Lawphongpanich / Hearn / Smith Mathematical and Computational Models for Congestion Charging

1. Auflage 2006
ISBN: 978-0-387-29645-6
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 101, 240 Seiten, eBook

Reihe: Applied Optimization

Although transportation economists have advocated the tolling of urban streets as a mechanism for controlling congestion and managing travel demands for over 50 years, it is only recently that this idea has become practical. When compared to the alternative of building more roads, congestion pricing - in particular via electronic tolling - is attractive and has been adopted in countries around the world. Recent implementations in London, Singapore, and various cities in Norway, as well as a number of projects in the United States, have been judged successful. This book presents rigorous treatments of issues related to congestion pricing. The chapters describe recent advances in areas such as mathematical and computational models for predicting traffic congestion, determining when, where, and how much to levy tolls, and analyzing the impact of tolls on transporation systems. The analyses and methodologies developed in this book provide:- Mechanisms that aid in determining and comparing congestion pricing schemes- Methodologies for evaluating the efficiency of existing and proposed congestion pricing schemes- A means to predict the impact of pricing on urban transporation systems- Information essential to the financial and political success of congestion pricing programs.

Zielgruppe

Research

Autoren/Hrsg.

Lawphongpanich, Siriphong

Hearn, Donald W.

Smith, Michael J.

Inhaltsverzeichnis

Improving Traffic Flows at No Cost.- Relaxed Toll Sets for Congestion Pricing Problems.- Dynamic Pricing: A Learning Approach.- Congestion Pricing of Road Networks with Users Having Different Time Values.- Network Equilibrium Models for Analyzing Toll Highways.- On the Applicability of Sensitivity Analysis Formulas for Traffic Equilibrium Models.- Park and Ride for the Day Period and Morning-Evening Commute.- Bilevel Optimisation of Prices and Signals in Transportation Models.- Minimal Revenue Network Tolling: System Optimisation under Stochastic Assignment.- An Optimal Toll Design Problem with Improved Behavioural Equilibrium Model: The Case of the Probit Model.

Leseproben

Relaxed Toll Sets for Congestion Pricing Problems (p. 23-24)

Lihui Bail, Donald W. Hearn and Siriphong Lawphongpanich3
College of Business Administration, Valparaiso University, Valparaiso, IN 46383,
U.S.A., Lihui BaiQvalpo. edu
Industrial and Systems Engineering Department, University of Florida,
Gainesville, FL 32611, U.S.A., Industrial and Systems Engineering Department, University of Florida,
Gainesville, FL 32611, U.S.A.,
Summary. Congestion or toll pricing problems in [HeR98] require a solution to the system problem (the traffic assignment problem that minimizes the total travel delay) to define the set of all valid tolls or the toll set. For practical problems, it may not be possible to obtain an exact solution to the system problem and the inaccuracy in an approximate system solution may render the toll set empty. When this occurs, this paper offers alternative toll sets based on relaxed optimality conditions. With carefully chosen parameters, tolls from the relaxed toll sets are shown theoretically and empirically (using four transportation networks in the literature) to induce route choices that are nearly system optimal.

Key words: Congestion Pricing, Traffic Equilibrium, Perturbation Analysis

1 Introduction

To encourage each traveller to choose a route in a transportation network that would collectively benefit all travellers, Hearn and Ramana [HeR98] proposed in 1998 a framework for determining the prices and locations a t which to toll the network. This framework requires solving a congestion or toll pricing problem, an optimization problem with linear constraints that describe the set of all valid tolls or the toll set. Coefficients for the constraints depend on an optimal solution to the system problem, i.e., the traffic assignment problem (see, e.g., Florian and Hearn, [FlH95]) that minimizes the total travel delay among all travellers.

For small transportation networks, it is possible to compute an exact op- timal solution to the system problem. However, obtaining such a solution for larger networks may be either impossible or impractical. When implemented on computers, algorithms for the system problem must perform all numerical computations using finite precision. This naturally induces small numerical inaccuracies because to perform some mathematical operations precisely requires infinite precision. Furthermore, the system problem is generally a non- linear program for which most algorithms require in theory an infinite number of iterations to reach an exact optimal solution. In practice, it is common to terminate these algorithms when they find a solution with a small optimality gap, e.g., 10E-4.

On the other hand, using an approximate solution for the system problem (or an approximate system solution) to determine the coefficients for the constraints defining the toll set may cause the toll pricing problem to become infeasible, numerically (e.g., because of finite precision) or otherwise. To over- come this infeasibility, Hearn and Ramana [HeR98] employ a penalty function approach and Hearn et al. [HYROl] relax one of the constraints defining the toll set. For the latter, the relaxation is based on a parameter defined by an optimal solution to the penalty problem in [HeR98].

This paper studies the viability of using an approximate system solution in defining the toll set. Specifically, when an approximate system solution makes the toll set empty, this paper alleviates this inconsistency by relaxing one or more constraints, some of which are similar to those used in [HYROl]. How- ever, our approach to relaxation does not require solving a penalty problem. Moreover, this paper also addresses three issues relating to the use of an ap- proximate system solution. The first issue is whether an approximate system solution yields a consistent set of constraints defining the toll set. When it does not, the second issue is to find practical methods for relaxing the constraints in order to generate tolls that causes travellers to use the transportation net- work in nearly the most efficient manner. Finally, the last issue is to ascertain how well these methods work theoretically and empirically.

The remainder of the paper assumes that the travel demands are fixed. Results for the elastic demand case are similar and given in the Appendix. Section 2 defines two types of toll sets, system and non-system, and discusses their properties. Section 3 derives a relaxed toll set using an approximate system solution and shows that the tolls from this set have the desirable property. Section 4 gives an alternate representation of the relaxed toll set. Section 5 reports encouraging results for four transportation networks from the literature and Section 6 concludes the paper.