Time-dependent area-based pricing for multimodal systems with heterogeneous users in an agent-based environment

In this paper, we investigate an area-based pricing scheme for congested multimodal urban networks with the consideration of user heterogeneity. We propose a time-dependent pricing scheme where the tolls are iteratively adjusted through a Proportional–Integral type feedback controller, based on the level of vehicular traffic congestion and traveler’s behavioral adaptation to the cost of pricing. The level of congestion is described at the network level by a Macroscopic Fundamental Diagram, which has been recently applied to develop network-level traffic management strategies. Within this dynamic congestion pricing scheme, we differentiate two groups of users with respect to their value-of-time (which related to income levels). We then integrate incentives, such as improving public transport services or return part of the toll to some users, to motivate mode shift and increase the efficiency of pricing and to attain equitable savings for all users. A case study of a medium size network is carried out using an agent-based simulator. The developed pricing scheme demonstrates high efficiency in congestion reduction. Comparing to pricing schemes that utilize similar control mechanisms in literature which do not treat the adaptivity of users, the proposed pricing scheme shows higher flexibility in toll adjustment and a smooth behavioral stabilization in long-term operation. Significant differences in behavioral responses are found between the two user groups, highlighting the importance of equity treatment in the design of congestion pricing schemes. By integrating incentive programs for public transport using the collected toll revenue, more efficient pricing strategies can be developed where savings in travel time outweigh the cost of pricing, achieving substantial welfare gain.     

Congestion and variable user charging as an effective travel demand management instrument

Interest at the political level in congestion charging is gaining pace as cities struggle with ways to reduce the effects of growing traffic congestion on the liveability of cities. Despite a long history of promotion of a wide array of travel demand management (TDM) initiatives, very few have had a noticeable impact on the levels of traffic on the road networks of metropolitan areas. TDM success in this context has almost become ‘band-aid’ in the absence of a pricing strategy that not only promotes efficient use of the system but also hypothecates revenues to support essential complementary infrastructure and services such as public transport. This paper takes a look at the stream of pricing consciousness that is surfacing around the world. Although very few jurisdictions have implemented congestion charging, or any form of efficient variable car and truck user charging, the winds of change are well in place. The adage “it is not a matter of if but of when” seems to be the prevailing view. Our overview of global trends in positioning the debate and hopefully follow-through commitment to implementation provides a backdrop to papers submitted for this special issue on travel demand management. The predominance of papers on pricing is indicative of the priority that must be given to efficient charging and revenue disbursement.     

Distance-dependent congestion pricing for downtown zones

A growing literature exploits macroscopic theories of traffic to model congestion pricing policies in downtown zones. This study introduces trip length heterogeneity into this analysis and proposes a usage-based, time-varying congestion toll that alleviates congestion while prioritizing shorter trips. Unlike conventional trip-based tolls the scheme is intended to align the fees paid by drivers with the actual congestion damage they do, and to increase the toll’s benefits as a result.The scheme is intended to maximize the number of people that finish their trips close to their desired times. The usage-based toll is compared to a traditional, trip-based toll which neglects trip length. It is found that, like trip-based tolls, properly designed usage-based tolls alleviate congestion. But they reduce schedule delay more than trip-based tolls and do so with much smaller user fees. As a result usage-based tolls leave most of those who pay with a large welfare gain. This may increase the tolls’ political acceptability.     

Drivers’ willingness-to-pay to reduce travel time: evidence from the San Diego I-15 congestion pricing project

The adoption of congestion pricing depends fundamentally upon drivers’ willingness to pay to reduce travel time during the congested morning peak period. Using revealed preference data from a congestion pricing demonstration project in San Diego, we estimate that willingness to pay to reduce congested travel time is higher than previous stated preference results. Our estimate of median willingness to pay to reduce commute time is roughly $30 per hour, although this may be biased upward by drivers’ perception that the toll facility provides safer driving conditions. Drivers also use the posted toll as an indicator of abnormal congestion and increase their usage of the toll facility when tolls are higher than normal.     

Urban highway congestion

This article examines urban highway congestion pricing in the instance in which it is not possible to levy a congestion toll on a major portion of the urban road system. This case is pertinent because of technical and/or political constraints. The article uses economic theory and numerical examples to show that the optimum second-best toll can vary appreciably from the optimal tolls in a regime in which efficient tolls can be imposed on all routes.     

