Tolling Strategies Research Articles

Exploring the willingness to pay for high-occupancy toll lanes under conditions of low familiarity

This study evaluates details of a progressive transportation development model, wherein high occupancy vehicle (HOV) lanes are transformed into high-occupancy toll (HOT) lanes. Although the management strategy of HOT lanes has been implemented for many years, the implementation of HOT lanes is limited in many regions, and thus, many people remain unfamiliar with the concept. This study aims to evaluate travelers' willingness to pay for HOT lanes based on a “low application” scenario in Shenzhen, China, wherein some HOV lanes are present and may potentially be transformed into HOT lanes, but not all area residents are aware of their intended purpose. According to the Diffusion of Innovation Theory, we leverage this situation to conduct a survey of perceptions and attitudes toward the HOT lanes and evaluate how these perspectives may translate to HOT lane utilization. We further proposed a hybrid utility and regret model considering the impacts of loss aversion caused by tolls or coordinated carpooling for single occupancy vehicles to explore relationships between travel behavior and surveyed demographic and socio-economic characteristics in the context of HOT lanes in places where they are unfamiliar. A sensitivity analysis is conducted to characterize any apparent changing influences. The results show that the model considering decision regret performs well, especially in the scenario with low tolls. Nearly 80% of travelers are willing to pay tolls for HOT lanes, even with limited prior exposure to the concept. The increased acceptance of HOT lanes can be expected to hurt total toll revenue, which may be triggered by easier access to carpool partners associated with the free pass. The study informs a deeper understanding of travelers’ willingness to pay for HOT lanes and helps policy-makers develop differentiated tolling strategies.

Designing Risk Mitigation Strategies for Agricultural Supply Chain: A Supply Chain Finance-Based Approach

Abstract The agricultural supply chain is distinguished from the manufacturing and service supply chains by its complexity and length. These characteristics emphasize the importance of risk management measures for this supply chain, which will increase farmer income, market stability, and food security. This research aims to design risk mitigation strategies, especially demand risk, in the rice farming supply chain in Tana Paser District, Paser Regency, East Kalimantan. Monte Carlo simulation was utilized to predict the average rice demand and conduct sensitivity analysis. Three financial scheme strategies were compared: soft tolling, hard tolling, and contract farming, to assess the best strategy that provides maximum profits for agricultural supply chain actors. From the simulation results, the average predicted value for rice demand was 2.78 tonnes. The optimal quantities of q1 (processed material), q2 (raw material), and q3 (seeds) obtained from sensitivity analysis were 2.2 tons, 2 tons, and 2 tons, respectively. The soft tolling strategy provides maximum profits for all agricultural supply chain players, with a total profit of IDR 17,471,000.00, considering that implementing this strategy involves all supply chain stakeholders in determining the contract decision (q).

Learning and managing stochastic network traffic dynamics: an iterative and interactive approach

ABSTRACT This study examines the potential of an iterative and interactive approach to learn network traffic dynamics and optimise tolling strategies considering time-varying stochastic traffic. A tractable ‘truth model’ based on the stochastic Macroscopic Fundamental Diagram is developed to represent the transportation system to be learned and managed. A ‘twin model’ that mirrors the truth model is formulated and calibrated for testing and optimising tolling adjustment strategies with the help of reinforcement learning. The optimised prices are then put into the ‘truth model’ to evaluate network efficiency improvement. The above procedure is iterative and interactive, which can be applied for congestion management in the period-to-period tolling adjustment fashion. Numerical studies show that the proposed iterative and interactive pricing strategy is able to enhance network efficiency even under limited information and/or inaccurate learning of the system. This illustrates the great potential of utilising iterative and interactive frameworks for congestion management.

