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.     

A dynamic pricing strategy for high occupancy toll lanes

High Occupancy Toll (HOT) lanes are emerging as a solution to the underutilization of High Occupancy Vehicle (HOV) lanes and also a means to generate revenue for the State Departments of Transportation. This paper proposes a method to determine the toll price dynamically in response to the changes in traffic condition, and describes the procedures for estimating the essential parameters. Such parameters include expected delays, available capacity for toll-paying vehicles and distribution of travelers’ value of time (VOT). The objective function of the proposed pricing strategy can be flexibly modified to minimize delay, maximize revenue or combinations of specified levels of delay and revenue. Real-world data from a 14-mile of freeway segment in the San Francisco Bay Area are used to demonstrate the applicability and feasibility of the proposed method, and findings and implications from this case study are discussed.     

Joint road toll pricing and capacity development in discrete transport network design problem

The paper demonstrates a method to determine road network improvements that also involve the use of a road toll charge, taking the perspective of the government or authority. A general discrete network design problem with a road toll pricing scheme, to minimize the total travel time under a budget constraint, is proposed. This approach is taken in order to determine the appropriate level of road toll pricing whilst simultaneously addressing the need for capacity. The proposed approach is formulated as a bi-level programming problem. The optimal road capacity improvement and toll level scheme is investigated with respect to the available budget levels and toll revenues.     

Development and comparison of choice models and tolling schemes for high-occupancy/toll (HOT) facilities

A high-occupancy/toll (HOT) lane is an increasingly popular form of traffic management strategy which reserves a set of freeway lanes for HOVs and transit users, while allowing low-occupancy vehicles (LOVs) to enter for a fee. In turn, HOT lanes maintain a minimal level of service by regulating the volume of entering LOVs. The focus of this paper is how to model the choice process of individual drivers, which dictates the volume of LOVs that choose to pay and take the HOT lane. Such models and the insights they provide can be very helpful for the toll setting process. Two simple formulations (an all-or-nothing assignment and an additive logit model) are compared with a proposed formulation based on the population value of time (VOT) distribution. Both static and dynamic toll setting algorithms are studied based on the proposed lane choice model, and their performance is compared under deterministic traffic behavior.     

Network reliability‐based optimal toll design

Optimal toll design from a network reliability point of view is addressed in this paper. Improving network reliability is proposed as a policy objective of road pricing. A reliability‐based optimal toll design model, where on the upper level network performance including travel time reliability is optimized, while on the lower level a dynamic user‐equilibrium is achieved, is presented. Road authorities aim to optimize network travel time reliability by setting tolls in a network design problem. Travelers are influenced by these tolls and make route and trip decisions by considering travel times and tolls. Network performance reliability is analyzed for a degradable network with elastic and fluctuated travel demand, which integrates reliability and uncertainty, dynamic network equilibrium models, and Monte Carlo methods. The proposed model is applied to a small hypothesized network for which optimal tolls are derived. The network travel time reliability is indeed improved after implementing optimal tolling system. Trips may have a somewhat higher, but more reliable, travel time.     

A model for optimizing electronic toll collection systems

This paper examines the deployment of electronic toll collection (ETC) and develops a model to maximize social welfare associated with a toll plaza. A payment choice model estimates the share of traffic using ETC as a function of delay, price, and a fixed cost of acquiring the in-vehicle transponder. Delay in turn depends on the relative number of ETC and manual collection lanes. Price depends on the discount given to users of the ETC lanes. The fixed cost of acquiring the transponder (not simply a monetary cost, but also the effort involved in signing up for the program) is a key factor in the model. Once a traveler acquires the transponder, the cost of choosing ETC in the future declines significantly. Welfare depends on the market share of ETC, and includes delay and gasoline consumption, toll collection costs, and social costs such as air pollution. This work examines the best combination of ETC lanes and toll discount to maximize welfare. Too many ETC lanes cause excessive delay to non-equipped users. Too high a discount costs the highway agency revenue needed to operate the facility. The model is applied to California’s Carquinez Bridge, and recommendations are made concerning the number of dedicated ETC lanes and the appropriate ETC discount.     

