Haynes and Fotheringham provide a comprehensive introduction to the four basic forms of gravity models. Gravity and spatial interaction -- extensively applied in forecasting -- has provided a major contribution to social science literature. The authors trace the different applications of the gravity model to market area analysis including: determining the boundaries of market areas, determining the demand for goods or services, and examining problems of operating the retail model. Six fully-developed, real-life examples of the use of these models are presented: planning a new service, defining retail shopping boundaries, forecasting migration and voting patterns, examining university enrollment by area, determining the optimal size of a shopping complex, and locating a facility to maximize custom. The discussion is kept at an elementary mathematical level and is aimed primarily at those unacquainted with the finer workings of gravity and spatial interaction models.

Mobility is fundamental to economic and social activities such as commuting, manufacturing, or supplying energy. Each movement has an origin, a potential set of intermediate locations, a destination, and a nature which is linked with geographical attributes. Transport systems composed of infrastructures, modes and terminals are so embedded in the socio-economic life of individuals, institutions and corporations that they are often invisible to the consumer. This is paradoxical as the perceived invisibility of transportation is derived from its efficiency. Understanding how mobility is linked with geography is main the purpose of this book. The third edition of The Geography of Transport Systems has been revised and updated to provide an overview of the spatial aspects of transportation. This text provides greater discussion of security, energy, green logistics, as well as new and updated case studies, a revised content structure, and new figures. Each chapter covers a specific conceptual dimension including networks, modes, terminals, freight transportation, urban transportation and environmental impacts. A final chapter contains core methodologies linked with transport geography such as accessibility, spatial interactions, graph theory and Geographic Information Systems for transportation (GIS-T). This book provides a comprehensive and accessible introduction to the field, with a broad overview of its concepts, methods, and areas of application. The accompanying website for this text contains a useful additional material, including digital maps, PowerPoint slides, databases, and links to further reading and websites. The website can be accessed at: http://people.hofstra.edu/geotrans This text is an essential resource for undergraduates studying transport geography, as well as those interest in economic and urban geography, transport planning and engineering.

This landmark textbook introduces students to the principles of regional science and focuses on the key methods used in regional analysis, including regional and interregional input-output analysis, econometrics (regional and spatial), programming and industrial and urban complex analysis, gravity and spatial interaction models, SAM and social accounting (welfare) analysis and applied general interregional equilibrium models. The coherent development of the materials contained in the set of chapters provides students with a comprehensive background and understanding of how to investigate key regional problems. For the research scholar, this publication constitutes an up-to-date source book of the basic elements of each major regional science technique. More significant, it points to new directions for future research and ways interregional and regional analytic approaches can be fused to realise much more probing attacks on regional and spatial problems - a contribution far beyond what is available in the literature.

Gravity models describe, and hence help predict, spatial flows of commuters, air-travelers, migrants, commodities and even messages. They are one of the oldest and most widely used of all social science models. This book presents an up-to-date, consistent and unified approach to the theory, methods and application of the gravity model - which spans from the axiomatic foundations of such models all the way to practical hints for their use. "I have found no better general method for use in applied research dealing with spatial interaction... It is against this background that the present book by Sen and Smith is most welcomed." Walter Isard

The availability of spatial databases and widespread use of geographic information systems has stimulated increasing interest in the analysis and modelling of spatial data. Spatial data analysis focuses on detecting patterns, and on exploring and modelling relationships between them in order to understand the processes responsible for their emergence. In this way, the role of space is emphasised , and our understanding of the working and representation of space, spatial patterns, and processes is enhanced. In applied research, the recognition of the spatial dimension often yields different and more meaningful results and helps to avoid erroneous conclusions. This book aims to provide an introduction into spatial data analysis to graduates interested in applied statistical research. The text has been structured from a data-driven rather than a theory-based perspective, and focuses on those models, methods and techniques which are both accessible and of practical use for graduate students. Exploratory techniques as well as more formal model-based approaches are presented, and both area data and origin-destination flow data are considered.

This edited volume provides an essential resource for urban morphology, the study of urban forms and structures, offering a much-needed mathematical perspective. Experts on a variety of mathematical modeling techniques provide new insights into specific aspects of the field, such as street networks, sustainability, and urban growth. The chapters collected here make a clear case for the importance of tools and methods to understand, model, and simulate the formation and evolution of cities. The chapters cover a wide variety of topics in urban morphology, and are conveniently organized by their mathematical principles. The first part covers fractals and focuses on how self-similar structures sort themselves out through competition. This is followed by a section on cellular automata, and includes chapters exploring how they generate fractal forms. Networks are the focus of the third part, which includes street networks and other forms as well. Chapters that examine complexity and its relation to urban structures are in part four.The fifth part introduces a variety of other quantitative models that can be used to study urban morphology. In the book’s final section, a series of multidisciplinary commentaries offers readers new ways of looking at the relationship between mathematics and urban forms. Being the first book on this topic, Mathematics of Urban Morphology will be an invaluable resource for applied mathematicians and anyone studying urban morphology. Additionally, anyone who is interested in cities from the angle of economics, sociology, architecture, or geography will also find it useful. "This book provides a useful perspective on the state of the art with respect to urban morphology in general and mathematics as tools and frames to disentangle the ideas that pervade arguments about form and function in particular. There is much to absorb in the pages that follow and there are many pointers to ways in which these ideas can be linked to related theories of cities, urban design and urban policy analysis as well as new movements such as the role of computation in cities and the idea of the smart city. Much food for thought. Read on, digest, enjoy." From the foreword by Michael Batty