Vehicle identification sensor models for origin–destination estimation

The traditional approach to origin–destination (OD) estimation based on data surveys is highly expensive. Therefore, researchers have attempted to develop reasonable low-cost approaches to estimating the OD vector, such as OD estimation based on traffic sensor data. In this estimation approach, the location problem for the sensors is critical. One type of sensor that can be used for this purpose, on which this paper focuses, is vehicle identification sensors. The information collected by these sensors that can be employed for OD estimation is discussed in this paper. We use data gathered by vehicle identification sensors that include an ID for each vehicle and the time at which the sensor detected it. Based on these data, the subset of sensors that detected a given vehicle and the order in which they detected it are available. In this paper, four location models are proposed, all of which consider the order of the sensors. The first model always yields the minimum number of sensors to ensure the uniqueness of path flows. The second model yields the maximum number of uniquely observed paths given a budget constraint on the sensors. The third model always yields the minimum number of sensors to ensure the uniqueness of OD flows. Finally, the fourth model yields the maximum number of uniquely observed OD flows given a budget constraint on the sensors. For several numerical examples, these four models were solved using the GAMS software. These numerical examples include several medium-sized examples, including an example of a real-world large-scale transportation network in Mashhad.     

Heterogeneous sensor location model for path reconstruction

A new traffic sensor location problem is developed and solved by strategically placing both passive and active sensors in a transportation network for path reconstruction. Passive sensors simply count vehicles, while active sensors can recognize vehicle plates but are more expensive. We developed a two-stage heterogeneous sensor location model to determine the most cost-effective strategies for sensor deployment. The first stage of the model adopts the path reconstruction model defined by Castillo et al. (2008b) to determine the optimal locations of active sensors in the network. In the second stage, an algebraic framework is developed to strategically replace active sensors so that the total installation cost can be reduced while maintaining path flow observation quality. Within the algebraic framework, a scalar product operator is introduced to calculate path flows. An extension matrix is generated and used to determine if a replacement scheme is able to reconstruct all path flows. A graph model is then constructed to determine feasible replacement schemes. The problem of finding the optimal replacement scheme is addressed by utilizing the theory of maximum clique to obtain the upper bound of the number of replaced sensors and then revising this upper bound to generate the optimal replacement scheme. A polynomial-time algorithm is proposed to solve the maximum clique problem, and the optimal replacement scheme can be obtained accordingly. Three numerical experiments show that our proposed two-stage method can reduce the total costs of transportation surveillance systems without affecting the system monitor quality. The locations of the active sensors play a more critical role than the locations of the passive sensors in the number of reconstructed paths.     

A novel permit scheme for managing parking competition and bottleneck congestion

Morning commuters may have to depart from home earlier to secure a parking space when parking supply in the city center is insufficient. Recent studies show that parking reservations can reduce highway congestion and deadweight loss of parking competition simultaneously. This study develops a novel tradable parking permit scheme to realize or implement parking reservations when commuters are either homogeneous or heterogeneous in their values of time. It is found that an expirable parking permit scheme with an infinite number of steps, i.e., the ideal-scheme, is superior to a time-varying pricing scheme in the sense that designing a permit scheme does not require commuters’ value of time information and the performance of the scheme is robust to the variation of commuters’ value of time. Although it is impractical to implement the ideal-scheme with an infinite number of steps, the efficiency loss of a permit scheme with finite steps can be bounded in both cases of homogeneous and heterogeneous commuters. Moreover, considering the permit scheme may lead to an undesirable benefit distribution among commuters, we propose an equal cost-reduction distribution of parking permits where auto commuters with higher value of time will receive fewer permits.     

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

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

Electronic road pricing: An idea whose time may never come

Hong Kong's experiment with electronic road pricing showed that the technology was completely feasible. However, the government was unable to implement the scheme due to strong opposition from a public that perceived it as an invasion of privacy and a tax increase. This outcome was partly a result of forces unique to Hong Kong's political culture as well as both strategic and tactical errors made by the Hong Kong government in presenting its proposal. However, the Hong Kong experience also raises serious questions about whether a sophisticated road pricing scheme will ever be acceptable in a democratic urban polity.     