What type of road pricing scheme might appeal to politicians? Viewpoints on the challenge in gaining the citizen and public servant vote by staging reform

The greatest hurdle facing road pricing reform is political commitment. With rare exception, efforts to introduce significant reform in road pricing, aimed at raising sufficient revenue to ensure that road investment and ongoing maintenance is secured, without an additional impost to users above current outlays, while at the same time reducing traffic congestion, has fallen largely on politically non-supportive ears. The big challenge is to convince politicians (and their advisers) that it is possible to reform road pricing so that users are made better off (at least the great majority) in terms of time spent travelling and monies outlaid, and that government secures growing levels of revenue, but with at least some funds being used to improve public transport and the existing road network. This paper identifies the major issues that make much of the academic research into road pricing somewhat limited in terms of achieving real change. Staging reform is an appealing way forward, but ensuring the order and timing of events to secure progress is the big challenge. We offer some suggestions, including some ideas on new language designed to increase the level of buy in, and recognise that progress through action will require compromises in respect of an ‘ideal’ economically efficient pricing reform agenda.     

Bottleneck congestion pricing and modal split: Redistribution of toll revenue

The paper examines the question of the redistribution of toll revenue as seen in a bottleneck congestion model. Our objective is to analyse the impact of this redistribution on total cost and on modal split between railroad and road. Following Tabuchi’s two-mode model (Tabuchi, T., 1993. Bottleneck congestion and modal split. Journal of Urban Economics 34, 414-431.), we integrate a redistribution of toll revenue towards public transport into our study. In this context, we investigate two kinds of road toll regimes: a fine toll and a uniform toll. We will consider two types of railroad fare: when it is set equal to the marginal cost and when it is set equal to average cost. These models allow us to show that toll policy to be more efficient as long as toll revenue is directed towards public transport when the railroad fare is equal to average cost.     

Electronic toll collection

Electronic toll collection (ETC) offers the opportunity for toll facility operators to supply a substantially greater amount of traffic capacity than any other currently available form of toll collection. The current interest in ETC derives from the proposals in a number of countries to introduce urban tollways, using the net toll receipts to recover the cost of the capital investment plus an acceptable profit margin for those taking the financial risk. This paper outlines the main economic, technical, and administrative features of ETC in the context of toll charges that are determined by the rules of capital cost recovery. Electronic road pricing (ERP) as a mechanism for implementing full road user charging (in line with economic principles of efficient use of road space) is not the topic of this paper, given the predominantly financial basis of setting tolls for private roads. The underlying rationale for toolroads in the political climate of most nations is not suggestive of any plan to revise the pricing regime in line with ERP upon reversion of the infrastructure to the public sector when the capital costs are repaid. It is assumed that the tollroads will revert to free roads in line with the existing road system, and that road users will continue to contribute towards the costs of maintaining the road system by the traditional pricing mechanisms (i.e. fuel taxes, vehicle registration, fees, etc.).     

Peak period tolls: Precepts and prospects

This article presents the economic rationale for road pricing and provides some scale on the magnitude of peak period tolls that might be justified. It discusses the impacts of such tolls on congestion, air quality and economic development and suggests a long term strategy towards areawide implementation of peak period pricing. It discusses current trends which are increasing the likelihood for implementation of congestion pricing and toll roads in the future. In particular, it discusses some aspects of the 1991 Intermodal Surface Transportation Efficiency Act (ISTEA) which will eliminate some of the current restraints on congestion pricing and toll highways.Abbreviations ETC Electronic toll collection - FHWA Federal Highway Administration - HOV High occupancy vehicle - ISTEA Intermodal Surface Transportation Efficiency Act - LOS Level of service - TCM Transportation control measure - V/C Volume-to-capacity ratio - VMT Vehicle mile(s) of travel - vphpl Vehicles per hour per lane     

Existence of self-financing and Pareto-improving congestion pricing: Impact of value of time distribution

This paper considers a static congestion pricing model in which travelers select a mode from either, driving on highway or taking public transit, to minimize a combination of travel time, operating cost and toll. The focus is to examine how travelers’ value of time (VOT), which is continuously distributed in a population, affects the existence of a pricing-refunding scheme that is both self-financing (i.e. requiring no external subsidy) and Pareto-improving (i.e. reducing system travel time while making nobody worse off). A condition that insures the existence of a self-financing and Pareto-improving (SFPI) toll scheme is derived. Our derivation reveals that the toll authority can select a proper SFPI scheme to distribute the benefits from congestion pricing through a credit-based pricing scheme. Under mild assumptions, we prove that an SFPI toll always exists for concave VOT functions, of which the linear function corresponding to the uniform distribution is a special case. Existence conditions are also established for a class of rational functions. These results can be used to analyze more realistic VOT distributions such as log-normal distribution. A useful implication of our analysis is that the existence of an SFPI scheme is not guaranteed for general functional forms. Thus, external subsidies may be required to ensure Pareto-improving, even if policy-makers are willing to return all toll revenues to road users.     

