Toll pricing framework under logit‐based stochastic user equilibrium constraints

This paper addresses the toll pricing framework for the first‐best pricing with logit‐based stochastic user equilibrium (SUE) constraints. The first‐best pricing is usually known as marginal‐cost toll, which can be obtained by solving a traffic assignment problem based on the marginal cost functions. The marginal‐cost toll, however, has rarely been implemented in practice, because it requires every specific link on the network to be charged. Thus, it is necessary to search for a substitute of the marginal cost pricing scheme, which can reduce the toll locations but still minimize the total travel time. The toll pricing framework is the set of all the substitute toll patterns of the marginal cost pricing. Assuming the users' route choice behavior following the logit‐based SUE principle, this paper has first derived a mathematical expression for the toll pricing framework. Then, by proposing an origin‐based variational inequality model for the logit‐based SUE problem, another toll pricing framework is built, which avoids path enumeration/storage. Finally, the numerical test shows that many alternative pricing patterns can inherently reduce the charging locations and total toll collected, while achieving the same equilibrium link flow pattern. Copyright © 2013 John Wiley & Sons, Ltd.     

Speed limits,speed selection and network equilibrium

This paper investigates the local and global impact of speed limits by considering road users’ non-obedient behavior in speed selection. Given a link-specific speed limit scheme, road users will take into account the subjective travel time cost, the perceived crash risk and the perceived ticket risk as determinant factors for their actual speed choice on each link. Homogeneous travelers’ perceived crash risk is positively related to their driving speed. When travelers are heterogeneous, the perceived crash risk is class-specific: different user classes interact with each other and choose their own optimal speed, resulting in a Nash equilibrium speed pattern. With the speed choices on particular roads, travelers make route choices, resulting in user equilibrium in a general network. An algorithm is proposed to solve the user equilibrium problem with heterogeneous users under link-specific speed limits. The models and algorithms are illustrated with numerical examples.     

Road Pricing models with maintenance cost

According to the Federal Highway Administration of the United States, maintenance expenditure takes up more than 25% of road revenue disbursement and this percentage has been increasing gradually. The reason for the increment in maintenance cost is that there lacks incentives for road users to take this cost component into their driving behavior. That is, different classes of vehicles should be levied different levels of congestion tax due to the different degrees of damage on the highway if a road pricing policy is implemented. This paper intends to incorporate this concept into road pricing literature by introducing two types of vehicles. After the analysis of the problem, we find that different types of vehicles should be charged different tolls. The toll includes not only the travel delay cost of one's own vehicle and the other types of vehicles, but also the marginal maintenance cost that is dependent on the traffic flow. A set of numerical examples is provided to demonstrate the theoretical analyses. The result shows that both the welfare and cost coverage rate will increase when the road pricing mechanism takes the maintenance cost factor into account.     

Modeling and optimization of multimodal urban networks with limited parking and dynamic pricing

Cruising-for-parking constraints mobility in urban networks. Car-users may have to cruise for on-street parking before reaching their destinations. The accessibility and the cost of parking significantly influence people's travel behavior (such as mode choice, or parking facility choice between on-street and garage). The cruising flow causes delays eventually to everyone, even users with destinations outside limited parking areas. It is therefore important to understand the impact of parking limitation on mobility, and to identify efficient parking policies for travel cost reduction. Most existing studies on parking fall short in reproducing the dynamic spatiotemporal features of traffic congestion in general, lack the treatment of dynamics of the cruising-for-parking phenomenon, or require detailed input data that are typically costly and difficult to collect. In this paper, we propose an aggregated and dynamic approach for modeling multimodal traffic with the treatment on parking, and utilize the approach to design dynamic parking pricing strategies. The proposed approach is based on the Macroscopic Fundamental Diagram (MFD), which can capture congestion dynamics at network-level for single-mode and bi-modal (car and bus) systems. A parsimonious parking model is integrated into the MFD-based multimodal modeling framework, where the dynamics of vehicular and passenger flows are considered with a change in the aggregated behavior (e.g. mode choice and parking facility choice) caused by cruising and congestion. Pricing strategies are developed with the objective of reducing congestion, as well as lowering the total travel cost of all users. A case study is carried out for a bi-modal city network with a congested downtown region. An elegant feedback dynamic parking pricing strategy can effectively reduce travel delay of cruising and the generic congestion. Remarkably, such strategy, which is applicable in real-time management with limited available data, is fairly as efficient as a dynamic pricing scheme obtained from system optimum conditions and a global optimization with full information about the future states of the system. Stackelberg equilibrium is also investigated in a competitive behavior between different parking facility operators. Policy indications on on-street storage capacity management and pricing are provided.     