Time-dependent area-based pricing for multimodal systems with heterogeneous users in an agent-based environment

In this paper, we investigate an area-based pricing scheme for congested multimodal urban networks with the consideration of user heterogeneity. We propose a time-dependent pricing scheme where the tolls are iteratively adjusted through a Proportional–Integral type feedback controller, based on the level of vehicular traffic congestion and traveler’s behavioral adaptation to the cost of pricing. The level of congestion is described at the network level by a Macroscopic Fundamental Diagram, which has been recently applied to develop network-level traffic management strategies. Within this dynamic congestion pricing scheme, we differentiate two groups of users with respect to their value-of-time (which related to income levels). We then integrate incentives, such as improving public transport services or return part of the toll to some users, to motivate mode shift and increase the efficiency of pricing and to attain equitable savings for all users. A case study of a medium size network is carried out using an agent-based simulator. The developed pricing scheme demonstrates high efficiency in congestion reduction. Comparing to pricing schemes that utilize similar control mechanisms in literature which do not treat the adaptivity of users, the proposed pricing scheme shows higher flexibility in toll adjustment and a smooth behavioral stabilization in long-term operation. Significant differences in behavioral responses are found between the two user groups, highlighting the importance of equity treatment in the design of congestion pricing schemes. By integrating incentive programs for public transport using the collected toll revenue, more efficient pricing strategies can be developed where savings in travel time outweigh the cost of pricing, achieving substantial welfare gain.     

A graphical approach to identify sensor locations for link flow inference

Information of link flows in a traffic network becomes increasingly critical in contemporary transportation practice and researches. The network sensor installation is carried out to supply such information. In this paper, we present a graphical approach to determine the smallest subset of links in a traffic network for counting sensor installation, so as to infer the flows on all remaining links. The elegant assumption-free character of the problem introduced by Hu, Peeta and Chu is still kept in this approach. This study points out the topological tree feature of solutions that makes it possible for traffic management agencies to easily and flexibly select links for sensor installation in practice. Addressing from the same graphical perspective, we provide solutions to four other important problems about sensor locations. The preceding two problems are, in traffic networks that already have sensors installed on some links, to identify the subset of links on which link flows can be inferred from sensor measurements and to determine the smallest subset of links on which counting sensors also need to be installed so as to infer link flows on all remaining non-equipped links. The third is to identify the optimal locations for a given number of sensors so as to infer flows on as many links as possible by gradually enlarging the number of links included in circuits. The last one is to determine the smallest subset of links on which to install sensors, in such a way that it becomes possible at the same time to satisfy prior requirements and infer the flows on all remaining links, through building a minimum spanning tree. These methods can be applied to all kinds of long-term planning and link-based applications in traffic networks.     

Pareto-improving transportation network design and ownership regimes

Private provision of public roads signifies co-existence of free, public-tolled and private-tolled roads. This paper investigates the Pareto-improving transportation network design problem under various ownership regimes by allowing joint choice of road pricing and capacity enhancement on free links. The problem of interest is formulated as a bi-objective mathematical programming model that considers the travel cost of road users in each origin-destination pair and the investment return of the whole network. The non-dominated Pareto-improving solutions of toll and/or capacity enhancement schemes are sought for achieving a win-win situation. A sufficient condition is provided for the existence of the non-dominated Pareto-improving schemes and then the properties of those schemes are analyzed. It is found that, under some mild assumptions, the optimal capacity enhancement is uniquely determined by the link flow under any non-dominated Pareto-improving scheme. As a result, the joint road pricing and capacity enhancement problem reduces to a bi-objective second-best road pricing problem. A revenue distribution mechanism with return rate guarantee is proposed to implement the non-dominated Pareto-improving schemes.     

Traffic rationing and pricing in a linear monocentric city

This paper presents a simple spatial equilibrium model for a linear monocentric city to investigate the effects of rationing and pricing on morning commuters' travel cost and modal choice behavior in each location. Under rationing and pricing, every day in the morning peak hour, each commuter is classified as either “free” or “rationed”. “Free” commuters are allowed to use the highway without paying the toll, whereas “rationed” commuters can avoid the toll only if they travel by transit. Each day, a fraction of commuters are rationed in their free use of the highway, and the rationing fractions are determined systematically so that everyone is equally rationed in a given period. It is found that Pareto‐improving rationing and pricing scheme might be obtained as a combination of the rationing degree and the toll associated with rationing. Extension to the rationing and pricing scheme with cordon and park‐and‐ride service has been made. Cordon and park‐and‐ride might help in improving the efficiency of rationing and pricing strategy although remains its Pareto‐improving property. Copyright © 2012 John Wiley & Sons, Ltd.     

