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.     

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.     

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.     

Distributional effects of road pricing: Assessment of nine scenarios for Paris

The starting point of this paper is to consider that there is no general answer to the question of the equity of urban road pricing. We therefore simulate and compare the distributional effects on commuters of nine toll scenarios for Paris, assuming that utility is nonlinear in income. We show that the distributional pattern across income groups depends crucially on the level of traffic reduction induced by tolling. Stringent tolls are more favourable to low-income motorists. Equity effects also vary with toll design. Compared to a reference scenario which uniformly charges all motorists driving within Paris, an inbound cordon toll is detrimental to low-incomes. Conversely, granting a rebate to low CO₂ emission cars slightly improves their situation while an exemption for Paris residents is neutral. Surprisingly, it matters little for social equity whether toll revenues are allocated to all commuters or solely to public transport users.     

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

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.     

Users’ perceptions and willingness to pay in interurban toll roads: identifying differences across regions from a nationwide survey in Spain

Users’ acceptability is considered one of the key drivers for the successful implementation of transport policy measures. This is especially crucial in the case of toll roads since they are financed through drivers’ contributions. Previous literature in this field has mainly focused on measuring users’ attitudes towards urban congestion pricing strategies. However limited research has been developed concerning interurban toll roads. Previous research shows that socioeconomic variables are not conclusive to explain users’ perceptions towards tolls. By contrast, other drivers such as regional differences seem to play a more important role, especially when charging conditions within the same nation greatly vary across regions. This paper analyzes regional differences in users’ attitudes within an asymmetrical distribution of the toll road network across regions. Based on a nationwide survey conducted to road users in interurban toll roads in Spain, we develop both a binomial logit and a censored regression (tobit) model to explore drivers’ perceptions and willingness to pay. The research concludes that users from regions with a more extensive tolled network generally show a more negative attitude towards charges, but not necessarily a lower willingness to pay. The paper also points out that an asymmetrical distribution of toll roads across regions may result in negative perceptions among those users perceiving to be unfairly treated when compared to citizens in other regions.     

Optimal tolls for multi-class traffic: Analytical formulations and policy implications

This paper puts together an analytical formulation to compute optimal tolls for multi-class traffic. The formulation is comprised of two major modules. The first one is an optimization component aimed at computing optimal tolls assuming a Stackelberg game in which the toll agency sets the tolls, and the equilibrating traffic plays the role of the followers. The optimization component is supported by a set of cost models that estimate the externalities as a function of a multivariate vector of traffic flows. These models were estimated using Taylor series expansions of the output obtained from traffic simulations of a hypothetical test case. Of importance to the paper is the total travel time function estimated using this approach that expresses total travel time as a multivariate function of the traffic volumes. The formulation presented in the paper is then applied to a variety of scenarios to gain insight into the optimality of current toll policies. The optimal tolls are computed for two different cases: independent tolls, and tolls proportional to passenger car equivalencies (PCE).The numerical results clearly show that setting tolls proportional to PCEs leads to lower values of welfare that are on average 15% lower than when using independent tolls, though, in some cases the total welfare could be up to 33% lower. This is a consequence of two factors. First, the case of independent tolls has more degrees of freedom than the case of tolls proportional to PCEs. Second, tolls proportional to PCEs do not account for externalities other than congestion, which is likely to lead to lower welfare values.The analytical formulations and numerical results indicate that, because the total travel time is a non-linear function of the traffic volumes, the marginal social costs and thus the optimal congestion tolls also depend on the traffic volumes for each vehicle class. As a result of this, for the relatively low volumes of truck traffic observed in real life, the optimal congestion tolls for trucks could indeed be either lower or about the same as for passenger cars. This stand in sharp contrast with what is implied in the use of PCEs, i.e., that the contribution to congestion are constant. This latter assumption leads to optimal truck congestion tolls that are always proportional to the PCE values.The comparison of the toll ratios (truck tolls divided by passenger car tolls) for both observed and optimal conditions suggests that the tolls for small trucks are about the right level, maybe a slightly lower than optimal. However, the analysis of the toll ratio for large trucks seems to indicate a significant overcharge. The estimates show that the average observed toll ratio for large trucks is even higher than the maximum optimal toll ratio found in the numerical experiments. This suggests that the tolls for large trucks are set on the basis of revenue generation principles while the passenger car tolls are being set based on a mild form of welfare maximization. This leads to a suboptimal cross-subsidization of passenger car traffic in detriment of an important sector of the economy.     