Optimal toll locations and toll levels in congestion pricing schemes: a case study of Stockholm

As congestion pricing has moved from theoretical ideas in the literature to real-world implementation, the need for decision support when designing pricing schemes has become evident. This paper deals with the problem of finding optimal toll levels and locations in a road traffic network and presents a case study of Stockholm. The optimisation problem of finding optimal toll levels, given a predetermined cordon, and the problem of finding both optimal toll locations and levels are presented, and previously developed heuristics are used for solving these problems. For the Stockholm case study, the possible welfare gains of optimising toll levels in the current cordon and optimising both toll locations and their corresponding toll levels are evaluated. It is shown that by tuning the toll levels in the current congestion pricing cordon used in Stockholm, the welfare gain can be increased significantly, and furthermore improved by allowing a toll on a major bypass highway. It is also shown that, by optimising both toll locations and levels, a congestion pricing scheme with welfare gain close to what can be achieved by marginal social cost pricing can be designed with tolls being located on only a quarter of the tollable links.     

Pareto-improving congestion pricing and revenue refunding with multiple user classes

This study investigates Pareto-improving congestion pricing and revenue refunding schemes in general transportation networks, which make every road user better off as compared with the situation without congestion pricing. We consider user heterogeneity in value of time (VOT) by adopting a multiclass user model with fixed origin–destination (OD) demands. We first prove that an OD and class-based Pareto-improving refunding scheme exists if and only if the total system monetary travel disutility is reduced. In view of the practical difficulty in identifying individual user’s VOT, we further investigate class-anonymous refunding schemes that give the same amount of refund to all user classes traveling between the same OD pair regardless of their VOTs. We establish a sufficient condition for the existence of such OD-specific but class-anonymous Pareto-improving refunding schemes, which needs information only on the average toll paid and average travel time for trips between each OD pair.     

Nonlinear pricing in linear cities with elastic demands

Nonlinear road pricing charges each traveler based on his/her trip’s corresponding particular attribute level. In order to help authorities in designing road pricing systems at a strategic level, this paper attempts to address two fundamental questions: (i) what is the value of pricing’s nonlinearity for mitigating traffic congestion? (ii) if a nonlinear toll function is implemented, should it be convex, concave or other shape? Specifically, we consider distance-based pricing in linear cities. For linear monocentric cities with heterogeneous travelers, we show that the system optimal distance-based pricing indeed exhibits nonlinearity. It is proved that: (i) the cost-based system optimal toll function is monotonically increasing and concave with respect to the traveled distance; (ii) the time-based system optimal toll function always exists and is unique. If the initial proportion of each traveler group is invariant along a corridor and the demand function is of exponential type, then the time-based system optimal toll function enables the travelers, living further away from a city center, to face a lower toll level per unit distance. For a linear polycentric city, we demonstrate: (i) there always exists the system optimal differentiated (in terms of city centers) toll functions; (ii) it is highly possible that the system optimal non-differentiated toll function does not exist. Hence, we further propose an optimal toll design model, prove the Lipschitz continuity of its objective and adopt a global-optimization algorithm to solve it.     

Introducing congestion pricing on a new toll road

This paper proposes a demonstration project to test the effectiveness of congestion pricing in an urban area. It reviews the general theoretical case for such pricing and summarizes recent international interest in congestion pricing. Next, it sets forth the reasons why demonstration projects are needed, both to add to our knowledge about how effective congestion pricing may prove to be, and to address political and other public-acceptance barriers to implementation of the concept. The paper then defines a specific proposed test site for congestion pricing: a new toll road being planned for Orange County, California. It is proposed that instead of charging flat-rate tolls, the transportation agency could charge peak and off-peak tolls, increasing the level of the peak charge each year over a period of up to 10 years unless or until toll revenues decline below the levels forecast under the flat-rate toll alternative. Measurements of traffic flow and ride-sharing behavior would be made, as well as calculations of emission-reduction effects. The paper concludes with a brief discussion of marketing and political considerations involved in conducting such a demonstration.Abbreviations ARB Air Resources Board - AVI Automatic Vehicle Identification - CDMG Corridor Design Management Group - HOV High-occupancy vehicle - SJHTC San Joaquin Hills Transportation Corridor - TCA Transportation Corridor Agency - VMT Vehicle miles traveled     

