A dynamic cordon pricing scheme combining the Macroscopic Fundamental Diagram and an agent-based traffic model

Pricing is considered an effective management policy to reduce traffic congestion in transportation networks. In this paper we combine a macroscopic model of traffic congestion in urban networks with an agent-based simulator to study congestion pricing schemes. The macroscopic model, which has been tested with real data in previous studies, represents an accurate and robust approach to model the dynamics of congestion. The agent-based simulator can reproduce the complexity of travel behavior in terms of travelers’ choices and heterogeneity. This integrated approach is superior to traditional pricing schemes. On one hand, traffic simulators (including car-following, lane-changing and route choice models) consider travel behavior, i.e. departure time choice, inelastic to the level of congestion. On the other hand, most congestion pricing models utilize supply models insensitive to demand fluctuations and non-stationary conditions. This is not consistent with the physics of traffic and the dynamics of congestion. Furthermore, works that integrate the above features in pricing models are assuming deterministic and homogeneous population characteristics. In this paper, we first demonstrate by case studies in Zurich urban road network, that the output of a agent-based simulator is consistent with the physics of traffic flow dynamics, as defined by a Macroscopic Fundamental Diagram (MFD). We then develop and apply a dynamic cordon-based congestion pricing scheme, in which tolls are controlled by an MFD. And we investigate the effectiveness of the proposed pricing scheme. Results show that by applying such a congestion pricing, (i) the savings of travel time at both aggregated and disaggregated level outweigh the costs of tolling, (ii) the congestion inside the cordon area is eased while no extra congestion is generated in the neighbor area outside the cordon, (iii) tolling has stronger impact on leisure-related activities than on work-related activities, as fewer agents who perform work-related activities changed their time plans. Future work can apply the same methodology to other network-based pricing schemes, such as area-based or distance-traveled-based pricing. Equity issues can be investigated more carefully, if provided with data such as income of agents. Value-of-time-dependent pricing schemes then can also be determined.     

Marginal cost congestion pricing based on the network fundamental diagram

Congestion pricing schemes have been traditionally derived based on analytical representations of travel demand and traffic flows, such as in bottleneck models. A major limitation of these models, especially when applied to urban networks, is the inconsistency with traffic dynamics and related phenomena such as hysteresis and the capacity drop. In this study we propose a new method to derive time-varying tolling schemes using the concept of the Network Fundamental Diagram (NFD). The adopted method is based on marginal cost pricing, while it also enables to account realistically for the dynamics of large and heterogeneous traffic networks. We derive two alternative cordon tolls using network-aggregated traffic flow conditions: a step toll that neglects the spatial distribution of traffic by simply associating the marginal costs of any decrease in production within the NFD to the surplus of traffic; and a step toll that explicitly accounts for how network performance is also influenced by the spatial variance in a 3D-NFD. This pricing framework is implemented in the agent-based simulation model MATSim and applied to a case study of the city of Zurich. The tolling schemes are compared with a uniform toll, and they highlight how the inhomogeneous distribution of traffic may compromise the effectiveness of cordon tolls.     

Implementation of cordon pricing on urban network with practical approach

The road pricing is regarded as a transport policy to realize the efficient use of urban network. The network analysis with variable demand has been often applied to describe the network level of congestion pricing on the urban network. In the study, the cordon pricing system is analyzed to implement in the urban area with practical approach. It is assumed that the congestion tolls are collected in crossing the cordon lines on the network. Therefore, the scale of cordon zones and the values of congestion tolls would be determined simultaneously to produce the maximum social net benefit. The combinatorial optimization with unit price is formulated. The genetic algorithm (GA) is applied as a practical method to provide the solutions for the combinatorial optimization problem. As the pattern of cordon pricing is determined, the performance of system is estimated to confirm the applicability. It is concluded that the cordon pricing can be applied with the practical approach.     

Reducing traffic externalities by multiple-cordon pricing

The second-best congestion pricing schemes including common optimum, one cordon, and multiple cordons schemes are compared with the first-best optimum pricing scheme. A cross-subsidy effect exists in these second-best pricing models. However, the scheme with more cordons will diminish the cross-subsidy and approach an efficient and equitable outcome. The relative efficiency of a cordon pricing scheme for the case of Taipei metropolis is very high. One single cordon yields excellent performance of 93% relative efficiency. There might be some factors causing the good results: the uncongested traffic condition, the linear unit distance cost in traffic flow forming a nonlinear cost function, and the trip demands with continuous space and the same destination (the central business district) in the network.     

