatial networks and presents a framework for the analysis of regions and the evaluation of the predictive potential of spatial networks for socio-economic patterns and the location of centres in regional contexts

Configraphics:

This dissertation reports a PhD research on mathematical-computational models, methods, and techniques for analysis, synthesis, and evaluation of spatial configurations in architecture and urban design. Spatial configuration is a technical term that refers to the particular way in which a set of spaces are connected to one another as a network. Spatial configuration affects safety, security, and efficiency of functioning of complex buildings by facilitating certain patterns of movement and/or impeding other patterns. In cities and suburban built environments, spatial configuration affects accessibilities and influences travel behavioural patterns, e.g. choosing walking and cycling for short trips instead of travelling by cars. As such, spatial configuration effectively influences the social, economic, and environmental functioning of cities and complex buildings, by conducting human movement patterns. In this research, graph theory is used to mathematically model spatial configurations in order to provide intuitive ways of studying and designing spatial arrangements for architects and urban designers. The methods and tools presented in this dissertation are applicable in: arranging spatial layouts based on configuration graphs, e.g. by using bubble diagrams to ensure certain spatial requirements and qualities in complex buildings; and analysing the potential effects of decisions on the likely spatial performance of buildings and on mobility patterns in built environments for systematic comparison of designs or plans, e.g. as to their aptitude for pedestrians and cyclists. The dissertation reports two parallel tracks of work on architectural and urban configurations. The core concept of the architectural configuration track is the ‘bubble diagram’ and the core concept of the urban configuration track is the ‘easiest paths’ for walking and cycling. Walking and cycling have been chosen as the foci of this theme as they involve active physical, cognitive, and social encounter of people with built environments, all of which are influenced by spatial configuration. The methodologies presented in this dissertation have been implemented in design toolkits and made publicly available as freeware applications