Equity effects of congestion pricing: Quantitative methodology and a case study for Stockholm

It is widely recognised that congestion pricing could be an effective measure to solve environmental and congestion problems in urban areas—a reform that normally also would generate a net welfare surplus. Despite this the implementation of congestion pricing has been very slow. One reason for a low public and political acceptance could be that equity impacts have not been given enough concern. In studies of distributional impacts of congestion pricing it has often been claimed that the reform is regressive rather than progressive even if there are studies claiming the opposite. We develop a method for detailed, quantitative assessment of equity effects of road pricing and apply it to a real-world example, namely a proposed congestion-charging scheme for Stockholm. The method simultaneously takes into account differences in travel behaviour, in preferences (such as values of time) and in supply of travel possibilities (car ownership, public transport level-of-service etc.). We conclude that the two most important factors for the net impact of congestion pricing are the initial travel patterns and how revenues are used. Differences in these respects dwarf differences in other factors such as values of time. This is accentuated by the fact that the total collected charges are more than three times as large as the net benefits. With respect to different groups, we find that men, high-income groups and residents in the central parts of the city will be affected the most. If revenues are used for improving public transport, this will benefit women and low-income groups the most. If revenues are used for tax cuts, the net benefits will be about equal for men and women on the average, while it naturally will benefit high-income groups. Given that it is likely that the revenues will be used to some extent to improve the public transport system, we conclude that the proposed congestion-charging scheme for Stockholm is progressive rather than regressive.     

Impact analysis of cordon-based congestion pricing on mode-split for a bimodal transportation network

This paper investigates the impact of cordon-based congestion pricing scheme on the mode-split of a bimodal transportation network with auto and rail travel modes. For any given toll-charge pattern, its impact on the mode-split can be estimated by solving a combined mode-split and traffic-assignment problem. Using a binary logit model for the mode-split, the combined problem is converted into a traffic-assignment problem with elastic demand. Probit-based stochastic user equilibrium (SUE) principle is adopted for this traffic-assignment problem, and a continuously distributed value of time (VOT) is assumed to convert the toll charges and transit fares into time-units. This combined mode-split and traffic-assignment problem is then formulated as a fixed-point model, which can be solved by a convergent Cost Averaging method. The combined mode-split and traffic-assignment problem is then used to analyze a multimodal toll design problem for cordon-based congestion pricing scheme, with the aim of increasing the mode-share of public transport system to a targeted level. Taking the fixed-point model as a constraint, the multimodal toll design problem is thus formulated as a mathematical programming with equilibrium constraints (MPEC) model. A genetic algorithm (GA) is employed to solve this MPEC model, which is then numerical validated by a network example.     

Surrogate‐based optimization of cordon toll levels in congested traffic networks

The benefit, in terms of social surplus, from introducing congestion charging schemes in urban networks is depending on the design of the charging scheme. The literature on optimal design of congestion pricing schemes is to a large extent based on static traffic assignment, which is known for its deficiency in correctly predict travel times in networks with severe congestion. Dynamic traffic assignment can better predict travel times in a road network, but are more computational expensive. Thus, previously developed methods for the static case cannot be applied straightforward. Surrogate‐based optimization is commonly used for optimization problems with expensive‐to‐evaluate objective functions. In this paper, we evaluate the performance of a surrogate‐based optimization method, when the number of pricing schemes, which we can afford to evaluate (because of the computational time), are limited to between 20 and 40. A static traffic assignment model of Stockholm is used for evaluating a large number of different configurations of the surrogate‐based optimization method. Final evaluation is performed with the dynamic traffic assignment tool VisumDUE, coupled with the demand model Regent, for a Stockholm network including 1240 demand zones and 17 000 links. Our results show that the surrogate‐based optimization method can indeed be used for designing a congestion charging scheme, which return a high social surplus. Copyright © 2016 John Wiley & Sons, Ltd.     

Road pricing for congestion control with unknown demand and cost functions

It is widely recognized that precise estimation of road tolls for various pricing schemes requires a few pieces of information such as origin–destination demand functions, link travel time functions and users’ valuations of travel time savings, which are, however, not all readily available in practice. To circumvent this difficulty, we develop a convergent trial-and-error implementation method for a particular pricing scheme for effective congestion control when both the link travel time functions and demand functions are unknown. The congestion control problem of interest is also known as the traffic restraint and road pricing problem, which aims at finding a set of effective link toll patterns to reduce link flows to below a desirable target level. For the generalized traffic equilibrium problem formulated as variational inequalities, we propose an iterative two-stage approach with a self-adaptive step size to update the link toll pattern based on the observed link flows and given flow restraint levels. Link travel time and demand functions and users’ value of time are not needed. The convergence of the iterative toll adjustment algorithm is established theoretically and demonstrated on a set of numerical examples.     

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.     