Freeway drivers’ willingness-to-pay for a distance-based toll rate

This paper applies the contingent valuation method to investigate and estimate the toll rate that freeway drivers are willing-to-pay (WTP) for each unit of distance they travel, after switching from per-entry based to distance-based tolling system. Due to a large portion of respondents who are unwilling to pay a toll at all, we adopt the spike model to avoid estimation errors. The estimation results show that average willingness to pay toll is TWD¹ 0.86/km, which can be refined further to TWD 0.81/km for short distance travelers, TWD 0.93/km for medium distance travelers, and TWD 0.97/km for long distance travelers. Additionally, the WTP toll rate of short distance travelers is significantly different on public holidays but not during peak hours. In contrast, the WTP toll rates of medium and long distance travelers significantly different during peak hours but not on public holidays.     

Hot lane policies and their implications

This research examined the major changes in a corridor due to high occupancy/toll (HOT) lane implementation. This was accomplished by comparing the impacts of HOT lanes on three pairs of HOT lanes with similar design and operational characteristics. These pairwise comparisons of similar HOT lanes reduced the impact of exogenous factors and removed the issue of comparing HOT lanes that were so dissimilar it would be impossible to isolate the reasons for difference in results from the lanes. With strict registration requirements for free high occupancy vehicle (HOV) 3+ travel on the I-95 Express Lanes (ELs) in Miami there were indications that some carpoolers switched to lower occupancy modes. Tolled access for HOV2s on I-95 and the SR-91 ELs near Los Angeles resulted in lower usage of those ELs by the HOV2s as compared to most HOV lanes where HOV2 access is free. On the SR167 (Seattle) and I-25 (Denver) HOT lanes, exogenous factors like the price of gas and the economic recession seemed to be the primary influence on the usage of those HOT lanes. In both cases, carpool usage increased along with the price of gas. On I-25, the increasing unemployment rate coincided with a decrease in toll paying travelers. On SR 167 there were also indications of mode shifts among the transit, carpool and toll paying SOVs due to the fluctuating price of gas.     

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.     

Dynamic pricing for managed lanes with multiple entrances and exits

Priced managed lanes are increasingly being used to better utilize the existing capacity of the roadway to relieve congestion and offer reliable travel time to road users. In this paper, we investigate the optimization problem for pricing managed lanes with multiple entrances and exits which seeks to maximize the revenue and minimize the total system travel time (TSTT) over a finite horizon. We propose a lane choice model where travelers make online decisions at each diverge point considering all routes on a managed lane network. We formulate the problem as a deterministic Markov decision process and solve it using the value function approximation (VFA) method for different initializations. We compare the performance of the toll policies predicted by the VFA method against the myopic revenue policy which maximizes the revenue only at the current timestep and two heuristic policies based on the measured densities on the managed and general purpose lanes (GPLs). We test the results on four different test networks. The primary findings from our research suggest the usefulness of the VFA method for determining dynamic tolls. The best-found objective value from the method at its termination is better than other heuristics for all test networks with average improvements in the objective ranging between 10% and 90% for revenue maximization and 0–27% for TSTT minimization. Certain VFA initializations obtain best-found toll profiles within first 5–50 iterations which warrants computational time savings. Our findings also indicate that the revenue-maximizing optimal policies follow the “jam-and-harvest” behavior where the GPLs are pushed towards congestion in the earlier time steps to generate higher revenue in the later time steps, a characteristic not observed for the policies minimizing TSTT.     