A utility-theory analysis of automobile speed under uncertainty of enforcement

Highway automobile speed and uncertain enforcement of the speed limit are introduced into a standard household utility model having time and income constraints. Due to uncertainty, expected utility is maximized to obtain the optimal speed (in excess of the speed limit). The optimal amounts of all other commodities and travel are also obtained. The key feature of the model is the risk attitude of the driver and the effect on optimal speed of such attitude. A related feature is the effect of risk attitude on the amount of speed self-insurance. An important finding is that the risk avert (seeking, neutral) driver charges himself an insurance premium that is larger than (smaller than, equal to) what is actuarially sufficient. The relationship between speed, risk attitude, and efficient cost of automobile travel is developed and implications are explored. A parametric analysis is conducted to establish the effect on optimal speed (and other variables) of changes in such policy instruments as the price of gasoline, the probability of being caught exceeding the speed limit, the unit speed fine, and the speed limit. Policy implications of the theoretical results are part of the conclusions.     

Optimal congestion taxes in a time allocation model

The purpose of this paper is to study optimal congestion taxes in a time-allocation framework. This makes it possible to distinguish taxes on inputs in the production of car trips and taxes on transport as an activity. Moreover, the model allows us to consider the implications of treating transport as a demand, derived from other activities. We extend several well known tax rules from the public finance literature and carefully interpret the implications for the optimal tax treatment of passenger transport services. The main findings of the paper are the following. First, if governments are limited to taxing market inputs into transport trip production, the time-allocation framework: (i) provides an argument for taxing congestion below marginal external cost, (ii) implies a favourable tax treatment for time-saving devices such as GPS, and (iii) provides a previously unnoticed argument for public transport subsidies. Second, if the government has access to perfect road pricing that directly taxes transport as an activity, all previous results disappear. Third, in the absence of perfect road pricing, the activity-specific congestion attracted by employment centres, by shopping centres or by large sports and cultural events should be corrected via higher taxes on market inputs in these activities (e.g., entry tickets, parking fees, etc.).     

Risk pricing inefficiency in public–private partnerships*

There is a drive towards delivering and operating public infrastructure through public–private partnership (PPP) rather than traditional public procurement. The assessment of the value for money achieved by the two alternative approaches rests in the cost of financing and their efficiency in delivery and operation. This paper focuses on the cost of financing, in particular the cost associated with transferring risk from the public to private sphere. If capital markets were efficient and complete, the cost of public (government) and private financing should be the same, with the relative delivery and operational efficiency remaining as the primary determinant of value-for-money. Evidence suggests, however, that the risk transfer to a PPP entails an inefficient risk pricing premium which goes beyond the direct cost of financing. We argue that a high price for PPPs results from large risk transfers, risk treatment within the private sector, and uncertainty around the past and future performance of public–private consortia. The corollary is that the efficiency gains from a PPP must be much higher than commonly expected to deliver a greater value for the money than under a traditional approach.     

Dynamic congestion pricing with day-to-day flow evolution and user heterogeneity

This paper investigates evolutionary implementation of congestion pricing schemes to minimize the system cost and time, measured in monetary and time units, respectively, with the travelers’ day-to-day route adjustment behavior and their heterogeneity. The travelers’ heterogeneity is captured by their value-of-times. First, the multi-class flow dynamical system is proposed to model the travelers’ route adjustment behavior in a tolled transportation network with multiple user classes. Then, the stability condition and properties of equilibrium is examined. We further investigate the trajectory control problem via dynamic congestion pricing scheme to derive the system cost, time optimum, and generally, Pareto optimum in the sense of simultaneous minimization of system cost and time. The trajectory control problem is modeled by a differential–algebraic system with the differential sub-system capturing the flow dynamics and the algebraic one capturing the pricing constraint. The explicit Runge–Kutta method is proposed to calculate the dynamic flow trajectories and anonymous link tolls. The method allows the link tolls to be updated with any predetermined periods and forces the system cost and/or time to approach the optimum levels. Both analytical and numerical examples are adopted to examine the efficiency of the method.     