Maximizing Efficiency in the Suez Canal: A New Approach to Evaluate the Impact of Optimal Time-Varying Tolls on Ship Arrival Times

In the existing literature, an optimal time-varying toll scheme has been proposed for the Suez Canal to address the inefficiency of numerous ships queuing and waiting at the anchorage area to enter the canal. The primary objective of this tolling strategy is to alleviate the significant issue of ships queuing at the canal’s anchorage area. This stands in contrast to the current tolling system employed by the Suez Canal, which primarily aims to recover the management and operational costs associated with ship passage through the canal. However, the existing literature has yet to explore how the arrival times of ships at the anchorage area will change after implementing the optimal time-varying toll scheme. The goal is to ensure that the equilibrium cost of each tolled ship does not result in losses and achieve maximum efficiency in eliminating queueing at the anchorage area. To address this gap, this paper adopts the principle of cost equilibrium conservation and utilizes the Point-Slope Form to derive two mathematical formulas representing all ships’ post-toll arrival times at the anchorage area of the Suez Canal. These formulas are specifically derived for two categories of tolled ships: those that enter the canal earlier than the latest entry time regulated by the canal authorities and those that enter later. The derived formulas are concise and comparative, strengthening the theoretical underpinnings of the current pricing model for a queuing canal. Furthermore, they serve as valuable references for canal authorities in devising pertinent measures, such as organizing the scheduling of canal pilots, to facilitate the implementation of the optimal time-varying toll scheme.

Congestion behavior and tolling strategies in a bottleneck model with exponential scheduling preference

<abstract><p>The bottleneck model has been widely used in the past fifty years to analyze the morning commute. To reduce the complexity of analysis, most previous studies adopted discontinuous scheduling preference (DSP). However, this handling destroys the continuity in departure rate and differentiability in travel time and cumulative departures. This paper considers an exponential scheduling preference (ESP), which supposes the unit schedule delay cost for commuters exponentially changes with time. With this scheduling preference, we analytically derive solutions and economic properties of user equilibrium and social optimum in the bottleneck model. The first-best, time-varying toll and the optimal single-step toll scheme with ESP are also studied. Results indicate that ESP eliminates the discontinuity in departure rate and non-differentiability in travel time and cumulative departures, which makes the process of morning commute smooth. The ignorance of ESP will lead to underestimation in the queueing time and bias in travel behavior analysis and policymaking.</p></abstract>

Departure time choice equilibrium and tolling strategies for a bottleneck with continuous scheduling preference

This paper develops a bottleneck model with continuous scheduling preference (CSP), which assumes that the unit cost of schedule delay penalty functions have continuously linear forms. In particular, the unit cost of schedule delay early is non-increasing with respect to arrival time, while the unit cost of schedule delay late is non-decreasing with respect to arrival time. We analyze the departure time choice equilibrium of commuters and find that the proposed bottleneck model with CSP is capable of eliminating the discontinuity of the departure rate curve, which occurs in the bottleneck model with discontinuous scheduling preference (DSP). In addition, the first-best and second-best congestion tolling strategies are designed in the bottleneck model with CSP. The analytical closed-form solutions of the bottleneck model with CSP under the time-varying toll, single-step coarse toll and multi-step toll are obtained and their effects on system performance are investigated. Finally, numerical examples are developed to illustrate the properties of the proposed models. Results shed light into the necessity of considering CSP in travel behavior analysis and congestion management. The ignorance of CSP can lead to overestimate of commuters’ bottleneck queuing time and the total system travel cost (TSTC), which finally reduces the efficiency of congestion tolling strategies.

Departure Time Choice Equilibrium and Tolling Strategies for a Bottleneck with Stochastic Capacity

This paper develops a bottleneck model in which the capacity of the bottleneck is assumed to be stochastic and follow a general distribution that has a positive upper bound. The user equilibrium principle in terms of mean trip cost is adopted to formulate commuters’ departure time choice in the stochastic bottleneck. We find that there exist five possible equilibrium departure patterns, which depend on both commuters’ unit costs of travel time, schedule delay early and late, and the uncertainty of the stochastic capacity of the bottleneck. All possible equilibrium departure patterns are analytically derived. Both the analytical and numerical results show that increasing the uncertainty of the capacity of the bottleneck leads to an increase of commuters’ individual mean trip cost. In addition, both a time-varying toll scheme and a single-step coarse toll scheme are designed within the proposed stochastic bottleneck model. We provide an analytical method to determine the detailed toll-charging schemes for both toll strategies. The numerical results show that the proposed toll schemes can indeed improve the efficiency of the stochastic bottleneck in terms of decreasing mean total social cost, and the time-varying toll scheme is more efficient than the single-step coarse toll scheme. However, as the uncertainty of the capacity of the bottleneck increases, the efficiency of the time-varying toll scheme decreases, whereas the efficiency of the single-step coarse toll scheme fluctuates slightly.