Bayesian network-based formulation and analysis for toll road utilization supported by traffic information provision

Congestion pricing has been proposed and investigated as an effective means of optimizing traffic assignment, alleviating congestion, and enhancing traffic operation efficiencies. Meanwhile, advanced traffic information dissemination systems, such as Advanced Traveler Information System (ATIS), have been developed and deployed to provide real-time, accurate, and complete network-wide traffic information to facilitate travelers’ trip plans and routing selections. Recent advances in ATIS technologies, especially telecommunication technology, allow dynamic, personalized, and multimodal traffic information to be disseminated and impact travelers’ choices of departure times, alternative routes, and travel modes in the context of congestion pricing. However, few studies were conducted to determine the impact of traffic information dissemination on toll road utilizations. In this study, the effects of the provisions of traffic information on toll road usage are investigated and analyzed based on a stated preference survey conducted in Texas. A Bayesian Network (BN)-based approach is developed to discover travelers’ opinions and preferences for toll road utilization supported by network-wide traffic information provisions. The probabilistic interdependencies among various attributes, including routing choice, departure time, traffic information dissemination mode, content, coverage, commuter demographic information, and travel patterns, are identified and their impacts on toll road usage are quantified. The results indicate that the BN model performs reasonably well in travelers’ preference classifications for toll road utilization and knowledge extraction. The BN Most Probable Explanation (MPE) measurement, probability inference and variable influence analysis results illustrate travelers using highway advisory radio and internet as their primary mode of receiving traffic information are more likely to comply with routing recommendations and use toll roads. Traffic information regarding congested roads, road hazard warnings, and accident locations is of great interest to travelers, who tend to acquire such information and use toll roads more frequently. Travel time formation for home-based trips can considerably enhance travelers’ preferences for toll road usage. Female travelers tend to seek traffic information and utilize toll roads more frequently. As expected, the information provided at both pre-trip and en-route stages can positively influence travelers’ preferences for toll road usage. The proposed methodology and research findings advance our previous study and provide insight into travelers’ behavioral tendencies concerning toll road utilization in support of traffic information dissemination.     

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.     

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.     

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.     

Risk-neutral second best toll pricing

We propose a risk-neutral second best toll pricing (SBTP) scheme to account for the possible nonuniqueness of user equilibrium solutions. The scheme is designed to optimize for the expected objective value as the UE solution varies within the solution set. We show that such a risk-neutral scheme can be formulated as a stochastic program, which complements the traditional risk-prone SBTP approach and the risk-averse SBTP approach we developed recently. The proposed model can be solved by a simulation-based optimization algorithm that contains three major steps: characterization of the UE solution set, random sampling over the solution set, and a two-phase simulation optimization step. Numerical results illustrate that the proposed risk-neutral design scheme is less aggressive than the risk-prone scheme and less conservative than the risk-averse scheme, and may thus be more preferable from a toll designer’s point of view.     

Auction-based tolling systems in a connected and automated vehicles environment: Public opinion and implications for toll revenue and capacity utilization

Autonomous and connected vehicles are expected to enable new tolling mechanisms, such as auction-based tolls, for allocating the limited roadway capacity. This research examines the public perception of futuristic auction-based tolling systems, with a focus on the public acceptance of such systems over current tolling practices on highways (e.g., dynamic and fixed tolling methodologies). Through a stated-preference survey, responses from 159 road-users residing in Virginia are elicited to understand route choice behavior under a descending price auction implemented on a hypothetical two-route network. Analysis of the survey data shows that there is no outright rejection of the presented auction-based tolling among those who are familiar with the current tolling methods. While males strongly support the new method, no clear pattern emerges among other demographic variables such as income and education level, and age. While high income respondents and regular commuters are more likely to pay higher tolls, no statistical significance between different genders, age groups, household sizes, and education levels is found. Based on the modeling results and the hypothetical road network, it is found that descending price tolling method yields higher average toll rates, and generates at least 70% more revenue when travel time saving is 30 min, and improves capacity utilization of the toll road significantly compared to fixed tolls.     

