Tolling traffic links under stochastic assignment: Modelling the relationship between the number and price level of tolled links and optimal traffic flows.

Stewart, Kathryn (2007) Tolling traffic links under stochastic assignment: Modelling the relationship between the number and price level of tolled links and optimal traffic flows. Transportation Research Part A Policy and Practice, 41 (7). pp. 644-654. ISSN 0965 8564

[img] PDF
Restricted to Registered users only

Download (241kB) | Request a copy


The classical road-tolling problem is to toll network links such that under the principles of Wardropian User Equilibrium Assignment a System Optimising (SO) flow pattern is obtained. Stochastic assignment methods are accepted to be more realistic than deterministic and it is of interest to examine the potential for optimal tolling in the case of Stochastic User Equilibrium (SUE). In examining the case of Stochastic User Equilibrium the ‘desired flow pattern’ to be created must first be determined. The classical economics solution of replacing unit-cost flow functions with marginal-cost flow functions which under deterministic assignment produces the System Optimal solution (where Total Network Travel Cost (TNTC) is minimised) does not generally result in TNTC being minimised in the Stochastic Case. Instead such tolls produce a ‘Stochastic System Optimal’ (SSO) solution where the Total Perceived Network Travel Cost (TPNTC) is minimised.

This paper examines and compares link-based tolling solutions to achieve both the SSO (TPNTC minimised) and true SO (TNTC minimised) under SUE and illustrates the concept with numerical examples. Such link-based tolling schemes produce network benefit by re-routing rather than traffic suppression as opposed to the cordon-based charging schemes which have been implemented in practice. Equity issues relating to charging schemes are discussed and the desirability of zero-toll routes is highlighted associated with greater potential political acceptability of charging schemes that do not impose excessive charges upon users (such as minimal or low revenue tolls). A heuristic is developed to toll network links in such a way as to balance the number of links tolled against the revenue required to produce a desired reduction in TNTC such that optimal network flow patterns are approached.

Item Type: Article
Print ISSN: 0965 8564
Uncontrolled Keywords: Congestion Charging; Traffic assignment; Stochastic user equilibrium; Optimal tolls; Marginal social costs;
University Divisions/Research Centres: Faculty of Engineering, Computing and Creative Industries > School of Engineering and the Built Environment
Dewey Decimal Subjects: 300 Social sciences > 300 Social sciences, sociology & anthropology > 304 Factors affecting social behavior
300 Social sciences > 380 Commerce, communications & transportation > 380 Commerce, communications & transportation
Library of Congress Subjects: H Social Sciences > HE Transportation and Communications
Item ID: 1922
Depositing User: RAE Import
Date Deposited: 23 Apr 2008 15:38
Last Modified: 25 May 2015 12:31

Actions (login required)

View Item View Item


Downloads per month over past year

View more statistics

Edinburgh Napier University is a registered Scottish charity. Registration number SC018373