Advanced pricing and rationing policies for large scale multimodal networks

The applying of simplified schemes, such as cordon pricing, as second-best solution to the toll network design problem is investigated here in the context of multiclass traffic assignment on multimodal networks. To this end a suitable equilibrium model has been developed, together with an efficient algorithm capable of simulating large scale networks in quite reasonable computer time. This model implements the theoretical framework proposed in a previous work on the toll optimization problem, where the validity of marginal cost pricing for the context at hand is stated. Application of the model to the real case of Rome shows us, not only that on multimodal networks a relevant share (up to 20%) of the maximum improvements in terms of social welfare achievable with marginal cost pricing can in fact be obtained through cordon pricing, but also that in practical terms rationing is a valid alternative to pricing, thus getting around some of the relevant questions (theoretical, technical, social) the latter raises. As a result we propose a practical method to analyze advanced pricing and rationing policies differentiated for user categories, which enables us to compare alternative operative solutions with an upper bound on social welfare based on a solid theoretical background.     

Analysis of regulation and policy of private toll roads in a build-operate-transfer scheme under demand uncertainty

The build-operate-transfer (BOT) approach is one of the privatization mechanisms for promoting transportation infrastructure developments by using private funds to construct new infrastructure facilities. In a BOT scheme, it often involves three parties: the government, whose objective is to maximize the benefit defined in terms of social welfare added to the society; the private investors, whose objective is to maximize the profit generated from the investment; and the road users, whose objective is to minimize the inequality of benefit distribution among the road users traveling from different origin–destination pairs. Each of these parties has different objectives that often conflict with each other. In this paper, we develop various optimal road pricing models under demand uncertainty for analyzing the tradeoffs among the three objectives. In addition, a project evaluation framework is developed for assessing the effects of government policy and regulation on the BOT project. Seven cases of the BOT road pricing problem are analyzed: (1) BOT without regulation, (2) BOT with price control regulation, (3) BOT with equity regulation, (4) BOT with construction cost subsidy, (5) BOT with concession period extension, (6) BOT with construction cost subsidy and concession period extension, and (7) BOT with multiple objectives. Numerical results using a real case study of the Ban Pong–Kanchananburi Motorway (BMK) in Thailand are provided to examine the above seven cases.     

Estimating the marginal cost of railway track renewals using corner solution models

Economic theory advocates marginal cost pricing for efficient utilisation of transport infrastructure. A growing body of literature has emerged on the issue of rail marginal infrastructure wear and tear costs, but the majority of the work is focused on costs for infrastructure maintenance. Railway track renewals are a substantial part of an infrastructure manager’s budget, but in disaggregated statistical analyses they cause problems for traditional regression models since there is a piling up of values of the dependent variable at zero. Previous econometric work has sought to circumvent the problem by aggregation in some way. In this paper we instead apply corner solution models to disaggregate (track-section) data, including the zero observations. We derive track renewal cost elasticities with respect to traffic volumes and in turn marginal renewal costs using Swedish railway renewal data over the period 1999–2009. This paper is the first attempt in the literature to apply corner solution models, and in particular the two-part model, to disaggregate renewal cost data in railways. It is also the first paper that we are aware of to report usage elasticities specifically for renewal costs and therefore adds important new evidence to the previous literature where there is a paucity of studies on renewals and considerable uncertainty over the effects of rail traffic on renewal costs. In the Swedish context, we find that the inclusion of marginal track renewal costs in the track access pricing regime, which currently only reflects marginal maintenance costs, would add substantially to the existing track access charge. EU legislation requires that access charges reflect the ‘costs directly incurred as a result of operating the train service’, which should include a marginal renewal cost component. This change would also increase the cost recovery ratio of the Swedish infrastructure manager, thus meeting a policy objective of the national government.     

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.     

