Toll pricing framework under logit‐based stochastic user equilibrium constraints

This paper addresses the toll pricing framework for the first‐best pricing with logit‐based stochastic user equilibrium (SUE) constraints. The first‐best pricing is usually known as marginal‐cost toll, which can be obtained by solving a traffic assignment problem based on the marginal cost functions. The marginal‐cost toll, however, has rarely been implemented in practice, because it requires every specific link on the network to be charged. Thus, it is necessary to search for a substitute of the marginal cost pricing scheme, which can reduce the toll locations but still minimize the total travel time. The toll pricing framework is the set of all the substitute toll patterns of the marginal cost pricing. Assuming the users' route choice behavior following the logit‐based SUE principle, this paper has first derived a mathematical expression for the toll pricing framework. Then, by proposing an origin‐based variational inequality model for the logit‐based SUE problem, another toll pricing framework is built, which avoids path enumeration/storage. Finally, the numerical test shows that many alternative pricing patterns can inherently reduce the charging locations and total toll collected, while achieving the same equilibrium link flow pattern. Copyright © 2013 John Wiley & Sons, Ltd.     

Capturing value of reliability through road pricing in congested traffic under uncertainty

Empirical studies showed that travel time reliability, usually measured by travel time variance, is strongly correlated with travel time itself. Travel time is highly volatile when the demand approaches or exceeds the capacity. Travel time variability is associated with the level of congestion, and could represent additional costs for travelers who prefer punctual arrivals. Although many studies propose to use road pricing as a tool to capture the value of travel time (VOT) savings and to induce better road usage patterns, the role of the value of reliability (VOR) in designing road pricing schemes has rarely been studied. By using road pricing as a tool to spread out the peak demand, traffic management agencies could improve the utility of travelers who prefer punctual arrivals under traffic congestion and stochastic network conditions. Therefore, we could capture the value of travel time reliability using road pricing, which is rarely discussed in the literature. To quantify the value of travel time reliability (or reliability improvement), we need to integrate trip scheduling, endogenous traffic congestion, travel time uncertainty, and pricing strategies in one modeling framework. This paper developed such a model to capture the impact of pricing on various costs components that affect travel choices, and the role of travel time reliability in shaping departure patterns, queuing process, and the choice of optimal pricing. The model also shows the benefits of improving travel time reliability in various ways. Findings from this paper could help to expand the scope of road pricing, and to develop more comprehensive travel demand management schemes.     

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.     

The role of volume-delay functions in forecasting and evaluating congestion charging schemes: the Stockholm case

This paper uses observations from before and during the Stockkholm congestion charging trial in order to validate and improve a transportation model for Stockholm. The model overestimates the impact of the charges on traffic volumes while at the same time it substantially underestimates the impact on travel times. These forecast errors lead to considerable underestimation of economic benefits which are dominated by travel time savings. The source of error lies in the static assignment that is used in the model. Making the volume-delay functions (VDFs) steeper only marginally improves the quality of forecast but strongly impacts the result of benefit calculations. We therefore conclude that the dynamic assignment is crucial for an informed decision on introducing measures aimed at relieving congestion. However, in the absence of such a calibrated dynamic model for a city, we recommend that at least a sensitivity analysis with respect to the slope of VDFs is performed.     

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.     

Trial and error method for optimal tradable credit schemes: The network case

Recent studies on the new congestion reduction method―tradable credit scheme rely on the full information of speed‐flow relationship, demand function, and generalized cost. As analytical travel demand, functions are difficult to establish in practice. This paper develops a trial and error method for selecting optimal credit schemes for general networks in the absence of demand functions. After each trial of tradable credit scheme, the credit charging scheme and total amount of credits to be distributed are updated by both observed link flows at traffic equilibrium and revealed credit price at market equilibrium. The updating strategy is based on the method of successive averages and its convergence is established theoretically. Our numerical experiments demonstrate that the method of successive averages based trial and error method for tradable credit schemes has a lower convergence speed in comparison with its counterpart for congestion pricing and could be enhanced by exploring more efficient methods that make full use of credit price information. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

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.     

