Behavioral adjustments and equity effects of congestion pricing: Analysis of morning commutes during the Stockholm Trial

This paper assesses the horizontal and vertical equity effects of the Stockholm Trial with Congestion Pricing for morning commuters, in terms of both travel behavioral adjustments and welfare effects, as a result of the toll’s direct effects and the behavioral adjustments. We consider specifically two behavioral adjustments: mode choice and departure time choice. Initial car drivers crossing the toll cordon had a 15 percentage-points higher rate of switching to public transit as compared with those not crossing the cordon. We also find some evidence of peak spreading, in particular toward a later departure time, as a result of the charging scheme, but most people choose a departure time within 15 min both before and during the trial. In the welfare analysis, we found no clear pattern of increasing burden by either increasing income or decreasing income, and the increase in the Gini Coefficient was insignificant. We also found no significant difference in either the mode-switching behavior or the average welfare effect for women versus for men.     

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.     

Distributional effects of road pricing: Assessment of nine scenarios for Paris

The starting point of this paper is to consider that there is no general answer to the question of the equity of urban road pricing. We therefore simulate and compare the distributional effects on commuters of nine toll scenarios for Paris, assuming that utility is nonlinear in income. We show that the distributional pattern across income groups depends crucially on the level of traffic reduction induced by tolling. Stringent tolls are more favourable to low-income motorists. Equity effects also vary with toll design. Compared to a reference scenario which uniformly charges all motorists driving within Paris, an inbound cordon toll is detrimental to low-incomes. Conversely, granting a rebate to low CO₂ emission cars slightly improves their situation while an exemption for Paris residents is neutral. Surprisingly, it matters little for social equity whether toll revenues are allocated to all commuters or solely to public transport users.     

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.     

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.     

Managing bottleneck congestion with tradable credits

We demonstrate the efficiency and effectiveness of a tradable credit system in managing the morning commute congestion with identical and nonidentical commuters. The credit system consists of a time-varying credit charged at the bottleneck and an initial credit distribution to the commuters, where the credits are universal in terms of time. Credits are tradable between the commuters and the credit price is determined by a competitive market. Under the assumption that late-arrival is not allowed, we prove that an optimal credit charging scheme, which completely eliminates the bottleneck queue, always exists despite how commuters vary in their value-of-time (VOT). The optimal charge rate is strictly increasing and convex with time, which therefore drives the commuters to depart in the increasing order of their VOT. The optimal credit charging scheme is pareto-improving, but may cause undesirable welfare distribution among the commuters. Our study shows that a combination of an initial credit distribution and an optimal credit charging scheme can simultaneously achieve system optimum and certain forms of equality (e.g., “numerical” or “proportional” equality), and that the commuters in the middle VOT bracket will receive the most credits under the proportionally equitable credit distribution.     

How much is too much for tolled road users: Toll saturation and the implications for car commuting value of travel time savings?

The current practice of forecasting the demand for new tolled roads typically assumes that car users are prepared to pay a higher toll for a shorter journey, and they will keep doing so as long as the toll cost is not higher than their current value of travel time savings. Practice ignores the possibility that there could be a point when motorists stop driving on toll roads due to a toll budget constraint. The unconstrained toll budget assumption may be valid in networks where the addition of a new toll road does not result in a binding budget constraint that car users may have for using toll roads (although it could also be invoked for existing tolled routes through a reduction in use of a tolled route). In a road network like Sydney which offers a growing number of (linked) tolled roads, the binding budget constraint may be invoked, and hence including additional toll links might in turn reduce the car users’ willingness to pay for toll roads to save the same amount of travel time. When this occurs, car users are said to reach a toll saturation point (or threshold) and begin to consider avoiding one or more toll roads. Whilst toll saturation has important implications for demand forecasting and planning of toll roads, this type of behaviour has not been explored in the literature. We investigate the influence that increasing toll outlays has on preferences of car commuters to use one or more tolled roads as the number of tolled roads increases. The Sydney metropolitan area offers a unique laboratory to test this phenomenon, with nine tolled roads currently in place and another five in planning. The evidence supports the hypothesis that the value of travel time savings decreases as a consequence of toll saturation.     

