RESEARCH ARTICLE
Power-Law Congestion Costs: Minimal Revenue (MR) Pricing and the Braess Paradox
Claude M. Penchina*
Department of Physics, King's College, Strand, London, WC2R-2LS, UK
ECE Department of UCSD, La Jolla, CA 92093, USA
Article Information
Identifiers and Pagination:
Year: 2008Volume: 2
First Page: 47
Last Page: 52
Publisher ID: TOTJ-2-47
DOI: 10.2174/1874447800802010047
Article History:
Received Date: 28/3/2008Revision Received Date: 28/4/2008
Acceptance Date: 26/6/2008
Electronic publication date: 6/8/2008
Collection year: 2008
open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: https://creativecommons.org/licenses/by/4.0/legalcode. This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Abstract
We describe a simpler proof for Calvert and Keady's (C-K) theorem showing the non-occurrence of the Braess Paradox in networks with power-law congestion costs. We extend the C-K theorem to the case of elastic demand. We then use the methods of these proofs to develop several new theorems about the optimality of flows and the piecewise stability of Minimal Revenue (MR)Tolls in transportation networks with power-law congestion costs, with and without fixed costs. The stability of MR tolls is an important attractive feature. For administrators it makes the tolls cheaper to collect. For users it makes the tolls more predictable.