Toll Scheme Research Articles

Policy lessons for regulating public–private partnership tolling schemes in urban environments

Public–private partnerships (P3s) are likely to impact entire transportation systems in fundamental ways. However, few studies have examined the potential impact of P3s on large-scale transportation networks. These studies have focused on modeling rather than on policy analysis. The literature thus does not offer guidance for designing and administering P3s to improve transportation system performance while maintaining profitability. Using Fresno, California's transportation network as a laboratory, we consider the effects of alternative P3 tolling approaches on profit maximization and system performance optimization at full urban transportation network scale. Based on system modeling results, we offer the following recommendations for policy makers to design and promote successful P3s in urban settings: (i) to promote a profitable and a socially beneficial system, toll rates should be set examining both profit-maximizing and system-optimal rates; (ii) even though tolls (i.e., higher travel costs) on a few roads help reduce travel demand they may, counter-intuitively, lead to higher total travel cost for the overall transportation system because of users’ decision to travel longer distances to avoid tolls, especially when high toll rates are applied; (iii) lower limit(s) on tolls (in addition to upper limits) may be required to enforce system-optimal tolling and avoid undercutting by private owners; (iv) a variable tolling approach (i.e., temporally- and spatially-varying tolls) significantly reduces congestion and increases profits relative to flat tolls; and (v) public officials should provide a comprehensive plan regarding past, current, and future P3 projects along with a detailed system-wide impact analysis to promote a more sustainable transportation system.

A network model for capped link-based tolls

Toll road operators and other toll facility stakeholders require analysis tools to estimate the ridership and projected income for an increasing variety of tolling schemes. Some tolling schemes commonly considered include link-based tolls as well as derived schemes, such as charging both a minimum and a maximum toll (or cap) for the use of the facility. In addition, different entry ramps may incur different tolls, which may be added to a link-based toll and subject the total toll to a toll cap value. Network equilibrium models that consider such tolls result in non-additive costs on the modeled network due to the capping. To obtain a more tractable equivalent model, a network transformation is used. The model uses the addition of a set of temporary links to the network, which inherit the delays and tolls of the original links. It considers the toll cost per link, as well as minimum and a maximum value of the tolls paid. It is shown that the modified and the original network formulations are equivalent. To solve the resulting multi-class network equilibrium model, a multi-threaded bi-conjugate variant of the linear approximation method has been adapted for the particular network model used. The method is illustrated with a small example as well as an instance of capped link-based toll modeling on a network originating from practice that employs the toll structure considered.

Sensor location problems in path-differentiated congestion pricing

Path-differentiated congestion pricing is a tolling scheme that imposes tolls on paths instead of individual links. One way to implement this scheme is to deploy automated vehicle identification sensors, such as toll tag readers or license plate scanners, on roads in a network. These sensors collect vehicles’ location information to identify their paths and charge them accordingly. In this paper, we investigate how to optimally locate these sensors for the purpose of implementing path-differentiated pricing. We consider three relevant problems. The first is to locate a minimum number of sensors to implement a given path-differentiated scheme. The second is to design an optimal path-differentiated pricing scheme for a given set of sensors. The last problem is to find a path differentiated scheme to induce a given target link-flow distribution while requiring a minimum number of sensors.

Optimal Urban Development Density along A Multi-Modal Linear Travel Corridor with Time-distance Toll Scheme

Consider a travel corridor with a multi-modal transport system (i.e., highway and railway) that connects a continuum of residential locations to a point of CBD. Both highway and railway are subject to congestion effects. All commuters travel along the corridor from home to work in the morning peak hour. The travel costs include travel time, schedule delay and monetary cost. The spatial dynamics of the traffic congestion on both transportation systems are determined by the trip-timing condition, that no traveler will experience a lower travel cost by departing at a different time or switching to a different mode. The flow dynamics on the highway will be considered by applying basic LWR model, while crowdedness (i.e., passenger density on the train) is used to describe the congestion on the railway. The simultaneous temporal and spatial dynamics of commute traffic pattern will be modeled by applying a second-order partial differential complementarity system approach. A time-distance road pricing scheme is applied to achieve the system optimal condition. The urban population is assumed to be located continuously along the corridor. However, the spatial population density distribution is regarded as variant. As is well known that the urban planning issue of population density distribution affects the transportation system significantly, this study aims to find the optimal urban population density distribution in a linear continuous travel corridor leading to optimal transportation system performance, with basic assumptions that it follows some given distribution pattern like negative exponential distribution. The problem is eventually formulated into a mathematical program with complementarity constraints and efficient solution algorithm is developed. Finally, numerical examples are conducted to test the model formulation validity and efficiency.

