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.     

Drivers’ willingness-to-pay to reduce travel time: evidence from the San Diego I-15 congestion pricing project

The adoption of congestion pricing depends fundamentally upon drivers’ willingness to pay to reduce travel time during the congested morning peak period. Using revealed preference data from a congestion pricing demonstration project in San Diego, we estimate that willingness to pay to reduce congested travel time is higher than previous stated preference results. Our estimate of median willingness to pay to reduce commute time is roughly $30 per hour, although this may be biased upward by drivers’ perception that the toll facility provides safer driving conditions. Drivers also use the posted toll as an indicator of abnormal congestion and increase their usage of the toll facility when tolls are higher than normal.     

Nonlinear pricing on private roads with congestion and toll collection costs

Nonlinear pricing (a form of second-degree price discrimination) is widely used in transportation and other industries but it has been largely overlooked in the road-pricing literature. This paper explores the incentives for a profit-maximizing toll-road operator to adopt some simple nonlinear pricing schemes when there is congestion and collecting tolls is costly. Users are assumed to differ in their demands to use the road. Regardless of the severity of congestion, an access fee is always profitable to implement either as part of a two-part tariff or as an alternative to paying a toll. Use of access fees for profit maximization can increase or decrease welfare relative to usage-only pricing for profit maximization. Hence a ban on access fees could reduce welfare.     

Step-tolling with price-sensitive demand: Why more steps in the toll make the consumer better off

Most dynamic models of congestion pricing use fully time-variant tolls. However, in practice, tolls are uniform over the day, or at most have just a few steps. Such uniform and step tolls have received surprisingly little attention from the literature. Moreover, most models that do study them assume that demand is insensitive to the price. This seems an empirically questionable assumption that, as this paper finds, strongly affects the implications of step tolling for the consumer. In the bottleneck model, first-best tolling has no effect on the generalised price, and thus consumer surplus remains the same as without tolling. Conversely, under price-sensitive demand, step tolling increases the price, making the consumer worse off. The more steps the toll has, the closer it approximates the first-best toll, thereby increasing the welfare gain and making consumers better off. This indicates the importance for real-world tolls to have as many steps as possible: this not only raises welfare, but may also increase the political acceptability of the scheme by making consumers better off.     

Optimal tolls for multi-class traffic: Analytical formulations and policy implications

This paper puts together an analytical formulation to compute optimal tolls for multi-class traffic. The formulation is comprised of two major modules. The first one is an optimization component aimed at computing optimal tolls assuming a Stackelberg game in which the toll agency sets the tolls, and the equilibrating traffic plays the role of the followers. The optimization component is supported by a set of cost models that estimate the externalities as a function of a multivariate vector of traffic flows. These models were estimated using Taylor series expansions of the output obtained from traffic simulations of a hypothetical test case. Of importance to the paper is the total travel time function estimated using this approach that expresses total travel time as a multivariate function of the traffic volumes. The formulation presented in the paper is then applied to a variety of scenarios to gain insight into the optimality of current toll policies. The optimal tolls are computed for two different cases: independent tolls, and tolls proportional to passenger car equivalencies (PCE).The numerical results clearly show that setting tolls proportional to PCEs leads to lower values of welfare that are on average 15% lower than when using independent tolls, though, in some cases the total welfare could be up to 33% lower. This is a consequence of two factors. First, the case of independent tolls has more degrees of freedom than the case of tolls proportional to PCEs. Second, tolls proportional to PCEs do not account for externalities other than congestion, which is likely to lead to lower welfare values.The analytical formulations and numerical results indicate that, because the total travel time is a non-linear function of the traffic volumes, the marginal social costs and thus the optimal congestion tolls also depend on the traffic volumes for each vehicle class. As a result of this, for the relatively low volumes of truck traffic observed in real life, the optimal congestion tolls for trucks could indeed be either lower or about the same as for passenger cars. This stand in sharp contrast with what is implied in the use of PCEs, i.e., that the contribution to congestion are constant. This latter assumption leads to optimal truck congestion tolls that are always proportional to the PCE values.The comparison of the toll ratios (truck tolls divided by passenger car tolls) for both observed and optimal conditions suggests that the tolls for small trucks are about the right level, maybe a slightly lower than optimal. However, the analysis of the toll ratio for large trucks seems to indicate a significant overcharge. The estimates show that the average observed toll ratio for large trucks is even higher than the maximum optimal toll ratio found in the numerical experiments. This suggests that the tolls for large trucks are set on the basis of revenue generation principles while the passenger car tolls are being set based on a mild form of welfare maximization. This leads to a suboptimal cross-subsidization of passenger car traffic in detriment of an important sector of the economy.     