Traffic congestion pricing methodologies and technologies

This paper reviews the methods and technologies for congestion pricing of roads. Congestion tolls can be implemented at scales ranging from individual lanes on single links to national road networks. Tolls can be differentiated by time of day, road type and vehicle characteristics, and even set in real time according to current traffic conditions. Conventional toll booths have largely given way to electronic toll collection technologies. The main technology categories are roadside-only systems employing digital photography, tag & beacon systems that use short-range microwave technology, and in-vehicle-only systems based on either satellite or cellular network communications. The best technology choice depends on the application. The rate at which congestion pricing is implemented, and its ultimate scope, will depend on what technology is used and on what other functions and services it can perform.     

Real-time congestion pricing strategies for toll facilities

This paper analyzes the dynamic traffic assignment problem on a two-alternative network with one alternative subject to a dynamic pricing that responds to real-time arrivals in a system optimal way. Analytical expressions for the assignment, revenue and total delay in each alternative are derived as a function of the pricing strategy. It is found that minimum total system delay can be achieved with many different pricing strategies. This gives flexibility to operators to allocate congestion to either alternative according to their specific objective while maintaining the same minimum total system delay. Given a specific objective, the optimal pricing strategy can be determined by finding a single parameter value in the case of HOT lanes. Maximum revenue is achieved by keeping the toll facility at capacity with no queues for as long as possible. Guidelines for implementation are discussed.     

Equity effects of congestion pricing: Quantitative methodology and a case study for Stockholm

It is widely recognised that congestion pricing could be an effective measure to solve environmental and congestion problems in urban areas—a reform that normally also would generate a net welfare surplus. Despite this the implementation of congestion pricing has been very slow. One reason for a low public and political acceptance could be that equity impacts have not been given enough concern. In studies of distributional impacts of congestion pricing it has often been claimed that the reform is regressive rather than progressive even if there are studies claiming the opposite. We develop a method for detailed, quantitative assessment of equity effects of road pricing and apply it to a real-world example, namely a proposed congestion-charging scheme for Stockholm. The method simultaneously takes into account differences in travel behaviour, in preferences (such as values of time) and in supply of travel possibilities (car ownership, public transport level-of-service etc.). We conclude that the two most important factors for the net impact of congestion pricing are the initial travel patterns and how revenues are used. Differences in these respects dwarf differences in other factors such as values of time. This is accentuated by the fact that the total collected charges are more than three times as large as the net benefits. With respect to different groups, we find that men, high-income groups and residents in the central parts of the city will be affected the most. If revenues are used for improving public transport, this will benefit women and low-income groups the most. If revenues are used for tax cuts, the net benefits will be about equal for men and women on the average, while it naturally will benefit high-income groups. Given that it is likely that the revenues will be used to some extent to improve the public transport system, we conclude that the proposed congestion-charging scheme for Stockholm is progressive rather than regressive.     

Optimal joint distance and time toll for cordon-based congestion pricing

This paper addresses the optimal toll design problem for the cordon-based congestion pricing scheme, where both a time-toll and a nonlinear distance-toll (i.e., joint distance and time toll) are levied for each network user’s trip in a pricing cordon. The users’ route choice behaviour is assumed to follow the Logit-based stochastic user equilibrium (SUE). We first propose a link-based convex programming model for the Logit-based SUE problem with a joint distance and time toll pattern. A mathematical program with equilibrium constraints (MPEC) is developed to formulate the optimal joint distance and time toll design problem. The developed MPEC model is equivalently transformed into a semi-infinite programming (SIP) model. A global optimization method named Incremental Constraint Method (ICM) is designed for solving the SIP model. Finally, two numerical examples are used to assess the proposed methodology.     

A note on the distortionary effects of revenue-neutral tolls in a bottleneck congestion game

This note demonstrates how the redistribution of revenue from a Pigouvian policy can distort incentives and handicap the social objectives of the policy by creating a moral hazard problem. Based on the Levinson (2005) game theory model, I develop a three-player bottleneck congestion game that emulates a repeated prisoner’s dilemma and derive efficient tolls. This conceptual game demonstrates the distortionary effects from a revenue-neutral toll policy with lump-sum revenue redistribution and the equity-efficiency tradeoff.