Time-dependent congestion pricing system for large networks: Integrating departure time choice,dynamic traffic assignment and regional travel surveys in the Greater Toronto Area

Congestion pricing is one of the widely contemplated methods to manage traffic congestion. The purpose of congestion pricing is to manage traffic demand generation and supply allocation by charging fees (i.e., tolling) for the use of certain roads in order to distribute traffic demand more evenly over time and space. This study presents a framework for large-scale variable congestion pricing policy determination and evaluation. The proposed framework integrates departure time choice and route choice models within a regional dynamic traffic assignment (DTA) simulation environment. The framework addresses the impact of tolling on: (1) road traffic congestion (supply side), and (2) travelers’ choice dimensions including departure time and route choices (demand side). The framework is applied to a simulation-based case study of tolling a major freeway in Toronto while capturing the regional effects across the Greater Toronto Area (GTA). The models are developed and calibrated using regional household travel survey data that reflect the heterogeneity of travelers’ attributes. The DTA model is calibrated using actual traffic counts from the Ontario Ministry of Transportation and the City of Toronto. The case study examined two tolling scenarios: flat and variable tolling. The results indicate that: (1) more benefits are attained from variable pricing, that mirrors temporal congestion patterns, due to departure time rescheduling as opposed to predominantly re-routing only in the case of flat tolling, (2) widespread spatial and temporal re-distributions of traffic demand are observed across the regional network in response to tolling a significant, yet relatively short, expressway serving Downtown Toronto, and (3) flat tolling causes major and counterproductive rerouting patterns during peak hours, which was observed to block access to the tolled facility itself.     

Minimizing CO2e emissions by setting a road toll

The main purpose of this paper is to develop a bi-level pricing model to minimize the CO₂e emissions and the total travel time in a small road network. In the lower level of the model, it is assumed that users of the road network find a dynamic user equilibrium which minimizes the total costs of those in the system. For the higher level of the model, different road toll strategies are applied in order to minimize the CO₂e emissions. The model has been applied to an illustrative example. It shows the effects on traffic flows, revenues, total time and CO₂e emissions for different numbers of servers collecting tolls and different pricing strategies over a morning peak traffic period. The results show that the CO₂e emissions produced can be significantly affected by the number of servers and the type of toll strategy employed. The model is also used to find the best toll strategy when there is a constraint on the revenue that is required to be raised from the toll and how this affects the emissions produced. Further runs compare strategies to minimize the CO₂e emissions with those that minimize total travel time in the road system. In the illustrative example, the results for minimizing CO₂e emissions are shown to be similar to the results obtained from minimizing the total travel time.     

Enhanced traffic information dissemination to facilitate toll road utilization: a nested logit model of a stated preference survey in Texas

This paper investigates the effects of the provision of traffic information on toll road usage based on a stated preference survey conducted in central Texas. Although many researchers have studied congestion pricing and traffic information dissemination extensively, most of them focused on the effects that these instruments individually produce on transportation system performance. Few studies have been conducted to elaborate on the impacts of traffic information dissemination on toll road utilization. In this study, 716 individuals completed a survey to measure representative public opinions and preferences for toll road usage in support of various traffic information dissemination classified by different modes, contents, and timeliness categories. A nested logit model was developed and estimated to identify the significant attributes of traffic information dissemination, traveler commuting patterns, routing behavior, and demographic characteristics, and analyze their impacts on toll road utilization. The results revealed that the travelers using dynamic message sign systems as their primary mode of receiving traffic information are more likely to choose toll roads. The potential toll road users also indicated their desire to obtain traffic information via internet. Information regarding accident locations, road hazard warnings, and congested roads is frequently sought by travelers. Furthermore, high-quality congested road information dissemination can significantly enhance travelers’ preferences of toll road usage. Specifically the study found that travelers anticipated an average travel time saving of about 11.3 min from better information; this is about 30 % of travelers’ average one-way commuting time. The mean value of the time savings was found to be about $11.82 per hour, close to ½ of the average Austin wage rate. The model specifications and result analyses provide in-depth insights in interpreting travelers’ behavioral tendencies of toll road utilization in support of traffic information. The results are also helpful to shape and develop future transportation toll system and transportation policy.     

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.