Will a driving restriction policy reduce car trips?—The case study of Beijing,China

A driving restriction policy, as one of the control-and-command rationing measures, is a politically acceptable policy tool to address traffic congestion and air pollution in some countries and cities in the world. Beijing is the first city in China to implement this policy. A one-day-a-week driving restriction scheme was expected to take 20% of cars off the road every week day. Using household survey and travel diary data, we analyze the short-term effect of this driving restriction policy on individual travel mode choice. The data also allow us to identify which demographic groups are more likely to break the restriction rule. The estimates reveal that the restriction policy in Beijing does not have significant influence on individuals’ decisions to drive, as compared with the policy’s influence on public transit. The rule-breaking behavior is constant and pervasive. We found that 47.8% of the regulated car owners didn’t follow the restriction rules, and drove “illegally” to their destination places. On average, car owners who traveled during peak hours and/or for work trips, and whose destinations were farther away from the city center or subway stations, were more likely to break the driving restriction rules. Therefore, Beijing is probably in need of more comprehensive and palatable policy instruments (e.g., a combination of congestion tolls, parking fees, fuel taxes, and high-speed transit facilities) to effectively alleviate traffic congestion and air pollution.     

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.     

Moving from trip-based to activity-based measures of accessibility

This paper studies the properties and performance of a new measure of accessibility, called the activity-based accessibility (ABA) measure, and compares it to traditional measures of accessibility, including isochrone, gravity and utility-based measures. The novel aspect of the ABA is that it measures accessibility to all activities in which an individual engages, incorporating constraints such as scheduling, and travel characteristics such as trip chaining. The ABA is generated from the day activity schedule (DAS) model system, an integrated system based on the concept of an activity pattern, which identifies the sequence and tour structure among all the activities and trips taken by an individual during a day. A byproduct is an individual’s expected maximum utility over the choices of all available activity patterns, and from this the ABA is derived. The ABA is related to the logsum accessibility measures frequently derived from destination and mode discrete choice models. The key difference is that it is generated not by examining a particular trip, but by examining all trips and activities throughout the day.A case study using data from Portland, Oregon, demonstrates the rich picture of accessibility made available by use of the ABA, and highlights differences between the ABA and more traditional measures of accessibility. The ABA is successful in (a) capturing taste heterogeneity across individuals (not possible with aggregate accessibility measures), (b) combining different types of trips into a unified measure of accessibility (not possible with trip-based measures), (c) reflecting the impact of scheduling and trip chaining on accessibility (not possible with trip-based measures), and (d) quantifying differing accessibility impacts on important segments of the population such as unemployed and zero auto households (not possible with aggregate measures, and limited with trip-based measures).     

Sensor location problems in path-differentiated congestion pricing

Path-differentiated congestion pricing is a tolling scheme that imposes tolls on paths instead of individual links. One way to implement this scheme is to deploy automated vehicle identification sensors, such as toll tag readers or license plate scanners, on roads in a network. These sensors collect vehicles’ location information to identify their paths and charge them accordingly. In this paper, we investigate how to optimally locate these sensors for the purpose of implementing path-differentiated pricing. We consider three relevant problems. The first is to locate a minimum number of sensors to implement a given path-differentiated scheme. The second is to design an optimal path-differentiated pricing scheme for a given set of sensors. The last problem is to find a path differentiated scheme to induce a given target link-flow distribution while requiring a minimum number of sensors.     