Design of income-equitable toll prices for high occupancy toll lanes in a single toll facility

Income inequity potentially exists under high occupancy toll (HOT) lanes whereby higher-income travelers may reap the benefits of the facility. An income-based multi-toll pricing approach is proposed for a single HOT lane facility in a network to maximize simultaneously the toll revenue and address the income equity concern, while ensuring a minimum level-of-service on the HOT lanes and that the toll prices do not exceed pre-specified thresholds. The problem is modeled as a bi-level optimization formulation. The upper level model maximizes revenue for the tolling authority subject to pre-specified upper bounds on tolls. The lower level model solves the stochastic user equilibrium problem. An agent-based solution approach is used to determine the toll prices by considering the tolling authority and commuters as agents. Results from numerical experiments indicate that a multi-toll pricing scheme is more equitable and can yield higher revenues compared to a single toll price scheme across travelers.     

Viability of new road infrastructure with heterogeneous users

This paper explores the importance of heterogeneity in value of time and route choice when assessing the viability of new road infrastructure to alleviate congestion problems. The model incorporates strategic interaction between road operators in a cost-benefit framework and several competitive regimes are considered. It is then employed to establish the financial and socio-economic viability of a congestion pricing demonstration entering Madrid city centre, where road users have to choose between a free but highly congested road and a priced free-flowing road (semi-private regime). A logit estimation is undertaken with information from a questionnaire among road users in the Eastern Madrid area to obtain users’ value of time and of congestion.The tolls obtained generate a traffic reallocation towards the new roadway such that revenues suffice to render the infrastructure socio-economically viable. The private and the low toll regimes generate similar welfare gains that are close to the first best. Yet the former supposes large losses to users. The low toll and the semi-private regimes do not raise such distributional concerns. However, the low toll regime requires a sufficiently high traffic growth rate to make it financially viable; this does not happen for the other competitive regimes.     

Step-tolling with price-sensitive demand: Why more steps in the toll make the consumer better off

Most dynamic models of congestion pricing use fully time-variant tolls. However, in practice, tolls are uniform over the day, or at most have just a few steps. Such uniform and step tolls have received surprisingly little attention from the literature. Moreover, most models that do study them assume that demand is insensitive to the price. This seems an empirically questionable assumption that, as this paper finds, strongly affects the implications of step tolling for the consumer. In the bottleneck model, first-best tolling has no effect on the generalised price, and thus consumer surplus remains the same as without tolling. Conversely, under price-sensitive demand, step tolling increases the price, making the consumer worse off. The more steps the toll has, the closer it approximates the first-best toll, thereby increasing the welfare gain and making consumers better off. This indicates the importance for real-world tolls to have as many steps as possible: this not only raises welfare, but may also increase the political acceptability of the scheme by making consumers better off.     

Nonlinear pricing on private roads with congestion and toll collection costs

Nonlinear pricing (a form of second-degree price discrimination) is widely used in transportation and other industries but it has been largely overlooked in the road-pricing literature. This paper explores the incentives for a profit-maximizing toll-road operator to adopt some simple nonlinear pricing schemes when there is congestion and collecting tolls is costly. Users are assumed to differ in their demands to use the road. Regardless of the severity of congestion, an access fee is always profitable to implement either as part of a two-part tariff or as an alternative to paying a toll. Use of access fees for profit maximization can increase or decrease welfare relative to usage-only pricing for profit maximization. Hence a ban on access fees could reduce welfare.     