Optimal Congestion Pricing with Day-to-Day Evolutionary Flow Dynamics: A Mean–Variance Optimization Approach

This paper investigates the optimal congestion pricing problem that considers day-to-day evolutionary flow dynamics. Under the circumstance that traffic flows evolve from day to day and the system might be in a non-equilibrium state during a certain period of days after implementing (or adjusting) a congestion toll scheme, it is questionable to use an equilibrium-based index under steady state as the objective to measure the performance of a congestion toll scheme. To this end, this paper proposes a mean–variance-based congestion pricing scheme, which is a robust optimization model, to consider the evolution process of traffic flow dynamics in the optimal toll design problem. More specifically, in the mean–variance-based toll scheme, travelers aim to minimize the variance of expected total travel costs (ETTCs) on different days to reduce risk in daily travels, while the average ETTC over the whole planning period is restricted to being no larger than a predetermined target value set by the authorities. A metaheuristic approach based on the whale optimization algorithm is designed to solve the proposed mean–variance-based day-to-day dynamic congestion pricing problem. Finally, a numerical experiment is conducted to validate the effectiveness of the proposed model and solution algorithm. Results show that the used 9-node network can reach a steady state within 18 days after implementing the mean–variance-based congestion pricing, and the optimal toll scheme can be also obtained with this toll strategy.

Implications of matching and pricing strategies for multiple-delivery-points service in a freight O2O platform

A multiple-delivery-points service that matches a vehicle to distribute goods from a merchant to multiple retailers is a novel and important business model in freight O2O platforms. Thus far, the distribution matching strategy that does not consider the pricing strategy has found wide use in practice. In this study, using mixed integer linear programming, we propose an assignment matching strategy that jointly optimizes the matching and pricing strategies with optimal delivery routes to multiple retailers. Based on practical data from Zallsoon, a famous freight O2O platform in China, the results show that the proposed assignment matching strategy has the potential to improve the pickup distance by 75–81.81%. Further, the choice of pricing strategies could contribute 60–93.33% in improvements to the transportation cost for cities with various order structures and promotion levels. Finally, the high starting fare and low extra charge rate strategy is preferred for high-tier cities, whereas the step toll strategy is recommended for low-tier cities.

Congestion pricing in a world of self-driving vehicles: An analysis of different strategies in alternative future scenarios

The introduction of autonomous (self-driving) and shared autonomous vehicles (AVs and SAVs) will affect travel destinations and distances, mode choice, and congestion. From a traffic perspective, although some congestion reduction may be achieved (thanks to fewer crashes and tighter headways), car-trip frequencies and vehicle miles traveled (VMT) are likely to rise significantly, reducing the benefits of driverless vehicles. Congestion pricing (CP) and road tolls are key tools for moderating demand and incentivizing more socially and environmentally optimal travel choices.This work develops multiple CP and tolling strategies in alternative future scenarios, and investigates their effects on the Austin, Texas network conditions and traveler welfare, using the agent-based simulation model MATSim. Results suggest that, while all pricing strategies reduce congestion, their social welfare impacts differ in meaningful ways. More complex and advanced strategies perform better in terms of traffic conditions and traveler welfare, depending on the development of the mobility landscape of autonomous driving. The possibility to refund users by reinvesting toll revenues as traveler budgets plays a salient role in the overall efficiency of each CP strategy as well as in the public acceptability.

Hybrid model predictive control based dynamic pricing of managed lanes with multiple accesses

We propose a hybrid model predictive control (MPC) based dynamic tolling strategy for high-occupancy toll (HOT) lanes with multiple accesses. This approach preplans and coordinates the prices for different OD pairs and enables adaptive utilization of HOT lanes by considering available demand information and boundary conditions. It also addresses such practical issues as prevention of recurrent congestion in HOT lanes, ensuring no higher toll for a closer toll exit and fairness among different OD groups at each toll entry, as well as the fact that high occupancy vehicles (HOVs) have free access to the HOT lanes. Taking the inflows at each toll entry as the control, traffic densities and vehicle queue length as observed system states, and boundary traffic as predicted exogenous input, we formulate a discrete-time piecewise affine traffic model. Optimal tolls are then derived from a one-to-one mapping based on the optimal toll entry flows. By properly formulating the constraints, we show that the MPC problem at each stage is a mixed-integer linear program and admits an explicit control law derived by multi-parametric programing techniques. A numerical experiment is presented for a representative freeway segment to validate the effectiveness of the proposed approach. The results show that our control model can react to demand and boundary condition changes by adjusting and coordinating tolls smoothly at adjacent toll entries and drive the system to a new equilibrium that minimizes the total person delay. Under the optimal prediction horizon, the on-line computational cost of the proposed control model is only about 4% and 8% of the modeling cycle of 30 s, respectively, for two typical traffic scenarios, which implies a potential of real-time implementation.

