 Convergence of piecewise-linear envelope curves in transportation designTomohisa Iida and David J. Lovell Transportation Research Part B: Methodological, 2007, vol. 41, issue 5, 527-539 Abstract: Many transportation design problems involve the demarcation of safe zones surrounding the intended guideway, either to prevent physical collisions or to provide clearance for other requirements such as sight distance. Typically, an instantaneous solution to one of these problems can be represented by a line in the plane; the entire solution is then the envelope of this infinite family of lines. In this paper the theory of envelope curves is applied to show how these infrastructure design problems can be solved in closed form. When the solution cannot be expressed in terms of familiar functions, an intuitive practical solution might be to use a finite set of lines to produce an approximate piecewise-linear solution. We show that under general conditions, such discrete solutions converge uniformly to a single continuous curve. In many cases the approximate solutions are perfectly acceptable with regard to error bounds and computation time; our results affirm the reasonableness of these approximate solutions by proving their convergence to the real solution. Date: 2007 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:transb:v:41:y:2007:i:5:p:527-539 Ordering information: This journal article can be ordered from Access Statistics for this article Transportation Research Part B: Methodological is currently edited by Fred Mannering More articles in Transportation Research Part B: Methodological from Elsevier |
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