How to road price in a world with electric vehicles and government budget constraints

In this paper we examine what characterizes second-best road prices targeting external costs from driving electric (EV) and conventional (ICEV) vehicles when there are distortionary labor taxes and binding government budget constraints. Further, we examine how this second-best pricing fits with government set goals of reducing CO₂ emissions. The paper further develops an analytical framework for assessing first- and second-best road prices on vehicle kilometers, extending it to include EVs and externalities that vary geographically and by time of day. We find that optimal road prices largely vary with external cost, but are also significantly affected by the interactions with the rest of the fiscal system. Not surprisingly, the highest road prices should be for ICEVs in large cities during peak hours due to high external costs. More surprisingly, we find that the road price for ICEVs in rural areas should be lower than that for EVs due to large fiscal interaction effects. These road prices give large welfare gains, but they lead to no reduction in carbon emissions when applying the currently recommended social cost of carbon.     

Bus congestion, optimal infrastructure investment and the choice of a fare collection system in dedicated bus corridors

Microeconomic optimisation of scheduled public transport operations has traditionally focused on finding optimal values for the frequency of service, capacity of vehicles, number of lines and distance between stops. In addition, however, there exist other elements in the system that present a trade-off between the interests of users and operators that have not received attention in the literature, such as the optimal selection of a fare payment system and a designed running speed (i.e., the cruising speed that buses maintain in between two consecutive stops). Alternative fare payment methods (e.g., on-board and off-board, payment by cash, magnetic strip or smart card) have different boarding times and capital costs, with the more efficient systems such as a contactless smart card imposing higher amounts of capital investment. Based on empirical data from several Bus Rapid Transit systems around the world, we also find that there is a positive relationship between infrastructure cost per kilometre and commercial speed (including stops), achieved by the buses, which we further postulate as a linear relationship between infrastructure investment and running speed. Given this context, we develop a microeconomic model for the operation of a bus corridor that minimises total cost (users and operator) and has five decision variables: frequency, capacity of vehicles, station spacing, fare payment system and running speed, thus extending the traditional framework. Congestion, induced by bus frequency, plays an important role in the design of the system, as queues develop behind high demand bus stops when the frequency is high. We show that (i) an off-board fare payment system is the most cost effective in the majority of circumstances; (ii) bus congestion results in decreased frequency while fare and bus capacity increase, and (iii) the optimal running speed grows with the logarithm of demand.     

The Smeed Report 50 years on: a role for the workplace parking levy?

Fifty years ago, Reuben Smeed chaired a study and produced a Report on the Economic and Technical Possibilities of Road Pricing. This report was to consider different methods of charging, including road pricing, to see if different pricing methods could reduce the problems associated with congestion as opposed to the traditional methods in place such as fuel tax. Since that time, various attempts have been made to introduce road pricing schemes but with only modest success so far. By contrast parking policies, a second-best alternative to road pricing, have been extensively used by local authorities as a means of managing congestion. The effectiveness of such policies, however, has been limited by an increase in the proportion of privately owned non-residential parking which is not under the control of local authorities. The aim of this paper is to present the results of an early-stage, post-implementation study of the Nottingham Workplace Parking Levy (WPL) – a measure that charges employers for the number of parking spaces they provide for their staff. Particular emphasis is placed on why a WPL was seen as being favourable compared to a road pricing alternative. The reason for this was that it could be introduced in a shorter time frame and at a lower cost, thus making it a lower risk option when compared with road pricing.     

Urban delivery industry response to cordon pricing, time-distance pricing, and carrier-receiver policies in competitive markets

The paper develops a set of analytical formulations to study the behavior of the urban delivery industry in response to cordon time-of-day pricing, time-distance pricing, and comprehensive financial policies targeting carriers and receivers. This is accomplished by modeling the behavior of receivers in response to financial incentives, and the ensuing behavior of the carrier in response to both pricing and the receivers’ decisions concerning off-hour deliveries. The analytical formulations consider both the base case condition, and a mixed operation with both regular hour and off-hour deliveries; two pricing schemes: cordon time of day, and time-distance pricing; two types of operations: single-tour, and multi-tour carriers; and three different scenarios in terms of profitability of the carrier operation, which include an approximation to the best case, the expected value, and the worst case. The analyses, both theoretical and numerical, highlight the limitations of pricing-only approaches. In the case of cordon time of day pricing, the chief conclusion is that it is of limited use as a freight demand management tool because: (1) in a competitive market the cordon toll cannot be transferred to the receivers as it is a fixed cost and (2) the structure of the cost function, that only provides an incentive to the carrier to switch to the off-hours when all the receivers in the tour switch to the off-hours. The analyses of time-distance pricing clearly indicate that, though its tolls could be transferred to the receivers and provide an incentive for behavior change, the magnitude of the expected toll transfers under real life conditions are too small to have any meaningful impact on receivers choice of delivery times. In essence, the key policy implication is that in order to change the joint behavior of carrier and receivers, financial incentives—or programs that foster unassisted off-hour deliveries—should be made available to receivers in exchange for their commitment to do off-hour deliveries. As the paper proves, if a meaningful number of receivers switch to the off-hours, the carriers are likely to follow suit.     