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.     

A forecast air pollution model applied to a hypothetical urban road pricing scheme: An empirical study in Madrid

Reducing the air pollution from increases in traffic congestion in large cities and their surroundings is an important problem that requires changes in travel behavior. Road pricing is an effective tool for reducing air pollution, as reflected currently urban road pricing outcomes (Singapore, London, Stockholm and Milan). A survey was conducted based on establishing a hypothetical urban road pricing system in Madrid (a random sample size n = 1298). We developed a forecast air pollution model with time series analysis to evaluate the consequences of possible air pollution decreases in Madrid. Results reveal that the hypothetical road pricing for Madrid could have highly significant effects on decreasing air pollution outside of the city and in the inner city during the peak operating time periods of maximum congestion (morning peak hours from 7:00 to 10:00 and evening peak hours from 18:00 to 20:00). Furthermore, this system could have significant positive effects on a shift toward using public transport and non-motorized modes inside the hypothetical toll zone. This reveals that the system has a high capacity to motivate a decrease in air pollution and impose more sustainable behavior for public transport users.     

Trial-and-error method for congestion pricing scheme under side-constrained probit-based stochastic user equilibrium conditions

A toll pattern that can restrict link flows on the tolled links to some predetermined thresholds is named as effective toll solution, which can be theoretically obtained by solving a side-constraint traffic assignment problem. Considering the practical implementation, this paper investigates availability of an engineering-oriented trial-and-error method for the effective toll pattern of cordon-based congestion pricing scheme, under side-constrained probit-based stochastic user equilibrium (SUE) conditions. The trial-and-error method merely requires the observed traffic counts on each entry of the cordon. A minimization model for the side-constrained probit-based SUE problem with elastic demand is first proposed and it is shown that the effective toll solution equals to the product of value of time and optimal Lagrangian multipliers with respect to the side constraints. Then, employing the Lagrangian dual formulation of the minimization method, this paper has built a convergent trial-and-error method. The trial-and-error method is finally tested by a numerical example developed from the cordon-based congestion pricing scheme in Singapore.     

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

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

Advanced pricing and rationing policies for large scale multimodal networks

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

Optimal distance- and time-dependent area-based pricing with the Network Fundamental Diagram

Given the efficiency and equity concerns of a cordon toll, this paper proposes a few alternative distance-dependent area-based pricing models for a large-scale dynamic traffic network. We use the Network Fundamental Diagram (NFD) to monitor the network traffic state over time and consider different trip lengths in the toll calculation. The first model is a distance toll that is linearly related to the distance traveled within the cordon. The second model is an improved joint distance and time toll (JDTT) whereby users are charged jointly in proportion to the distance traveled and time spent within the cordon. The third model is a further improved joint distance and delay toll (JDDT) which replaces the time toll in the JDTT with a delay toll component. To solve the optimal toll level problem, we develop a simulation-based optimization (SBO) framework. Specifically, we propose a simultaneous approach and a sequential approach, respectively, based on the proportional-integral (PI) feedback controller to iteratively adjust the JDTT and JDDT, and use a calibrated large-scale simulation-based dynamic traffic assignment (DTA) model of Melbourne, Australia to evaluate the network performance under different pricing scenarios. While the framework is developed for static pricing, we show that it can be easily extended to solve time-dependent pricing by using multiple PI controllers. Results show that although the distance toll keeps the network from entering the congested regime of the NFD, it naturally drives users into the shortest paths within the cordon resulting in an uneven distribution of congestion. This is reflected by a large clockwise hysteresis loop in the NFD. In contrast, both the JDTT and JDDT reduce the size of the hysteresis loop while achieving the same control objective. We further conduct multiple simulation runs with different random seed numbers to demonstrate the effectiveness of different pricing models against simulation stochasticity. However, we postulate that the feedback control is not applicable with guaranteed convergence if the periphery of the cordon area becomes highly congested or gridlocked.     

