Change search
ReferencesLink to record
Permanent link

Direct link
A Note on Two Papers by Dial
KTH, School of Architecture and the Built Environment (ABE), Transport Science, Transport and Location Analysis.
2010 (English)Report (Other academic)
Abstract [en]

This note discusses some shortcomings of two papers by Dial. In these insightful but somewhat confused papers Dial studies the problem of determining “optimal” congestion tolls. The papers have several flaws, as well as outright errors. Moreover the presentation often is not very clear, often leaving the reader in doubt of what is proved about what. In this note we try to pinpoint the main flaws of the papers.

Place, publisher, year, edition, pages
2010. , 6 p.
National Category
Transport Systems and Logistics
URN: urn:nbn:se:kth:diva-116094OAI: diva2:588676

TSC import 2273 2013-01-15. QC 20131206

Available from: 2013-01-15 Created: 2013-01-15 Last updated: 2013-12-06Bibliographically approved
In thesis
1. Aspects of Static Multi-Class Traffic equilibria under Congestion Pricing
Open this publication in new window or tab >>Aspects of Static Multi-Class Traffic equilibria under Congestion Pricing
2010 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Congestion charging is a now accepted means of influencing traffic to behave in a more socio-economic optimal way, like e.g. in the Stockholm project. Already early work, in the 1920’s, showed that road use can be inefficient due externalities, i.e. that users don’t experience their own (negative) effect on other users: an extra car on a traffic link causes delays for other cars, but the driver himself does not experience this cost.In the 1950’s it was further shown - for a congested road network with homogeneous users – that if each user is charged a toll equal to the total value of time loss incurred on other users of the network, then -if we have fixed travel demand - this will induce an equilibrium that is system optimal in the sense that the total cost of network usage is minimal (assuming that all users have fixed and identical time values).  But toll charges need to be levied in monetary units, and different travelers have different values of time. Therefore, to account for the effects of tolls, and to be able to compute equilibria, one needs to introduce different user classes, differing in their time values.

In this thesis, consisting of four papers, we study congestion pricing of road networks with users differing only in their time values. In particular, we analyze marginal social cost (MSC) pricing, a tolling scheme that charges each user a penalty corresponding to the value of the delays inflicted on other users, as well as its implementation through fixed tolls.

Paper III contains the main theoretical work of the thesis. In that paper we show that the variational inequalities characterizing the equilibria in question can be stated in symmetric or non-symmetric forms. The symmetric forms correspond to optimization problems, convex in the fixed-toll case and non-convex in the MSC case, which hence may have multiple equilibria. The objective of the latter problem is the total value of travel time, which thus is minimized at the global optima of that problem. Implementing close-to-optimal MSC tolls as fixed tolls leads to equilibria with possibly non-unique class specific flows, but with identical close-to-optimal values of the total value of travel time. Finally we give an adaptation, to the MSC setting, of the Frank-Wolfe algorithm, which is further applied to some test cases, including Stockholm.

Paper I is an early application using Frank-Wolfe, after having realized the possibility to symmetrize the problem.

Paper II gives a convexification of non-convex equilibrium problem for MSC tolls. We have used these convexifications to compute lower bounds when computing equilibria.

Paper IV is a short note commenting some flaws in two papers by Dial on MSC tolls.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2010. 7 p.
Trita-TEC-LIC, ISSN 1653-445X ; 10-002
traffic, congestion pricing, equilibria, marginal social cost
National Category
Other Civil Engineering
urn:nbn:se:kth:diva-12963 (URN)978-91-85539-54-3 (ISBN)
2010-06-11, E35, Lindstetsv. 3, Stockholm, 09:00 (English)

QC 20100610

Available from: 2010-06-10 Created: 2010-05-20 Last updated: 2013-12-06Bibliographically approved

Open Access in DiVA

Working paper(44 kB)65 downloads
File information
File name FULLTEXT01.pdfFile size 44 kBChecksum SHA-512
Type fulltextMimetype application/pdf

Search in DiVA

By author/editor
Lindberg, Per Olov
By organisation
Transport and Location Analysis
Transport Systems and Logistics

Search outside of DiVA

GoogleGoogle Scholar
Total: 65 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 50 hits
ReferencesLink to record
Permanent link

Direct link