A model for optimizing electronic toll collection systems

This paper examines the deployment of electronic toll collection (ETC) and develops a model to maximize social welfare associated with a toll plaza. A payment choice model estimates the share of traffic using ETC as a function of delay, price, and a fixed cost of acquiring the in-vehicle transponder. Delay in turn depends on the relative number of ETC and manual collection lanes. Price depends on the discount given to users of the ETC lanes. The fixed cost of acquiring the transponder (not simply a monetary cost, but also the effort involved in signing up for the program) is a key factor in the model. Once a traveler acquires the transponder, the cost of choosing ETC in the future declines significantly. Welfare depends on the market share of ETC, and includes delay and gasoline consumption, toll collection costs, and social costs such as air pollution. This work examines the best combination of ETC lanes and toll discount to maximize welfare. Too many ETC lanes cause excessive delay to non-equipped users. Too high a discount costs the highway agency revenue needed to operate the facility. The model is applied to California’s Carquinez Bridge, and recommendations are made concerning the number of dedicated ETC lanes and the appropriate ETC discount.     

The impact of signal control on land-side traffic patterns at the Dallas/Fort worth airport

The Parkway Corridor is the primary ground facility at the Dallas/Fort Worth (D/FW) International Airport. It consists of an expressway for passengers to-and-from terminals and a service road mainly for employees of airline-associated agencies to access the service areas. As the Parkway Corridor is a natural short cut in the region, it has attracted more and more through commuters who usually choose to use the service road so as to circumvent the toll plazas on the expressway. The dramatic increase in both the volume and speed of through commuting traffic in recent years not only impedes service activities, but also raises safety concerns. The D/FW Airport Board is considering the installation of a series of traffic signals to regulate the cruise speed and thereby discourage use of the service road by commuters. This research is conducted to evaluate its effectiveness and potential impact on traffic patterns along the Parkway Corridor. A systematic approach, integrating queueing theories (G/M/m), discrete models, and traffic assignment, is proposed in this research, which allows the user to project the traffic distribution on each route with only the information obtained by traffic counts. Numerical results of alternate control strategies and a sensitivity analysis with respect to key parameters, such as the toll and cycle length of traffic signals are also reported.     

Pricing scheme design of ridesharing program in morning commute problem

This paper examines the dynamic user equilibrium of the morning commute problem in the presence of ridesharing program. Commuters simultaneously choose departure time from home and commute mode among three roles: solo driver, ridesharing driver, and ridesharing rider. Considering the congestion evolution over time, we propose a time-varying compensation scheme to maintain a positive ridesharing ridership at user equilibrium. To match the demand and the supply of ridesharing service over time, the compensation scheme should be set according to the inconvenience cost functions and the out-of-pocket cost functions. When the price charged per time unit is higher than the inconvenience cost per time unit perceived by the ridesharing drivers, the ridesharing participants will travel at the center of peak hours and solo drivers will commute at the two tails. Within the feasible region with positive ridership, the ridesharing program can reduce the congestion and all the commuters will be better off. To support system optimum (SO), we derive a time-varying toll combined with a flat ridesharing price from eliminating queuing delay. Under SO toll, the ridesharing program can attract more participants and have an enlarged feasible region. This reveals that the commuters are more tolerant to the inconvenience caused by sharing a ride at SO because of the lower travel time. Compared with no-toll equilibrium, both overall congestion and individual travel cost are further reduced at SO.     

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.     