Efficiency and equity comparison of cordon- and area-based road pricing schemes using a trip-chain equilibrium model

This paper compares performances of cordon- and area-road pricing regimes on their social welfare benefit and equity impact. The key difference between the two systems is that the cordon charges travellers per crossing whereas the area scheme charges the travellers for an entry permit (e.g. per day). For the area licensing scheme, travellers may decide to pay or not to pay the toll depending on the proportion between their travel costs for the whole trip-chains during a valid period of the area license and the toll level. A static trip-chain equilibrium based model is adopted in the paper to provide a better evaluation of the area-based tolls on trip-chain demands. The paper proposes a modified Gini coefficient taking in account assumptions of revenue re-distribution to measure the spatial equity impact. The model is tested with the case study of the Utsunomiya city in Japan. The results demonstrate a higher level of optimal tolls and social welfare benefits of the area-based schemes compared to those of the cordon-based schemes. Different sizes of the charging boundary have significant influences on the scheme benefits. The tests also show an interesting result on the non-effect of the boundary design (for both charging types) on their equity impacts. However, when comparing between charging regimes it is clear that the area schemes generate more inequitable results.     

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.     

集聚经济视角下轨道交通投资对城市系统均衡的影响

随着城镇化进程加快,城市规模增加所带来的集聚效应和交通拥堵等负外部性之间的矛盾越来越突出,优化城市交通基础设施建设是缓解该矛盾的重要举措。本文同时考虑了集聚经济和交通拥挤两种外部性,构建并求解了一个两区域城市空间结构模型,分三种情况探究了轨道交通的投资引入和道路容量的优化对城市规模和城市空间结构均衡的影响。结果表明,轨道交通的投资引入能够增加城市人口规模和社会福利,使城市结构更加紧凑。但是,随着集聚经济水平的提高,城市规划者应逐步完善公交配套设施,以降低公交拥挤成本,提高公交出行分担率;还应制定相应的福利政策,避免由于个体效用下降而导致人口流出。     

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.     

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.     

Transport policy prioritisation for Dublin

Internalisation of the external costs of transport is currently the subject of much debate. Estimation of costs such as those of pollution and congestion is a primary element in any strategy involving policies for use in the internalisation of these costs. The objective of the TRENEN II STRAN project, funded by the EU, was to develop a methodology for estimation of the marginal external costs of transport. The model developed during the project was used in a series of case studies. One of the case studies, that conducted for Dublin, is reported in this paper. A brief summary of the TRENEN approach is presented followed by the results for Dublin produced from policies such as Do Nothing, Uniform pricing (internalising external costs by means of fuel taxation), Congestion Pricing (cordon pricing) and a first-best policy, the Full Optimum where one assumes that the policy maker has perfect pricing instruments available. As one would expect, the model shows that the greatest reduction in traffic level and external costs would occur if it were possible to introduce a highly differentiated and sophisticated pricing system. Increased taxation on fuel is not an efficient policy as it does not address the marginal external costs of congestion in a way that time-differentiated road-use pricing would. The results from testing of the different measures are interesting particularly those relating to parking and the way in which residents within the CBD and commuters to the CBD are dealt with. This revised version was published online in June 2006 with corrections to the Cover Date.     

The Gothenburg congestion charge. Effects,design and politics

This paper summarizes the traffic effects of the Gothenburg congestion charges introduced in 2013. The system is similar to the system introduced in Stockholm in 2006; both are designed as time-of-day dependent cordon pricing systems. We find that many effects and adaptation strategies are similar to those found in Stockholm, indicating a high transferability between smaller and larger cities with substantial differences in public transport use. However, there are also important differences regarding some of the effects, the accuracy of the model forecasts and public support arising from different topologies, public transport use, congestion levels and main objectives communicated to the public. Finally, the Gothenburg case suggests that whether congestion charges are introduced or not depends on the support among the political parties, and that this is determined primarily by the prevailing institutional setting and power over revenues, and to a lower extent by the public support, and benefits from congestion reduction.     

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.     

Accuracy of the Gothenburg congestion charges forecast

This paper explores the accuracy of the transport model forecast of the Gothenburg congestion charges, implemented in 2013. The design of the charging system implies that the path disutility cannot be computed as a sum of link attributes. The route choice model is therefore implemented as a hierarchical algorithm, applying a continuous value of travel time (VTT) distribution. The VTT distribution was estimated from stated choice (SC) data. However, based on experience of impact forecasting with a similar model and of impact outcome of congestion charges in Stockholm, the estimated VTT distribution had to be stretched to the right. We find that the forecast traffic reductions across the cordon and travel time gains were close to those observed in the peak. However, the reduction in traffic across the cordon was underpredicted off-peak. The necessity to make the adjustment indicates that the VTT inferred from SC data does not reveal the travellers’ preferences, or that there are factors determining route choice other than those included in the model: travel distance, travel time and congestion charge.     

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.