RESEARCH ARTICLE


Power-Law Congestion Costs: Minimal Revenue (MR) Pricing and the Braess Paradox



Claude M. Penchina*
Department of Physics, Hasbrouck Laboratory, University of Massachusetts at Amherst, Amherst Massachusetts 01003, USA.

Department of Physics, King's College, Strand, London, WC2R-2LS, UK

ECE Department of UCSD, La Jolla, CA 92093, USA




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Creative Commons License
© 2008 Claude M. Penchina .;

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.

* Address correspondence to this author at the Department of Physics, Hasbrouck Laboratory, University of Massachusetts at Amherst, Amherst Massachusetts 01003, USA; E-mail: cmpenchina@gmail.com


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.

Keywords: Braess's paradox, congestion costs, network theorems, power law non-linearities wheatstone bridge.