Miles,speed, and technology: Traffic safety under oligopolistic insurance

We study road safety when insurance companies have market power, and can influence drivers’ behavior via insurance premiums. We obtain first- and second-best premiums for different insurance market structures. The insurance program consists of an insurance premium, and marginal dependencies of that premium on speed and own safety technology choice of drivers. A private monopolist internalizes collision externalities up to the point where compensations to users’ benefit matches the full (intangible) costs; in oligopolistic markets, insurers do not fully internalize collision externalities. Analytical results demonstrate how insurance firms’ incentives to influence traffic safety coincide with or deviate from socially optimal incentives. Our results may be useful for design of pay-as-you-speed and alike insurances as well as policies related to driving safety.     

Transaction costs and tradable mobility credits

Artificial markets for mobility credits have been proposed as an alternative to conventional congestion pricing schemes. This paper examines the effects of transaction costs on two types of markets: an auction market and a negotiated market. In an auction market, users purchase all of the needed mobility credits through a competitive bidding process. In a negotiated market, the users initially receive certain amount of mobility credits from the government and trade with each other through negotiation to fulfill their needs. We assume that a brokerage service is built in both markets to facilitate transactions and accordingly, the users have to pay a commission fee proportional to the value of trade. The users are also given the option to purchase credits from the government if for some reasons they cannot use or wish to avoid the markets. Our analyses suggest that the auction market can achieve the desired equilibrium allocation of mobility credits as long as the government sets its price properly and the unit transaction cost is lower than the price that the market would reach in absence of transaction costs. However, in the negotiated market, transaction costs could divert the system from the desired equilibrium regardless of their magnitude. More importantly, the initial allocation of mobility credits may affect the final equilibrium even when marginal transaction costs are constant.     

Do people drive safer when accidents are more expensive: Testing for moral hazard in experience rating schemes

Using individual policies and claims data from the Croatian mandatory motor insurance we test the theoretical proposition that under moral hazard, experience rated pricing scheme should generate the negative state dependence in claims, i.e. that drivers should drive more safely after they had an accident. The empirical challenge in these tests is to disentangle the state dependence from unobserved heterogeneity. We propose a simple approach based on the explicit reliance on the cost of future accidents function which is used to filter out the pure incentives effect, whereas the bonus-malus scale is used to control for pure heterogeneity. Our results confirm the existence of negative dependence in claims indicating the presence of significant moral hazard effect. Increasing a 3-year cost of having an accident by approximately US$20 decreases the probability of having an accident by 6.5%.     

Measuring risk aversion to guide transportation policy: Contexts,incentives, and respondents

Road pricing may provide a solution to increasing traffic congestion in metropolitan areas. Route, departure time and travel mode choices depend on risk attitudes as commuters perceive the options as having uncertain effects on travel times. We propose that Experimental Economics methods can deliver data that uses real consequences and where the context can be varied by the researcher. The approach relies on the controlled manipulation of contexts, similar to what is done in the Stated Choice approach, but builds in actual consequences, similar to the Revealed Preference approach. This paper investigates some of the trade-offs between the cost of conducting Experimental Economics studies and the behavioral responses elicited. In particular, we compare responses to traditional lottery choice tasks to the route choice tasks in simulated driving environments. We also compare students (a low cost convenient participant pool) to field participants recruited from the driving population. While we see initial differences across our treatment groups, we find that their risk taking behavior converge with minimal repetition.