Convergence of Piecewise-Linear Envelope Curves in Transportation Design

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. The authors show that, under general conditions, such discrete solutions converge uniformly to form a single continuous curve. In many cases the approximate solutions are perfectly acceptable with regard to error bounds and computation time; results affirm the reasonableness of these approximate solutions by proving their convergence to the real solution.

• Record URL:
  http://www.sciencedirect.com/science/article/B6V99-4MGVHV9-1/2/22852e42e5352b29512d18e3f241779d
• Availability:
  • Find a library where document is available. Order URL: http://worldcat.org/issn/01912615
• Supplemental Notes:
  • Abstract reprinted with permission from Elsevier
• Authors:
  • Iida, Tomohisa
  • Lovell, David J
• Publication Date: 2007-6

Language

• English

Media Info

• Media Type: Print
• Features: Figures; References;
• Pagination: pp 527-539
• Serial:
  • Transportation Research Part B: Methodological
  • Volume: 41
  • Issue Number: 5
  • Publisher: Elsevier
  • ISSN: 0191-2615
  • Serial URL: http://www.sciencedirect.com/science/journal/01912615

Subject/Index Terms

• TRT Terms: Approximation (Mathematics); Crashes; Curves (Geometry); Finite differences; Highway transportation; Infrastructure; Mathematical models; Planning and design; Prevention; Safety; Sight distance; Theory
• Uncontrolled Terms: Closed form solutions; Computation time; Convergence; Error bounds; Horizontal clearance; Lateral clearance; Safety zones
• Subject Areas: Highways; Planning and Forecasting; Safety and Human Factors; Security and Emergencies; I72: Traffic and Transport Planning;

Filing Info

• Accession Number: 01045444
• Record Type: Publication
• Files: TRIS, ATRI
• Created Date: Mar 28 2007 12:52PM