Cordon tolls and competition between cities with symmetric and asymmetric interactions

The aim of this paper is to model the impacts of competition between cities on both the optimal welfare generating tolls and upon longer-term decisions such as business and residential location choices. The research uses a dynamic land use transport interaction model of two neighbouring cities and analyses the impacts by setting up a game between the two cities to maximise the welfare of their own residents. The work builds on our earlier research which studied competition in a small network using a static equilibrium approach for private car traffic without accounting for the land use responses to the change in accessibility. This paper extends the earlier work by setting up a dynamic model which includes active modes of travel and the more usual car and public transport in a realistic twin city setting and assesses the longer term relocation responses. This paper firstly sets out the competition between two hypothetical identical cities i.e. the symmetric case; and then sets out the real world asymmetric case in which the cities are of different size representative of Leeds and Bradford in the UK but equally applicable elsewhere too. We found that the level of interaction between the two cities is a key determinant to the optimal tolls and welfare gains. Our findings show that the competition between cities could lead to a Nash Trap at which both cities are worse off in terms of welfare gains. On the other hand, we found that cities, if regulated, would gain in terms of welfare and yet charge only half the toll compared with tolls under competition. We then show that the effect of competition increases with increased interaction between cities. In terms of residential location, cities with higher charges benefit from an increase in residents, though as with other studies, the relative change in population in response to cordon charging is small. The policy implications are threefold—(i) while there is an incentive to cooperate at local authority level, this is not achieved due to competition; (ii) where cities compete they may fall into a Nash Trap where both cities will be worse off compared to the regulated solution; and (iii) regulation is recommended when there is a strong interaction between the cities but that the benefits of regulation decrease as interaction between cities decreases and the impact of competition is lessened.     

Social welfare analysis of investment public–private partnership approaches for transportation projects

This paper has two objectives: (i) to introduce a new approach in order to gain widespread support for road pricing; and (ii) to develop a detailed social welfare analysis for road pricing schemes. We first describe our novel approach that stimulates public support for road pricing, which we refer to as an investment public–private partnership, or IP3. This approach returns a significant portion of the economic value created by road pricing back to the citizens who own the newly priced facility. We then present a social welfare framework that estimates the benefits and costs of using the IP3 approach on an urban transportation network. A P3 project’s impact on overall social welfare provides a more comprehensive evaluation criterion than the often-used Value for Money (VfM) analysis. Apart from several theoretical studies, a detailed social welfare analysis that includes all major P3 project stakeholders is absent from the literature. We use Fresno, California as our case study in order to conduct a welfare analysis on IP3s. Our results show that system-optimal tolling favors average users, but that government—and consequently taxpayers—should pay for costly tolling systems (negative profits). In contrast, unlimited profit-maximizing tolls raise substantial profits for government, for the infrastructure’s citizen-owners, and for the private sector, but the average user is worse off. From a social-welfare perspective, one should search for a Pareto improvement under which all major stakeholders are better off. Our estimates indicate that a mixed public and private tolling scheme offers such an improvement.     

Road user charging design: dealing with multi-objectives and constraints

This paper proposes an innovative approach for designing a road user charging scheme to meet multiple policy objectives. Three practical features are integrated into the design methodology including (i) cordon formation, (ii) a set of design constraints, and (iii) multiple objectives of the scheme. The methods also consider possible responses of road travellers to the charging scheme. Two methods based on genetic algorithms (GA) are developed for optimising a charging cordon scheme with constraints and with multiple objectives. The dynamic self-adaptive penalty GA and Non-dominated Sorting GA II (NSGA-II) are applied to the constrained design and multi-objective design respectively. The objective functions or constraints considered include social welfare improvement, revenue generation, and distributional equity impact. A case study of the City of Edinburgh is presented and common characteristics of charging cordon designs which perform well against the three objectives are discussed.

Bottleneck congestion: Differentiating the coarse charge

The traditional bottleneck model for road congestion promotes the implementation of a triangular, and time varying, charge as the optimal solution for the road congestion externality. However, cognitive and technological barriers put a practical limit to the degree of differentiation real world implementations can handle. The traditional approach to accommodate for this concern has been a step toll, with the single step coarse charge as its simplest case.In this paper we study how efficiency of the coarse charge can be improved by differentiating its level and timing across groups of travellers. We use the traditional bottleneck model to analyse how the coarse charge can be differentiated over two groups of travellers assuming inelastic peak-hour demand.The results of our analysis indicate that differentiating the coarse charge across two groups of travellers considerably improves its efficiency without increasing cognitive effort and decision making costs for the individual traveller. A numeric illustration reveals a welfare gain of 69% of the first-best charge, up from 53% for the generic coarse charge. This increase is similar to what is obtained by moving from the coarse charge to a generic two step toll. Once different groups have been defined, one could in fact achieve the same gains by temporal separation of drivers, for example by use of licence plate numbers.The presented charging regime has a considerable degree of flexibility with respect to the share of travellers to attribute to each scheme, which further adds to its merits in practical applicability.     