Bottleneck model revisited: An activity-based perspective

The timing of commuting trips made during morning and evening peaks has typically been investigated using Vickrey’s bottleneck model. However, in the conventional trip-based approach, the decisions that commuters make during the day about their activity schedules and time use are not explicitly considered. This study extends the bottleneck model to address the scheduling problem of commuters’ morning home-to-work and evening work-to-home journeys by using an activity-based approach. A day-long activity-travel scheduling model is proposed for the simultaneous determination of departure times for morning and evening commutes, together with allocations of time during the day among travel and activities undertaken at home or at the workplace. The proposed model maximizes the total net utility of the home-based tour, which is the difference between the benefits derived from participating in activities and the disutility incurred by travel between activity locations. The properties of the model solution are analytically explored and compared with the conventional bottleneck model for a special case with constant marginal-activity utility. For the case with linear marginal-activity utility, we develop a heuristic procedure to seek the equilibrium scheduling solution. We also explore the effects of marginal-work utility (or the employees’ average wage level) and of flexible work-hour schemes on the scheduling problem in relation to the morning and evening commuting tours.     

Measuring the equity effects of a carbon charge on car commuters: A case study of Manchester Airport

This papers attempts to quantify the equity effect of a hypothesized economic instrument, a carbon charge on car commuters, for reducing carbon dioxide emissions produced by commuters on airport surface access. Manchester Airport is taken as a case study using staff Survey data from 2008 and 2010. Consumer welfare change is analysed for measuring the equity effects of carbon charge by user group, which considers the changes of travel mode choice, the carbon dioxide emissions reduction, the revenue from a carbon charge and how it is distributed. First, the individual carbon footprint in terms of gram passenger kilometre, and the damage cost of carbon by commuters on airport surface access are estimated. Next, the impact of carbon charge on travel behaviour is investigated by the nested logit model. Finally, the net effect of carbon charges is assessed by travel mode user, gender, job type, and age group. The results show some impacts of the carbon charge on car users and carbon reduction, and the positive effects on lower income group and less carbon commuters. The quantified results provide the evidences for the mitigation policies to combine monetary incentives with disincentives for travel behaviour change, and demonstrate the different equity effects among commuter groups.     

On the existence of pricing strategies in the discrete time heterogeneous single bottleneck model

In this paper, we study the pricing strategies in the discrete time single bottleneck model with general heterogeneous commuters. We first prove that in the system optimal assignment, the queue time must be zero for all the departures. Based on this result, the system optimal problem is formulated as a linear program. The solution existence and uniqueness are discussed. Applying linear programming duality, we then prove that the optimal dual variable values provide an optimal toll with which the system optimal solution is also an equilibrium solution. Extensive computational results are reported to demonstrate the insights gained from the formulations in this paper. These results confirm that a system optimal equilibrium can be found using the proposed approach.     

Private road competition and equilibrium with traffic equilibrium constraints

Toll road competition is one of the important issues under a build-operate-transfer (BOT) scheme, which is being encountered nowadays in many cities. When there are two or more competing firms and each firm operates a competitive toll road, their profits are interrelated due to the competitors' choices and demand inter-dependence in the network. In this paper we develop game-theoretic approaches to the study of the road network, on which multiple toll roads are operated by competitive private firms. The strategic interactions and market equilibria among the private firms are analyzed both in determining their supply (road capacity) and price (toll level) over the network. The toll road competition problems in general traffic equilibrium networks are formulated as an equilibrium program with equilibrium constraints or bi-level variational inequalities. Heuristic solution methods are proposed and their convergences are demonstrated with simple network examples. It is shown that private pricing and competition can be both profitable and welfare-improving.     