Evaluating the benefits of a combined route guidance and road pricing system in a traffic network with recurrent congestion

When drivers do not have complete information on road travel time and thus choose their routes in a stochastic manner or based on their previous experience, separate implementations of either route guidance or road pricing cannot drive a stochastic network flow pattern towards a system optimum in a Wardropian sense. It is thus of interest to consider a combined route guidance and road pricing system. A road guidance system could reduce drivers' uncertainty of travel time through provision of traffic information. A driver who is equipped with a guidance system could be assumed to receive complete information, and hence be able to find the minimum travel time routes in a user-optimal manner, while marginal-cost road pricing could drive a user-optimal flow pattern toward a system optimum. Therefore, a joint implementation of route guidance and road pricing in a network with recurrent congestion could drive a stochastic network flow pattern towards a system optimum, and thus achieve a higher reduction in system travel time. In this paper the interaction between route guidance and road pricing is modeled and the potential benefit of their joint implementation is evaluated based on a mixed equilibrium traffic assignment model. The private and system benefits under marginal-cost pricing and varied levels of market penetration of the information systems are investigated with a small and a large example. It is concluded that the two technologies complement each other and that their joint implementation can reduce travel time more efficiently in a network with recurrent congestion.     

Optimal cordon pricing in a non-monocentric city

This paper examines the effect of cordon pricing based on an urban spatial model of a non-monocentric city where trips may occur between any pair of locations in the city. The model describes the spatial distribution of trip demand and traffic congestion under alternative pricing schemes. We evaluate the efficiency of resource allocation by comparing three schemes: no-toll equilibrium, first-best optimum, and optimal cordon pricing. Optimal cordon pricing is defined as a combination of cordon location and toll level that maximizes the social surplus in a city. Simulations show that cordon pricing is not always effective for congestion management: cordon pricing tends to be effective as the urban structure is more monocentric.     

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.     

Dynamic operations and pricing of electric unmanned aerial vehicle systems and power networks

The emergence of electric unmanned aerial vehicle (E-UAV) technologies, albeit somewhat futuristic, is anticipated to pose similar challenges to the system operation as those of electric vehicles (EVs). Notably, the charging of EVs en-route at charging stations has been recognized as a significant type of flexible load for power systems, which often imposes non-negligible impacts on the power system operator’s decisions on electricity prices. Meanwhile, the charging cost based on charging time and price is part of the trip cost for the users, which can affect the spatio-temporal assignment of E-UAV traffic to charging stations. This paper aims at investigating joint operations of coupled power and electric aviation transportation systems that are associated with en-route charging of E-UAVs in a centrally controlled and yet dynamic setting, i.e., with time-varying travel demand and power system base load. Dynamic E-UAV charging assignment is used as a tool to smooth the power system load. A joint pricing scheme is proposed and a cost minimization problem is formulated to achieve system optimality for such coupled systems. Numerical experiments are performed to test the proposed pricing scheme and demonstrate the benefits of the framework for joint operations.     

A cost–benefit analysis of the Stockholm congestion charging system

This paper presents a cost–benefit analysis of the Stockholm congestion charging system, based on the observed rather than on the model-forecasted data. The most important data sources are travel time and traffic flow measurements made in the year before the charges were introduced (during April 2005) and during the first spring with the charges (during April 2006, 4 months after the charges were introduced). Using matrix calibration, effects on the non-observed link flows and travel times are extrapolated, enabling us to calculate the social value of changes in travel times and travel costs. Impacts on traffic safety and emissions are calculated using standard Swedish CBA relationships. The system is shown to yield a significant social surplus, well enough to cover both investment and operating costs, provided that it is kept for a reasonable lifetime: investment and startup costs are “recovered” in terms of social benefits in around 4 years.     