Optimal non-queuing pricing for the Suez Canal

After the 2010 canal deepening project, the permissible draft through the Suez Canal was increased from 62 to 66 feet. Most types of container ships and bulk carriers can pass through the Canal. The queuing problem at the anchorage of the Canal is worsening because an increasing number of ships are willing to cross the Canal to reach their destination ports. To solve this problem, this article introduces the analytic mathematical approach to establish the optimal non-queuing toll scheme that will effectively disperse all ship arrival times to achieve equilibrium. Consequently, queuing at both entrances of the Suez Canal can be totally eliminated. The article also shows the arrival rates of all ships both before and after implementing the toll scheme. The ratio of all early (or delayed) arrivals to the total number of ships passing through the Canal before tolling will be identical to that after tolling.

A reinforcement learning approach for distance‐based dynamic tolling in the stochastic network environment

SummaryThis paper proposes a novel dynamic tolling model based on distance and accounts for uncertain traffic demand and supply conditions. The distance‐based tolling controller is modeled as an intelligent agent interacting within the stochastic network environment dynamically by taking actions, which are to decide different distance‐based tolling rates of vehicles. The distance‐based tolls are determined according to various metrics, for example, total traffic flow throughput, delay time, vehicular emissions, which are set as objectives in the modeling framework. The optimal tolling rate is determined by an R‐Markov Average Reward Technique based reinforcement learning algorithm. In the numerical case study, we test the proposed tolling scheme on a benchmark test network—the Sioux Falls network—where specified links are candidate toll links. The result shows that the total travel time of tolling links reduces by 25% over simulation runs. Copyright © 2014 John Wiley & Sons, Ltd.

Which Protocol? Mutual Interaction of Heterogeneous Congestion Controllers

A large number of congestion control protocols have been proposed in the last few years, with all having the same purpose—to divide available bandwidth resources among different flows in a fair manner. Each protocol operates on the paradigm of some conception of link price (such as packet losses or packet delays) that determines source transmission rates. Recent work on network utility maximization has brought forth the idea that the fundamental price or Lagrange multiplier for a link is proportional to the queue length at that link, and that different congestion metrics (such as delays or drops) are essentially ways of interpreting such a Lagrange multiplier. We thus ask the following question: Suppose that each flow has a number of congestion control protocols to choose from, which one (or combination) should it choose? We introduce a framework wherein each flow has a utility that depends on throughput and also has a disutility that is some function of the queue lengths encountered along the route taken. Flows must choose a combination of protocols that would maximize their payoffs. We study both the socially optimal, as well as the selfish cases to determine the loss of system-wide value incurred through selfish decision making, so characterizing the “price of heterogeneity.” We also propose tolling schemes that incentivize flows to choose one of several different virtual networks catering to particular needs and show that the total system value is greater, hence making a case for the adoption of such virtual networks.

A comparative analysis of the effects of economic policy instruments in promoting environmentally sustainable transport

This paper presents a comparative analysis of the effects of economic policy instruments in promoting environmentally sustainable transport. Promoting environmentally sustainable transport is defined as follows: (1) Reducing the volume of motorised travel; (2) Transferring travel to modes generating less external effects, and (3) Modifying road user behaviour in a way that will reduce external effects of transport. External effects include accidents, congestion, traffic noise and emissions to air. Four economic policy instruments are compared: (1) Prices of motor fuel; (2) Congestion charges; (3) Toll schemes; (4) Reward systems giving incentives to reduce driving or change driver behaviour. The effects of these policy instruments are stated in terms of elasticities. All four economic policy instruments have negative elasticities, which means that they do promote environmentally sustainable transport. Long-term elasticities tend to be larger than short term elasticities. The long-term elasticities of reward systems are unknown.