Integrating congestion pricing and transit investment planning

This paper develops a mathematical model and solution procedure to identify an optimal zonal pricing scheme for automobile traffic to incentivize the expanded use of transit as a mechanism to stem congestion and the social costs that arise from that congestion. The optimization model assumes that there is a homogenous collection of users whose behavior can be described as utility maximizers and for which their utility function is driven by monetary costs. These monetary costs are assumed to be the tolls in place, the per mile cost to drive, and the value of their time. We assume that there is a system owner who sets the toll prices, collects the proceeds from the tolls, and invests those funds in transit system improvements in the form of headway reductions. This yields a bi-level optimization model which we solve using an iterative procedure that is an integration of a genetic algorithm and the Frank–Wolfe method. The method and solution procedure is applied to an illustrative example.     

Pricing local emission exposure of road traffic: An agent-based approach

This paper proposes a new approach to iteratively calculate local air pollution exposure tolls in large-scale urban settings by taking the exposure times and locations of individuals into consideration. It explicitly avoids detailed air pollution concentration calculations and is therefore characterized by little data requirements, reasonable computation times for iterative calculations, and open-source compatibility. In a first step, the paper shows how to derive time-dependent vehicle-specific exposure tolls in an agent-based model. It closes the circle from the polluting entity, to the receiving entity, to damage costs, to tolls, and back to the behavioral change of the polluting entity. In a second step, the approach is applied to a large-scale real-world scenario of the Munich metropolitan area in Germany. Changes in emission levels, exposure costs, and user benefits are calculated. These figures are compared to a flat emission toll, and to a regulatory measure (a speed reduction in the inner city), respectively. The results indicate that the flat emission toll reduces overall emissions more significantly than the exposure toll, but its exposure cost reductions are rather small. For the exposure toll, overall emissions increase for freight traffic which implies a potential conflict between pricing schemes to optimize local emission exposure and others to abate climate change. Regarding the mitigation of exposure costs caused by urban travelers, the regulatory measure is found to be an effective strategy, but it implies losses in user benefits.     

Behavioral adjustments and equity effects of congestion pricing: Analysis of morning commutes during the Stockholm Trial

This paper assesses the horizontal and vertical equity effects of the Stockholm Trial with Congestion Pricing for morning commuters, in terms of both travel behavioral adjustments and welfare effects, as a result of the toll’s direct effects and the behavioral adjustments. We consider specifically two behavioral adjustments: mode choice and departure time choice. Initial car drivers crossing the toll cordon had a 15 percentage-points higher rate of switching to public transit as compared with those not crossing the cordon. We also find some evidence of peak spreading, in particular toward a later departure time, as a result of the charging scheme, but most people choose a departure time within 15 min both before and during the trial. In the welfare analysis, we found no clear pattern of increasing burden by either increasing income or decreasing income, and the increase in the Gini Coefficient was insignificant. We also found no significant difference in either the mode-switching behavior or the average welfare effect for women versus for men.     

Designing Emission Charging Schemes for Transportation Conformity

This paper designs emission charging schemes to ensure traffic emissions not exceeding the emission budgets in emission regulation areas. In a network where all links are tollable, we prove that, under mild conditions, there exists a non‐negative link‐based toll scheme that achieves the transportation conformity requirement while minimizing total emissions. We further consider only tolling in the emission regulation areas and formulate a model to determine optimal area‐based emission charges to ensure the conformity. The model is formulated as a mathematical program with complementarity constraints. A solution framework is developed to solve the model, leveraging on a derivative‐free pattern search algorithm and integrating MOVES to estimate vehicular emissions more accurately. The proposed models are demonstrated on two numerical examples. Copyright © 2013 John Wiley & Sons, Ltd.     

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.