The evening commute with cars and transit: Duality results and user equilibrium for the combined morning and evening peaks

This paper extends Vickrey’s (1969) commute problem for commuters wishing to pass a bottleneck for both cars and transit that share finite road capacity. In addition to this more general framework considering two modes, the paper focuses on the evening rush, when commuters travel from work to home. Commuters choose which mode to use and when to travel in order to minimize the generalized cost of their own trips, including queueing delay and penalties for deviation from a preferred schedule of arrival and departure to and from work. The user equilibrium for the isolated morning and evening commutes are shown to be asymmetric because the schedule penalty in the morning is the difference between the departure and wished curves, and the schedule penalty in the evening is the difference between the arrival and wished curves. It is shown that the system optimum in the morning and evening peaks are symmetric because queueing delay is eliminated and the optimal arrival curves are the same as the departure curves.The paper then considers both the morning and evening peaks together for a single mode bottleneck (all cars) with identical travelers that share the same wished times. For a schedule penalty function of the morning departure and evening arrival times that is positive definite and has certain properties, a user equilibrium is shown to exist in which commuters travel in the same order in both peaks. The result is used to illustrate the user equilibrium for two cases: (i) commuters have decoupled schedule preferences in the morning and evening and (ii) commuters must work a fixed shift length but have flexibility when to start. Finally, a special case is considered with cars and transit: commuters have the same wished order in the morning and evening peaks. Commuters must use the same mode in both directions, and the complete user equilibrium solution reveals the number of commuters using cars and transit and the period in the middle of each rush when transit is used.     

The effect of complex models of externalities on estimated optimal tolls

Transport externalities such as costs of emissions and accidents are increasingly being used within appraisal and optimisation frameworks alongside the more traditional congestion analysis to set optimal transport policies. Models of externalities and costs of externalities may be implemented by a simple constant cost per vehicle-km approach or by more complex flow and speed dependent approaches. This paper investigates the impact of using both simple and more complex models of CO₂ emissions and cost of accidents on the optimal toll for car use and upon resulting welfare levels. The approach adopted is to use a single link model with a technical approach to the representation of the speed-flow relationship as this reflects common modelling practice. It is shown that using a more complex model of CO₂ emitted increases the optimal toll significantly compared to using a fixed cost approach while reducing CO₂ emitted only marginally. A number of accident models are used and the impact on tolls is shown to depend upon the assumptions made. Where speed effects are included in the accident model, accident costs can increase compared to the no toll equilibrium and so tolls should in this case be reduced compared to the congestion optimal toll. Finally it is shown that the effect of adding variable CO₂ emission models along with a fixed cost per vehicle-km for accidents can increase the optimal toll by 44% while increasing the true welfare gained by only 8%. The results clearly demonstrate that model assumptions for externalities can have a significant impact on the resulting policies and in the case of accidents the policies can be reversed.

Employment suburbanisation, reverse commuting and travel behaviour by residents of the central city in the Paris metropolitan area

This paper analyses the relationship between employment suburbanisation in the Paris metropolitan area, the growth of reverse commuting and changes in the weekday travel behaviour of working residents of the central city over a 20-year period. The results show that the number of reverse commuters has significantly increased because the municipality of Paris has lost many jobs but few working residents whilst employment has developed in the suburbs. Reverse commuters are mainly and increasingly high-income professionals whose workplace is located close to the central city in employment sub-centres that are well served by public transport. Consequently reverse commuters have lower than average car use although differences exist and are related to their professional status. The policy implications of these findings are discussed in the conclusion.     

A quantum evolutionary algorithm for the second-best congestion pricing problem in urban traffic networks

This paper investigates the congestion pricing problem in urban traffic networks. A first-best strategy, a second-best strategy for toll leveling in closed cordons and a second-best strategy for determining both toll levels and toll points are considered. The problem is known to be a mixed integer programming model and formulated as a bi-level optimization problem, with an objective of maximizing the social welfare. A method is presented to solve the problem, based on a novel metaheuristic algorithm, namely quantum evolutionary algorithm (QEA). To verify the proposed method, the widely used genetic algorithm (GA) is also applied to solve the problem. The problem is solved for a medium-size urban traffic network and the results of the QEA are compared against the conventional GA. Computational results show that the QEA outperforms the GA in solution quality.     

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.