Evaluation of a Strategic Road Pricing Scheme Accounting for Day-to-Day and Long-Term Demand Uncertainty

Transport network pricing schemes are an integral traffic management strategy that can be implemented to reduce congestion, among other network impacts. However, the problem of determining tolls becomes much more complex when multiple sources of demand uncertainty are considered. This paper proposes a novel tolling model based on a particular variant of strategic user equilibrium in which users base their route choice decisions on a known demand distribution. The study showed that by using an average daily demand, a marginal social cost–based tolling approach could induce near optimal conditions in a strategic network. However, uncertainty was associated with the long-term future planning demand; inaccurate forecasts of future demand could result in poor realized tolling scheme performance. Therefore, this paper also proposes a method to test the robustness of a tolling scheme, which is the reliability of the link tolls under a range of future demand scenario realizations. Results demonstrated that evaluations of strategic tolling schemes differed when both the short-term and the long-term uncertainty in demand were accounted for, and furthermore suggested that future research into the integration of multiple sources of uncertainty into the pricing scheme evaluation is merited.

Robust Tolling Schemes for High-Occupancy Toll Facilities under Variable Demand

High-occupancy toll (HOT) lanes have become an increasingly prevalent form of congestion management pricing in the United States in the past few decades. The success of a HOT facility depends on the pricing scheme, which determines the utilization of the HOT lane, and the corresponding congestion relief on the parallel general purpose lanes. An additional complexity in determining HOT rates arises from the inevitable variability in travel demand inherent to transport networks. A successful tolling scheme must therefore be robust to changes in travel demand. Various tolling schemes for HOT facilities are examined in efforts to identify robust pricing policies. The expected performance and the corresponding variability of the facility are evaluated under each pricing scheme for different demand profiles. The focus is on noncorrelated demand uncertainties (i.e., number of arrivals during given time interval is independent of number of arrivals in preceding and following time intervals), which are modeled by considering the number of arrivals in each minute as an independent random variable with known distribution and time-of-day dependent mean. The performance model for a given demand realization is deterministic. Results show that a fixed toll can achieve about two-thirds of the benefit of an ideal HOT system. The performance of a prescheduled toll system is between the fixed toll and the ideal system: closer to the ideal when the coefficient of variation is below 40% and closer to the fixed toll otherwise. The performance of a relatively simple real-time system, with density-based linear adjustment to the prescheduled toll, is practically equivalent to that of the ideal system.

Pareto-improving toll and subsidy scheme on transportation networks

This paper presents an original study on the economics of a link-based Toll and Subsidy Scheme (TSS) on a general transportation network. Different from a traditional congestion pricing scheme, the combination of toll and subsidy is found to be able to serve more planning purposes simultaneously, such as efficiency, fairness, and public acceptance. We first demonstrate that on a one-origin or one-destination network, a pareto-improving, system-optimal and revenue-neutral TSS always exists and can be obtained by solving a set of linear equations. Recognizing that such a scheme may not always exist for a multi-origin network, we then define the maximum-revenue problem with pareto-improving constrains to find the maximum possible revenue collected by the toll and subsidy scheme with optimal arc flows and non-increasing origin-destination travel costs. We discover that the problem is actually the dual problem of a balanced transportation problem, which can thus be solved efficiently by existing algorithms. At the end of the paper, a numerical example with a small synthetic network is provided for the comparison of toll and subsidy scheme with other existing toll schemes in terms of OD travel disutilities.