Analysis of the optimal length of road expansion – A case study of the Taipei metropolitan area

This study explores the optimal investment in the length of an expanded section of road to mitigate the congestion on a transportation corridor. It is assumed that one end of the road is in the central business district (CBD) and that the households are uniformly distributed along the road. Each individual makes trips from his/her residence to the CBD. Trip demand is elastic and depends on the cost of the trip (including congestion costs). During the first stage, the government determines the length of the expanded section given the width of that section. In the second stage, road users determine their trip demands by taking into consideration the trip cost function. In the process of solving this problem, the equilibrium traffic volume is first solved using differential equations. The optimal length of the expanded section is then solved by maximizing the social welfare. The analysis is then applied to the case of the Tucheng city – Banciao city – Taipei CBD corridor in the Taipei metropolitan area. The scheme of road expansion without tolling performs closely to the first-best scheme for the case of a high potential demand. This study’s approach can serve as valuable reference for city planners engaged in road planning in a transportation corridor between the CBD and satellite cities in a metropolitan area.     

Congestion pricing and roadspace rationing: an application to the San Francisco Bay Bridge corridor

This paper presents an empirical application of a congestion–alleviation strategy that C. Daganzo [Transportation Research B 29 (1995) 139–154] proposed as a “hybrid between rationing and pricing”. This strategy is applied to the San Francisco Bay Bridge corridor, in search of a practical and Pareto-improving solution to the Bridge's congestion. The work relies on a mode-split model for work trips across four different income groups residing in 459 origin zones, and it applies an equilibrium analysis based on Bridge performance. Results indicate that modal utilities (and thus choices) are sensitive to the specific combination of toll and rationing rate, as well as to the Bridge's travel-time (or performance) function, and the length of the congested section. Though no combination of tolls plus rationing rates was found to benefit all groups of travelers studied, further investigations may improve upon these results by refining some of the assumptions made here.     

Users’ perceptions and willingness to pay in interurban toll roads: identifying differences across regions from a nationwide survey in Spain

Users’ acceptability is considered one of the key drivers for the successful implementation of transport policy measures. This is especially crucial in the case of toll roads since they are financed through drivers’ contributions. Previous literature in this field has mainly focused on measuring users’ attitudes towards urban congestion pricing strategies. However limited research has been developed concerning interurban toll roads. Previous research shows that socioeconomic variables are not conclusive to explain users’ perceptions towards tolls. By contrast, other drivers such as regional differences seem to play a more important role, especially when charging conditions within the same nation greatly vary across regions. This paper analyzes regional differences in users’ attitudes within an asymmetrical distribution of the toll road network across regions. Based on a nationwide survey conducted to road users in interurban toll roads in Spain, we develop both a binomial logit and a censored regression (tobit) model to explore drivers’ perceptions and willingness to pay. The research concludes that users from regions with a more extensive tolled network generally show a more negative attitude towards charges, but not necessarily a lower willingness to pay. The paper also points out that an asymmetrical distribution of toll roads across regions may result in negative perceptions among those users perceiving to be unfairly treated when compared to citizens in other regions.     

Can Hong Kong price-manage its cross-harbor-tunnel congestion?

Hong Kong drivers face daily congestion, especially at the Cross Harbor Tunnel (CHT) whose tolls are substantially lower than those of the drivers’ other two tunnel options: the Eastern Harbor Crossing (EHC) and the Western Harbor Crossing (WHC). In 2013, the Hong Kong Special Administrative Region (HKSAR) Government issued a consultation paper, seeking public comments on three toll-change proposals that would raise the CHT’s tolls and lower the EHC’s tolls. The WHC’s tolls would remain unchanged due to its congested connecting roads. Using monthly crossing data available from the HKSAR’s Transport Department for 2000–2012, this paper uses a Generalized Leontief demand system to document that the usage patterns of the three tunnels is price-responsive. Hence, we conclude that the proposed toll changes are likely to be effective in transportation demand management, by shifting a portion of the CHT’s usage to the EHC and WHC, thereby relieving the CHT’s congestion.     