Robust network sensor location for complete link flow observability under uncertainty

The link observability problem is to identify the minimum set of links to be installed with sensors that allow the full determination of flows on all the unobserved links. Inevitably, the observed link flows are subject to measurement errors, which will accumulate and propagate in the inference of the unobserved link flows, leading to uncertainty in the inference process. In this paper, we develop a robust network sensor location model for complete link flow observability, while considering the propagation of measurement errors in the link flow inference. Our model development relies on two observations: (1) multiple sensor location schemes exist for the complete inference of the unobserved link flows, and different schemes can have different accumulated variances of the inferred flows as propagated from the measurement errors. (2) Fewer unobserved links involved in the nodal flow conservation equations will have a lower chance of accumulating measurement errors, and hence a lower uncertainty in the inferred link flows. These observations motivate a new way to formulate the sensor location problem. Mathematically, we formulate the problem as min–max and min–sum binary integer linear programs. The objective function minimizes the largest or cumulative number of unobserved links connected to each node, which reduces the chance of incurring higher variances in the inference process. Computationally, the resultant binary integer linear program permits the use of a number of commercial software packages for its globally optimal solution. Furthermore, considering the non-uniqueness of the minimum set of observed links for complete link flow observability, the optimization programs also consider a secondary criterion for selecting the sensor location scheme with the minimum accumulated uncertainty of the complete link flow inference.     

Solving the bicriterion routing and scheduling problem for hazardous materials distribution

Hazardous materials routing and scheduling decisions involve the determination of the minimum cost and/or risk routes for servicing the demand of a given set of customers. This paper addresses the bicriterion routing and scheduling problem arising in hazardous materials distribution planning. Under the assumption that the cost and risk attributes of each arc of the underlying transportation network are time-dependent, the proposed routing and scheduling problem pertains to the determination of the non-dominated time-dependent paths for servicing a given and fixed sequence of customers (intermediate stops) within specified time windows. Due to the heavy computational burden for solving this bicriterion problem, an alternative algorithm is proposed that determines the k-shortest time-dependent paths. Moreover an algorithm is provided for solving the bicriterion problem. The proximity of the solutions of the k-shortest time-dependent path problem with the non-dominated solutions is assessed on a set of problems developed by the authors.     

Network-wide adaptive tolling for connected and automated vehicles

This article proposes Δ-tolling, a simple adaptive pricing scheme which only requires travel time observations and two tuning parameters. These tolls are applied throughout a road network, and can be updated as frequently as travel time observations are made. Notably, Δ-tolling does not require any details of the traffic flow or travel demand models other than travel time observations, rendering it easy to apply in real-time. The flexibility of this tolling scheme is demonstrated in three specific traffic modeling contexts with varying traffic flow and user behavior assumptions: a day-to-day pricing model using static network equilibrium with link delay functions; a within-day adaptive pricing model using the cell transmission model and dynamic routing of vehicles; and a microsimulation of reservation-based intersection control for connected and autonomous vehicles with myopic routing. In all cases, Δ-tolling produces significant benefits over the no-toll case, measured in terms of average travel time and social welfare, while only requiring two parameters to be tuned. Some optimality results are also given for the special case of the static network equilibrium model with BPR-style delay functions.     

Distributional impacts of road pricing: The truth behind the myth

This paper shows that road pricing can be regressive, progressive or neutral, and refutes the generalised idea that road pricing is always regressive. The potential distributional impacts of a road pricing scheme are assessed in three English towns. It is found that impacts are town specific and depend on where people live, where people work and what mode of transport they use to go to work. Initial impacts may be progressive even before any compensation scheme for losers is taken into account. When the situation before the scheme is implemented is such that majority of drivers entering the area where the scheme would operate come from households with incomes above the average, it can be expected that, once the scheme is implemented, these drivers coming from rich households will continue to cross the cordon and will be prepared to pay the charge. In such a case the overall effect will be that on average, rich people will pay the toll and poor people will not.     

Voluntary internalization of speeding externalities with vehicle insurance

High speed is an important determinant of accidents for speeders as well as for other motorists. This paper develops a framework for analyzing instruments that encourage drivers to internalize the full consequences of their behavior with respect to choice of speed using Pay-As-You-Speed (PAYS) insurance, possibly as an extension of Pay-As-You-Drive (PAYD) insurance. We demonstrate how the combination of a Pigovian taxation scheme and PAYS can be designed in a setting involving two principals (the state and an insurance company) that affect the incentives of commuters to choose between driving and other modes of transport and for those that use the car mode to drive carefully. While the government is assumed to maximize overall social efficiency and therefore wants to implement marginal cost pricing, insurance companies do actuarial pricing, i.e. average cost pricing within risk classes that are homogeneous to the degree that the insurers have information about actual behavior. PAYS insurance improves the insurance industry’s possibility to differentiate premiums according to behavior and therefore to target risk classes in a better way than today. Moreover, since our framework is designed to accomplish differentiation by self-selection, compulsory regulation is not necessary, although there may be reason for the government to facilitate the implementation of the new technology.     

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.