Optimising time-varying network flows by low-revenue tolling under dynamic user equilibrium

This paper presents a dynamic congestion charging framework that includes a dynamic user equilibrium (DUE) network model to optimize a tolling scheme, whose objective(s) may be determined by the transport planner. The framework presented may be utilised to evaluate potential charging regimes; this paper concentrates on the feasibility of extending the concept of minimal-revenue tolls from the static to time-varying environment. We discuss the limitations in the transference of this optimisation objective and propose a pragmatic approach designed to allow the planner to balance the effect of extracting additional toll revenue against achievable network benefit. We investigate the ability of this framework to incorporate various tolling scenarios and to illustrate the production of low-revenue tolls. The numerical tests use a fixed toll across the entire time period for a range of demand scenarios and a fairly stable tolling solution is observed.

Optimal Road Toll Design from the Perspective of Sustainable Development

This paper investigates the optimal road toll design problem from the perspective of sustainable development at network-wide level. In this paper the sustainable development level of transportation system is quantitatively described with the total vehicular emission, total fuel consumption, and total travel time in the network. In order to simultaneously consider the impacts of all these three indicators on sustainability of transportation system, we integrate them into a sustainable development index (SD-index) by a linear combination, and then we establish the corresponding bilevel optimization model. The upper level problem is the network toll design problem to maximize the SD-index from the viewpoint of traffic managers, and the lower level problem is to depict travelers’ route choice behavior under a certain road toll scheme. Finally, a combined genetic algorithm and gradient projection algorithm (GA-GP) is used to solve the bilevel model, in which the GP algorithm solves the traffic assignment problem with road toll scheme in the lower level. In order to verify the proposed model and algorithm, we take the Nguyen-Dupuis network for the numerical example, and the computing results show that the model and algorithm are effective and efficient.

The Impact of Transforming a Road Financing Toll Scheme to a Congestion Charging Scheme – The Case of Oslo

The current Oslo toll ring system was implemented in 1990 to generate funds for road investments in the larger Oslo area. Currently, about 60% of the toll income is being used for investments and maintenance of public transport. The use of a large share of toll income on public transport may be seen as strategy to induce people to use public transport. However, congestion in peak periods is still a major problem in the Oslo area and has attracted public attention. Congestion imposes a major social cost. All else equal, congested traffic produces more air pollution, increases travel time and consumes more energy than smooth traffic flow. Given that the Oslo toll ring with flat rates is already in place, planners have started to address the question of whether the system in place can be converted to a marginal cost-based scheme to reduce the prevalent congestion. In this paper we examine the benefits of converting the already existing Oslo toll ring with flat rates to a congestion-based charging scheme. To do so, we first develop a theoretical model along the lines of Arnott et al.(1993). The theoretical model is then combined with a more practical and empirical model for estimating the optimal tolls and assessing the effects of a congestion scheme. The findings show that transforming the current toll ring system into a congestion-pricing system, where peak traffic is charged a higher toll than off-peak traffic, holds great potential for easing traffic congestion and improving the environment. Further, it will improve the efficiency of both public and private transport while at the same time it can raise more revenues compared to the current situation. Thus, such a move will not be in conflict with the current road financing toll. These results have direct policy implications in that they should appeal to decision-makers and hence are relevant for the marketing of congestion pricing.

A Review and Advance of High-Occupancy Toll Lanes’ Toll Schemes

This paper reviews the pricing of high-occupancy toll (HOT) lanes and finds that 1) existing dynamic pricing adjusts every 3-15 minutes according to such parameters as speed, density, and/or volume, 2) tolls increase progressively with traffic to ensure free flow HOT lanes, 3) for multi-zone HOT lanes, tolls tend to be determined by the most congested zone, 4) the reaction of motorists to toll adjustments is either unspecified or oversimplified, and 5) a toll boundary is essential to mediate extreme fluctuations. Based on values of time savings and reliability, a novel toll scheme was proposed as a function of speed of general-purpose lanes; tolls in a selected 10-mile HOT corridor varied between $0.77 and $12.64 per use, of which the value of reliability accounted for 24% to 44% while that of time savings accounted for the remainder. The proposed toll scheme can be applied to time-of-day or dynamic HOT pricing.

