The role of city geometry in determining the utility of a small urban light rail/tram system
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The role of city geometry in determining the utility of a small urban light rail/tram system Michael Mc Gettrick1 Accepted: 26 December 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this work, we show the importance of considering a city’s shape, as much as its population density figures, in urban transport planning. We consider in particular cities that are “circular” (the most common shape) compared to those that are “rectangular”: for the latter case we show greater utility for a single line light rail/tram system. We introduce the new concepts of Infeasible Regions and Infeasibility Factors, and show how to calculate them numerically and (in some cases) analytically. A particular case study is presented for Galway City.
1 Introduction There are many factors to consider when constructing a light rail/tram system in a city. Some of these factors can be scientifically analyzed (as is the case in this paper), but others perhaps not (aspects that are political, sociological, financial,....). These latter aspects are of course important, but are not analyzed here. Further, amongst considerations that lend themselves to scientific analysis, we restrict to small tram systems (we have in mind initially small cities, though our results will apply in large cities where political, financial or other considerations dictate the construction of a transit system only servicing a small fraction of the city). While we look a little at a two-line system, most of this paper considers a single-line system. To make the model tractable, in this current work we restrict ourselves to circular or rectangular “geometries” (which should nonetheless approximate many real-world city shapes). Recent work by Barthelemy (2016) and by Aldous and Barthelemy (2019) has considered large cities with non-uniform (though isotropic) population density. They ask (and answer) the problem of determining, as the city increases, how does the optimal tram network change (e.g. radial, circular, grid,...). In our model, we fix a * Michael Mc Gettrick [email protected] 1
School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Galway, Ireland
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1- or 2-line system, fix uniform population density, and answer the problem of determining for which city shape will this line (or two lines) give the best service. Thus our work is complementary to that of Aldous and Barthelemy [and indeed overlaps a bit when they consider uniform density in Sect. 4 of Aldous and Barthelemy 2019]. Both models are restricted, theirs by the isotropy assumption, and ours by the uniform populaton distribution assumption. We point out here that rectangular cities (often occuring along the edge of a sea/ocean/lake) cannot fit into their model: At the center of a rectangle, the view “east-west” will be different from looking “north-south”. Okabe et al. (1992), Okabe and Suzuki (1997) tackle the problem of locational optimization using Voronoi diagrams. Their
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