Urban highway congestion

This article examines urban highway congestion pricing in the instance in which it is not possible to levy a congestion toll on a major portion of the urban road system. This case is pertinent because of technical and/or political constraints. The article uses economic theory and numerical examples to show that the optimum second-best toll can vary appreciably from the optimal tolls in a regime in which efficient tolls can be imposed on all routes.     

Dynamic network equilibrium for daily activity-trip chains of heterogeneous travelers: application to large-scale networks

Applications of dynamic network equilibrium models have, mostly, considered the unit of traffic demand either as one-way trip, or as multiple independent trips. However, individuals’ travel patterns typically follow a sequence of trips chained together. In this study we aim at developing a general simulation-based dynamic network equilibrium algorithm for assignment of activity-trip chain demand. The trip chain of each individual trip maker is defined by the departure time at origin, sequence of activity destination locations, including the location of their intermediate destinations and their final destination, and activity duration at each of the intermediate destinations. Spatial and temporal dependency of subsequent trips on each other necessitate time and memory consuming calculations and storage of node-to-node time-dependent least generalized cost path trees, which is not practical for very large metropolitan area networks. We first propose a reformulation of the trip-based demand gap function formulation for the variational inequality formulation of the Bi-criterion Dynamic User Equilibrium (BDUE) problem. Next, we propose a solution algorithm for solving the BDUE problem with daily chain of activity-trips. Implementation of the algorithm for very large networks circumvents the need to store memory-intensive node-to-node time-dependent shortest path trees by implementing a destination-based time-dependent least generalized cost path finding algorithm, while maintaining the spatial and temporal dependency of subsequent trips. Numerical results for a real-world large scale network suggest that recognizing the dependency of multiple trips of a chain, and maintaining the departure time consistency of subsequent trips provide sharper drops in gap values, hence, the convergence could be achieved faster (compared to when trips are considered independent of each other).     

Integrating congestion pricing and transit investment planning

This paper develops a mathematical model and solution procedure to identify an optimal zonal pricing scheme for automobile traffic to incentivize the expanded use of transit as a mechanism to stem congestion and the social costs that arise from that congestion. The optimization model assumes that there is a homogenous collection of users whose behavior can be described as utility maximizers and for which their utility function is driven by monetary costs. These monetary costs are assumed to be the tolls in place, the per mile cost to drive, and the value of their time. We assume that there is a system owner who sets the toll prices, collects the proceeds from the tolls, and invests those funds in transit system improvements in the form of headway reductions. This yields a bi-level optimization model which we solve using an iterative procedure that is an integration of a genetic algorithm and the Frank–Wolfe method. The method and solution procedure is applied to an illustrative example.     

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.     

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

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

Optimal 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.     

Overcoming public aversion to congestion pricing

We have completed a survey of Southern California residents designed to examine whether the details of policy design can make congestion pricing more attractive to the motoring public. A congestion fee proposal is often regarded as simply a tax increase; also, especially in the US, motorists apparently regard the use of congestion fees as coercive, in that they often have few if any practical alternatives to paying the fee. Unlike most opinion surveys on congestion pricing, our survey was quite explicit about the fate of the collected revenues. For example, we presented respondents with policies that returned a substantial portion of the revenues to the public, either in the form of cash (through reductions in sales taxes and vehicle registration fees or through income tax credits) or in the form of coupons to be used for vehicle emissions equipment repair, transit, and the like. In addition, we examined whether the typically intense opposition to congestion pricing if applied only to a part of a roadway, leaving the motorist free to choose between free lanes and toll lanes. We find that a promise to offset the imposition of congestion fees by other taxes can result in a 7% point increase in support for congestion pricing policies, and the restriction of congestion pricing to a single lane on a freeway attracts from 9% to 17% points of additional support.