Surrogate‐Based Optimization of Expensive‐to‐Evaluate Objective for Optimal Highway Toll Charges in Transportation Network

AbstractThis article adopts a family of surrogate‐based optimization approaches to approximate the response surface for the transportation simulation input–output mapping and search for the optimal toll charges in a transportation network. The computational effort can thus be significantly reduced for the expensive‐to‐evaluate optimization problem. Meanwhile, the random noise that always occurs through simulations can be addressed by this family of approaches. Both one‐stage and two‐stage surrogate models are tested and compared. A suboptimal exploration strategy and a global exploration strategy are incorporated and validated. A simulation‐based dynamic traffic assignment model DynusT (Dynamic Urban Systems in Transportation) is utilized to evaluate the system performance in response to different link‐additive toll schemes implemented on a highway in a real road transportation network. With the objective of minimizing the network‐wide average travel time, the simulation results show that implementing the optimal toll predicted by the surrogate model can benefit society in multiple ways. The travelers gain from the 2.5% reduction (0.45 minutes) of the average travel time. The total reduction in the time cost during the extended peak hours would be around US$65,000 for all the 570,000 network users assuming a US$15 per hour value of time. Meanwhile, the government benefits from the 20% increase of toll revenue compared to the current situation. Thus, applying the optimized pricing scheme in real world can be an encouraging policy option to enhance the performance of the transportation system in the study region.

The optimal toll scheme for ships queuing at the entrance of Panama Canal

As the insufficiency of watercourses and the limitation of breadth are leading to long queues at Panama Canal, the plan of canal expansion is undertaken by the authorities to increase the service capacity. In order to avoid ships queuing at the entrance of the canal, this research establishes an optimal toll scheme, which will effectively disperse ship arrival times and eliminate long queues. The research shows all ship arrival rates at the entrance of canal before and after implementing the optimal toll scheme.

Design of Sustainable Cordon Toll Pricing Schemes in a Monocentric City

This paper addresses the design issue of sustainable cordon toll pricing schemes in a monocentric city. An analytical model that maximizes the total social welfare of urban system is first proposed for simultaneous optimization of the cordon toll location and charge level. The solution properties of the model with/without considering traffic congestion and/or environmental effects are explored and compared analytically. The proposed model is then extended to explicitly incorporate the effects of subsidizing the retrofit of old vehicles on reduction in average vehicle emissions. The optimal subsidy scheme for maximizing the social welfare of the system is also determined. Finally, a numerical example is given to illustrate the model applications. Insightful findings are reported on the interrelationships among cordon toll scheme, traffic congestion and environmental effects, urban population distribution, and subsidy scheme as well as their implications in practice.

Optimal and Long-Term Dynamic Transport Policy Design: Seeking Maximum Social Welfare through a Pricing Scheme

ABSTRACT This article presents an alternative approach to the decision-making process in transport strategy design. The study explores the possibility of integrating forecasting, assessment and optimization procedures in support of a decision-making process designed to reach the best achievable scenario through mobility policies. Long-term evaluation, as required by a dynamic system such as a city, is provided by a strategic Land-Use and Transport Interaction (LUTI) model. The social welfare achieved by implementing mobility LUTI model policies is measured through a cost-benefit analysis and maximized through an optimization process throughout the evaluation period. The method is tested by optimizing a pricing policy scheme in Madrid on a cordon toll in a context requiring system efficiency, social equity and environmental quality. The optimized scheme yields an appreciable increase in social surplus through a relatively low rate compared to other similar pricing toll schemes. The results highlight the different considerations regarding mobility impacts on the case study area, as well as the major contributors to social welfare surplus. This leads the authors to reconsider the cost-analysis approach, as defined in the study, as the best option for formulating sustainability measures.

Study on Traffic Congestion Pricing for Large Scale Multimodal Networks in City

Traffic congestion brings more and more negative effects on the urban economy and society safety. This paper analyzes and extends the travel mode split problem for urban multimodal networks based on the game theory and Arnotts bottleneck model. Firstly, we present a theoretical model of traffic behavior under various tolling schemes such as no-toll and dynamic toll. Secondly, several important behavioral features related to the response of users to the congestion pricing strategy are provided. Such features include the travelers relative valuations of early arrival, late arrival, and the bus conditions. Finally, we put forward numerical examples to explain the model.