Conceptual development and economic evaluation of Multilevel Premium Highways

A variety of innovative value pricing schemes have been applied in the US to mitigate traffic congestion in a sustainable manner. This paper proposes a new concept, called Multilevel Premium Highways (MPH), to tackle traffic congestion with different options addressing travelers' diverse needs. The new concept is featured by: (i) a fully priced highway with hierarchical speeds designated on different lanes; (ii) a discriminated toll strategy; and (iii) a package of complementary services directly funded by the toll revenues. To examine the effectiveness of MPH, this paper firstly develops a qualitative comparison with the conventional value pricing (VP) schemes, and conducts a spreadsheet-based benefit-cost analysis under two scenarios with the realistic input data, and then performs a sensitivity analysis to examine the impacts of key factors (e.g., traffic demand and travelers’ willingness-to-pay). Discrete choice models are also applied to unveil the impacts of heterogeneous travelers on the performance of MPH. Results show that MPH appears to be economically and financially sustainable for large-scale applications, although the initial settings (e.g., the designated speeds and toll values) of highway lanes influence the relative performance between MPH and the conventional VP schemes.

A time-varying parameters vector auto-regression model to disentangle the time varying effects between drivers’ responses and tolling on high occupancy toll facilities

High Occupancy Toll (HOT) lane systems are considered one of most effective countermeasures to mitigate freeway congestion. Existing studies have largely focused on developing optimal tolling strategies to maximize the benefits of congestion pricing. Limited effort has been made to model the dynamic feedback mechanism of drivers’ responses to tolling. A thorough understanding of how the interactive relationship between demands (in both HOT lane and general purpose lanes) and toll rates evolves over time is necessary. The underlying mechanism can be used directly for guiding future HOT facilities investment decisions. This study builds upon the traditional vector autoregressive model and enables its parameters to be time-varying. Such a relaxation, namely, time-varying parameter vector autoregressive model (TVP-VAR), is used to answer the following two questions: (1) Is there a time varying effect between general purpose lane volume, HOT lane volume and dynamic toll rate? (2) If there is, how to quantify such time-varying interdependencies? Based on the empirical data from loop detectors and toll logs on Washington State Route 167 (SR167), we identified the existence of time-varying effects between drivers’ responses and toll rates, and quantified the evolving interactions amongst HOT demand, general purpose demand and tolling via time-varying impulse responses. In addition, we found that drivers’ perceptions on HOT lanes across distinct geographical locations are significantly different.

Bi-level programming model of truck congestion pricing at container terminals

Port traffic network design is different from urban traffic flow. Port truck congestion, one of the critical port traffic network design problems, is discussed in this paper. To alleviate the truck congestion in container terminals, issues of modeling truck congestion pricing are addressed. A bi-level programming model is developed to determine the optimal toll rates. The upper level model is to minimize the average truck waiting time by optimizing toll rates of different periods. The lower level is user equilibrium model in which each truck driver chooses its arrival time according to the toll strategy of upper level model. The feedback of upper-level and lower-level model forms the optimal toll strategy. To solve the model, a method based on memetic heuristic is designed. Finally, numerical experiments are provided to illustrate the validity of the proposed model and algorithm. Results indicate that congestion toll can decrease truck’s queuing time effectively. The developed toll pricing model reflects the benefit of truckers and terminal operators, which promotes the use of toll as an efficient tool to alleviate the truck congestion and improve the terminal efficiency.

