Optimal Spatial Interaction And The Gravity Model
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Author | : Sven Svenaeus |
Publisher | : Springer Science & Business Media |
Total Pages | : 106 |
Release | : 2012-12-06 |
Genre | : Business & Economics |
ISBN | : 3642455158 |
This book has grown out of a desire to explore the possibilities of using optimizing models in transportation planning. This approach has been followed throughout. Models which combine descriptive and optimizing elements are not treated. The gravity model is here studied as the solution to an optimizing model. In spite of this approach, much of the material shoula be of general interest. Algorithms are not discussed. The author has benefited from discussions with many colleagues. M. Florian suggested the term "interacti vi ty". N. F. Stewart and P. Smeds gave many valu able comments on a first draft. M. Beckmann made me think once more about the final chapters. R. Grubbstrem and K. Jornsten helped clarifYing some things in the same chapters. Remaining insufficiencies are due to the author. Gun Mannervik typed with great patience. Linkoping in October 1979 Sven Erlander ABSTRACT The book proposes extended use of optimizing models in transportation plann ing. An entropy constrained linear program for the trip distribution problem is formulated and shown to have the ordinarJ doubly constrained gravity model as its solution. Entropy is here used as a measure of interactivity, which is constrained to be at a prescribed level. In this way the variation present in the reference trip matrix is preserved. (The properties of entropy as a dispersion measure are shortly discussed. ) The detailed mathematics of the optimal solutions as well as of sensitivity and duality are given.
Author | : F. Svenaeus |
Publisher | : Springer |
Total Pages | : 113 |
Release | : 2014-03-12 |
Genre | : Business & Economics |
ISBN | : 9783642455162 |
This book has grown out of a desire to explore the possibilities of using optimizing models in transportation planning. This approach has been followed throughout. Models which combine descriptive and optimizing elements are not treated. The gravity model is here studied as the solution to an optimizing model. In spite of this approach, much of the material shoula be of general interest. Algorithms are not discussed. The author has benefited from discussions with many colleagues. M. Florian suggested the term "interacti vi ty". N. F. Stewart and P. Smeds gave many valu able comments on a first draft. M. Beckmann made me think once more about the final chapters. R. Grubbstrem and K. Jornsten helped clarifYing some things in the same chapters. Remaining insufficiencies are due to the author. Gun Mannervik typed with great patience. Linkoping in October 1979 Sven Erlander ABSTRACT The book proposes extended use of optimizing models in transportation plann ing. An entropy constrained linear program for the trip distribution problem is formulated and shown to have the ordinarJ doubly constrained gravity model as its solution. Entropy is here used as a measure of interactivity, which is constrained to be at a prescribed level. In this way the variation present in the reference trip matrix is preserved. (The properties of entropy as a dispersion measure are shortly discussed. ) The detailed mathematics of the optimal solutions as well as of sensitivity and duality are given.
Author | : Kingsley E. Heynes |
Publisher | : |
Total Pages | : 88 |
Release | : 1984 |
Genre | : |
ISBN | : 9780608011417 |
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.
Author | : Jean-Paul Rodrigue |
Publisher | : Routledge |
Total Pages | : 432 |
Release | : 2013-07-18 |
Genre | : Science |
ISBN | : 1136777326 |
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.
Author | : A. Fotheringham |
Publisher | : |
Total Pages | : 254 |
Release | : 1989 |
Genre | : Business & Economics |
ISBN | : |
Author | : Walter Isard |
Publisher | : Taylor & Francis |
Total Pages | : 515 |
Release | : 2017-07-05 |
Genre | : Political Science |
ISBN | : 1351917900 |
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.
Author | : Alan Wilson |
Publisher | : Routledge |
Total Pages | : 175 |
Release | : 2013-01-11 |
Genre | : Mathematics |
ISBN | : 1136498524 |
First published in 1970, this groundbreaking investigation into Entropy in Urban and Regional Modelling provides an extensive and detailed insight into the entropy maximising method in the development of a whole class of urban and regional models. The book has its origins in work being carried out by the author in 1966, when he realised that the well-known gravity model could be derived on the basis of an analogy with statistical, rather than Newtonian, mechanics. Subsequent investigation demonstrated that the entropy maximising method stems from an even higher level of generality, and the beginning of the book is devoted to an account of its importance and use as a general modelling tool. This reissue will be welcomed by a range of students and professionals from fields as diverse as urban and regional studies, economics, geography, planning, civil engineering, mathematics and statistics.
Author | : John R. Roy |
Publisher | : Springer Science & Business Media |
Total Pages | : 260 |
Release | : 2004-01-15 |
Genre | : Business & Economics |
ISBN | : 9783540205289 |
In this book, the author's strong commitment to the multi-disciplinary field of regional science emerges to provide a unifying framework between spatial modelling traditions from quantitative geography and those from spatial economics, whereby each is enhanced. Starting with a detailed discussion of each field illustrated with numerical examples, the two traditions are brought together by either making the economic models probabilistic or transforming the objectives of the geographic models to reflect both utility theory and production theory. The ideas are applied to develop urban models of activity analysis, face-to-face contacts and housing supply, as well as regional models in the areas of input-output analysis, imperfect competition and interregional migration.
Author | : Manfred M. Fischer |
Publisher | : Springer Science & Business Media |
Total Pages | : 85 |
Release | : 2011-08-05 |
Genre | : Business & Economics |
ISBN | : 3642217206 |
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.
Author | : A Stewart Fotheringham |
Publisher | : SAGE |
Total Pages | : 529 |
Release | : 2008-12-22 |
Genre | : Social Science |
ISBN | : 1446206505 |
The widespread use of Geographical Information Systems (GIS) has significantly increased the demand for knowledge about spatial analytical techniques across a range of disciplines. As growing numbers of researchers realise they are dealing with spatial data, the demand for specialised statistical and mathematical methods designed to deal with spatial data is undergoing a rapid increase. Responding to this demand, The Handbook of Spatial Analysis is a comprehensive and authoritative discussion of issues and techniques in the field of Spatial Data Analysis. Its principal focus is on: • why the analysis of spatial data needs separate treatment • the main areas of spatial analysis • the key debates within spatial analysis • examples of the application of various spatial analytical techniques • problems in spatial analysis • areas for future research Aimed at an international audience of academics, The Handbook of Spatial Analysis will also prove essential to graduate level students and researchers in government agencies and the private sector.