Congestion and variable user charging as an effective travel demand management instrument

Interest at the political level in congestion charging is gaining pace as cities struggle with ways to reduce the effects of growing traffic congestion on the liveability of cities. Despite a long history of promotion of a wide array of travel demand management (TDM) initiatives, very few have had a noticeable impact on the levels of traffic on the road networks of metropolitan areas. TDM success in this context has almost become ‘band-aid’ in the absence of a pricing strategy that not only promotes efficient use of the system but also hypothecates revenues to support essential complementary infrastructure and services such as public transport. This paper takes a look at the stream of pricing consciousness that is surfacing around the world. Although very few jurisdictions have implemented congestion charging, or any form of efficient variable car and truck user charging, the winds of change are well in place. The adage “it is not a matter of if but of when” seems to be the prevailing view. Our overview of global trends in positioning the debate and hopefully follow-through commitment to implementation provides a backdrop to papers submitted for this special issue on travel demand management. The predominance of papers on pricing is indicative of the priority that must be given to efficient charging and revenue disbursement.     

Road pricing modeling for hyper-congestion

Recently there has been a resurgence in the interest of road pricing. Most studies adopt the static modeling paradigm, typically using either separable monotone or backward-bending link travel time functions for the analysis. In this study, through the shockwave analysis, we show that separable backward-bending functions are not appropriate for modeling hyper-congestion and hence road pricing. In the absence of queue spillback, link travel time is a monotone increasing function of inflow. However, in the presence of queue spillback, we show that the static paradigm even with a monotone travel time function cannot adequately portray the congestion phenomenon. In some cases, the tolls determined by the static paradigm can be even detrimental, worsening rather than alleviating the congestion problem. In the end, to model congested networks properly, perhaps one has no other choices but to adopt a modeling paradigm that faithfully captures both the temporal as well as the spatial dimensions of traffic queuing.     

Road pricing with complications

The rationale for congestion charges is that by internalising the marginal external congestion cost, they restore efficiency in the transport market. In the canonical model underlying this view, congestion is a static phenomenon, users are taken to be homogenous, there is no travel time risk, and a highly stylised model of congestion is used. The simple analysis also ignores that real pricing schemes are only rough approximations to ideal systems and that inefficiencies in related markets potentially affect the case for congestion charges. The canonical model tends to understate the marginal external congestion cost because it ignores user heterogeneity and trip timing inefficiencies. With respect to the relevance of interactions between congestion and congestion charges and tax distortions and distributional concerns, recent insights point out that there is no general case for modifying charges for such interactions. Therefore the simple Pigouvian rule remains a good first approximation for the design of road charging systems.     

Network user equilibrium of battery electric vehicles considering flow-dependent electricity consumption

This paper addresses the equilibrium traffic assignment problem involving battery electric vehicles (BEVs) with flow-dependent electricity consumption. Due to the limited driving range and the costly/time-consuming recharging process required by current BEVs, as well as the scarce availability of battery charging/swapping stations, BEV drivers usually experience fear that their batteries may run out of power en route. Therefore, when choosing routes, BEV drivers not only try to minimize their travel costs, but also have to consider the feasibility of their routes. Moreover, considering the potential impact of traffic congestion on the electricity consumption of BEVs, the feasibility of routes may be determined endogenously rather than exogenously. A set of user equilibrium (UE) conditions from the literature is first presented to describe the route choice behaviors of BEV drivers considering flow-dependent electricity consumption. The UE conditions are then formulated as a nonlinear complementarity model. The model is further formulated as a variational inequality (VI) model and is solved using an iterative solution procedure. Numerical examples are provided to demonstrate the proposed models and solution algorithms. Discussions of how to evaluate and improve the system performance with non-unique link flow distribution are offered. A robust congestion pricing model is formulated to obtain a pricing scheme that minimizes the system travel cost under the worst-case tolled flow distribution. Finally, a further extension of the mathematical formulation for the UE conditions is provided.     

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.     

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.     

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.