Skip to main content

Traffic Plans

  • Chapter
  • 1731 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 1955)

Abstract

In this chapter, directly inspired from [11]. we define almost all notions used throughout this book: traffic plan, its irrigated and irrigating measure, its transference plan, its parameterization, its fibers, the stopping time of each fiber and the multiplicity (or flow) at each point. After addressing some measurability issues we prove semicontinuity properties for all quantities of interest (average length of fibers, stopping time and multiplicity). All of these notions are first applied to the classical Monge-Kantorovich existence theory of optimal transports. Finally an existence theorem is given for traffic plans with prescribed irrigating and irrigated measures (the irrigation problem) and with prescribed transference plan (the who goes where problem).

Keywords

  • Lower Semicontinuity
  • Measurable Subset
  • Optimal Transport
  • Lower Semicontinuous Function
  • Monotone Convergence Theorem

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Rights and permissions

Reprints and Permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

(2009). Traffic Plans. In: Optimal Transportation Networks. Lecture Notes in Mathematics, vol 1955. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69315-4_3

Download citation