Ridesharing User Equilibrium and Its Implications for High-Occupancy Toll Lane Pricing

Shared mobility—ridesharing in particular—has become an important research topic in recent years because of the ability to relieve traffic congestion, reduce travel costs, and reduce energy consumption. However, researchers in transportation science still lack an understanding of how to incorporate ridesharing into the transportation planning process, specifically in the traffic assignment problem. This paper presents ridesharing user equilibrium (RUE) as a path-flow–based nonlinear complementarity problem with side constraints. This formulation is extended by considering the presence of high-occupancy toll lanes. A numerical example is given to illustrate the relationships of the path cost coefficients on RUE and on the occurrence of the Braess paradox. The performance of two tolling strategies is compared: one charges single-occupancy vehicles, and the other charges both single-occupancy vehicles and vehicles carrying only one passenger.

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.

Enabling Network-Wide Tolling-Strategy Assessment via Customized Route-Choice Simulation Module

AbstractTolling has been one of the most effective countermeasures against traffic congestion in metropolitan areas. Prior to the implementation of a tolling strategy, it was necessary to systematically evaluate the toll impacts on the transportation network. Microscopic simulation has been widely utilized as an evaluation tool in many traffic operation studies and practice. Most simulation tools on today’s market, however, do not carry the functionality needed for customized toll-strategy assessment with the built-in modules. With the booming adoption of congestion pricing nationwide, it is highly desirable to enable simulation-based evaluation of various tolling strategies through external module development for widely-used simulation tools. This paper presents an innovative method for developing highly customized tolling strategy simulation through external routing modules compatible with a widely-used simulation tool. Using a publicly-available module, customized tolling schemes and routing algorithms...

Self-Adaptive Tolling Strategy for Enhanced High-Occupancy Toll Lane Operations

In this paper, a self-adaptive tolling strategy (SATS) is developed for dynamically and systematically enhancing highoccupancy toll (HOT) lane system operations. This strategy enhances the overall system performance of both the HOT and general purpose (GP) lanes by better utilizing the HOT lane capacity while maintaining high speed and/or high travel-time reliability for HOT lane traffic when GP lanes are congested. To formulate SATS, the Lighthill-Whitham-Richards kinematic wave model is used to characterize HOT lane traffic flow evolution, and the unilateral Laplace transform is used to convert the system representation from the time domain to the frequency domain. Then, an adaptive tolling controller is designed with both the proportional and integral control components. Real-time traffic measurements, including lane occupancy, average speed, and flow rate, are utilized for toll rate calculations. Following a dual-phase control scheme, the appropriate flow rate for HOT lane utilization is computed, and the corresponding toll is estimated backward. To examine the effectiveness of the proposed tolling strategy, microscopic traffic simulation experiments are conducted using VISSIM. The experiment results demonstrate that the proposed tolling strategy performs reasonably well in improving the overall operations of HOT lane systems under various traffic conditions.

A congestion-pricing problem with a polycentric region and multi-class users: a continuum modelling approach

Consider a region of arbitrary shape with multiple cities competing for multi-class users that are distributed continuously over the region. Within this region, the road network is represented as a continuum and users patronise in a two-dimensional continuum transportation system to their chosen city. A logit-type distribution function is specified to model the probabilistic destination choices made by the different classes of users. In this article, two different congestion-pricing models for this multi-class and multi-city continuum transportation system are studied. The first model focused on utility maximisation, which determines the optimal toll rates that maximise the total utility of the system, while the second model is a cordon-based congestion-pricing model that offers a sub-optimal but more practical tolling strategy. Both models are solved by finite element method and a promising Newtonian-based solution algorithm. A numerical example is given to show the effectiveness of the mathematical program and solution algorithm.

Dynamic Congestion and Tolls with Mobile Source Emission

This paper proposes a dynamic congestion pricing model that takes into account mobile source emissions. We consider a tollable vehicular network where the users selfishly minimize their own travel costs, including travel time, early/late arrival penalties and tolls. On top of that, we assume that part of the network can be tolled by a central authority, whose objective is to minimize both total travel costs of road users and total emission on a network-wide level. The model is formulated as a mathematical programming with equilibrium constraints (MPEC) problem and then reformulated as mathematical programming with complementarity constraints (MPCC). The MPCC is solved using a quadratic penalty- based gradient projection algorithm. A numerical study on a toy network illustrates the effectiveness of the tolling strategy and reveals a Braess-type paradox in the context of traffic-derived emission.