RESEARCH ARTICLE
Minimal Revenue Tolls: Price Stability for Networks With BPR Cost Function
Claude M. Penchina*
Article Information
Identifiers and Pagination:
Year: 2009Volume: 3
First Page: 87
Last Page: 92
Publisher ID: TOTJ-3-87
DOI: 10.2174/1874447800903010087
Article History:
Received Date: 9/11/2008Revision Received Date: 3/3/2009
Acceptance Date: 5/5/2009
Electronic publication date: 4/9/2009
Collection year: 2009
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
Marginal-Cost (MC) tolls are known to produce economic efficiency of network flows. Yet, MC pricing has not been widely adopted, because of various perceived unpopular aspects, such as complexity, collection costs, and inequities. Minimal Revenue (MinRev) pricing has been suggested as a means to achieve most of the economic improvements of MC pricing with fewer unpopular aspects. One claimed improvement of MinRev tolls is the ability to maintain fixed tolls while flows change. We show that single-power-law congestion costs are sufficient (but not always necessary) conditions for the stability (flow independence) of Minimal-Revenue (MinRev) tolls in transportation networks, so long as the links that are actually used do not change. This is particularly important because the usual Bureau of Public Roads (BPR) cost function recommended as a good representation of real road traffic, has this single power-law congestion cost. For cases of elastic demand, these MinRev tolls do not achieve the full economic efficiency of Marginal-Cost (MC) tolls. However, they may still prove desirable because of greater stability, greater simplicity, lower out-ofpocket costs, and greater perceived equity. Furthermore, in cases of major congestion problems, where all links are used, the MinRev tolls are totally stable, i.e. totally independent of flows; also, if demand is relatively insensitive to price, the flows are nearly equal to the optimal flows obtained by MC pricing. The discussion is based on the equilibrium assignment method, with tolls to encourage System Optimal (SO) flows rather than User Optimal (UO) flows. Results are obtained for general networks, and also illustrated with a very simple example.