First-best Tolls Research Articles

A theoretic analysis of expressed toll lane pricing policy targeting for a guaranteed level of service

This study compares the first-best toll algorithm that is theoretically appealing with the density-based toll algorithm that is more popular in practice. The comparison shows that both toll schemes can serve as a travel demand management strategy. Although the first-best scheme always leads to minimal total travel time, it is not necessarily attractive from toll operators' perspective. The density-based scheme is (1) more reliable for ensuring the federally mandated minimal level of services when the demand is high, (2) simpler for data collection and implementation, and (3) can generate higher revenues. From the users' perspective, the first-best scheme leads to less total costs in many cases, but the density-based scheme could also lead to less total costs under certain conditions. Traffic patterns could converge in both cases under a day-to-day framework. The speed of convergence for traffic dynamics is faster under the density-based scheme in most cases.

Integrated pricing framework for optimal power and semi‐dynamic traffic flow problem

Large-scale fast charging of electric vehicles inextricably entwines the operation of power and transportation systems. This study examines the integrated pricing of electricity and roads to maximise the social welfare associated with the coupled systems, i.e. minimising the total travel time and energy generation costs. While electric demand and transportation network conditions vary significantly over the day, most of the work, however, considers only static network flows for a single time period. This study proposes a multi-period integrated pricing model that can describe the variations of electricity and travel demands. Specifically, the distribution of traffic flows is characterised by a semi-dynamic traffic assignment model to consider flow propagation between adjacent time periods. To determine the optimal prices of electricity and road tolls, a marginal-cost pricing scheme based on the first-best tolls and locational marginal prices is developed. Mathematically, the multi-period pricing model is formulated as a convex optimisation problem. Moreover, a decentralised collaborative pricing framework is developed for independent power and transportation system operators to attain the optimal pricing strategies. Numerical experiments are conducted to demonstrate the effectiveness of the pricing method.

Partial peak-load pricing of a transportation bottleneck with homogeneous and heterogeneous values of time

The first-best solution for a transportation bottleneck is to impose a first-best peak-load toll that varies continuously over time, reaching its maximum value at the most desirable crossing time. This eliminates all wasteful queueing. With homogeneous values of time, the private costs of consumers are unchanged, but the large maximum value of the first-best toll may make it politically infeasible. In this paper, I consider continuously time-varying partial peak-load tolls that have a much lower maximum value, but which still achieve a large fraction of the efficiency gain of the first-best toll. With heterogeneous values of time, a partial peak-load toll can leave all consumers with unchanged or decreased private costs even when the first-best toll does not do this.

Robust network pricing and system optimization under combined long-term stochasticity and elasticity of travel demand

Network pricing serves as an instrument for congestion management, however, agencies and planners often encounter problems of estimating appropriate toll prices. Tolls are commonly estimated for a single-point deterministic travel demand, which may lead to imperfect policy decisions due to inherent uncertainties in future travel demand. Previous research has addressed the issue of demand uncertainty in the pricing context, but the elastic nature of demand along with its uncertainty has not been explicitly considered. Similarly, interactions between elasticity and uncertainty of demand have not been characterized. This study addresses these gaps and proposes a framework to estimate nearest optimal first-best tolls under long-term stochasticity in elastic demand. We show first that the optimal tolls under the deterministic-elastic and stochastic-elastic demand cases coincide when cost and demand functions are linear, and the set of equilibrium paths is constant. These assumptions are restrictive, so three larger networks are considered numerically, and the subsequent pricing decisions are assessed. The results of the numerical experiments suggest that in many cases, optimal pricing decisions under the combined stochastic-elastic demand scenario resemble those when demand is known exactly. The applications in this study thus suggest that inclusion of demand elasticity offsets the need of considering future demand uncertainties for first-best congestion pricing frameworks.

An ordinary differential equation formulation of the bottleneck model with user heterogeneity

Considering heterogeneous values of time and schedule delay early, in this paper we develop an ordinary differential equation formulation of the bottleneck model without allowance of arriving late. We show that in no-toll equilibrium, the generalized travel cost increases with departure time as the ratio of value of schedule delay to value of time increases with these two values, and commuters with higher values would experience higher generalized costs. We then derive the first-best toll and analyses its efficiency and distributional impacts. We obtain the sufficient Pareto-improving condition for the first-best scheme without imposing specific functional forms on heterogeneity. It is a Pareto improvement when the gap between values of time and schedule delay early increases as the ratio of value of schedule delay early to value of time increases. The proposed approach is applied to deal with such user heterogeneity that both the values of time and schedule delay early follow uniform distributions. In this case, the Pareto-improving condition is not only sufficient but also necessary. The individual gain from tolling is strictly monotonically increasing with respect to values of time and schedule delay early. Outside this condition, the first-best toll scheme makes users with relatively higher values of time and schedule delay early better off and those with relatively lower values worse off. And, users with higher values of time and schedule delay early could gain more or lose less from tolling. In contrasts with previous literature, our approach is robust in the sense that it can deal with not only discrete but also continuous user heterogeneity.

Cordon tolling in a city with congested bridges

This paper analyzes cordon tolling using a simple model where space is discrete rather than continuous, with commuting costs incurred only on two congested bridges. The first-best regime requires tolls on both bridges, whereas only the inner bridge is tolled under the cordon-toll regime. While less realistic than the continuous-space frameworks used in previous work, this simple setup allows the derivation of a number of analytical results, which were mostly unavailable to authors relying on more-complex models. The paper derives the rule for the optimal cordon toll, showing that it points to a toll level higher than first-best toll on the same bridge. In addition, the analysis shows that cordon tolling leads to a redistribution of population away from the zone immediately outside the cordon, with residents moving to the central zone or to the suburbs. The analysis also shows that the cordon toll raises more revenue than is necessary to pay for the bridge where it is levied, while also tending to increase the capacity of the untolled suburban bridge.

Finding second-best toll locations and levels by relaxing the set of first-best feasible toll vectors

This paper provides a framework for optimizing toll locations and levels in congestion pricing schemes for large urban road networks, with the objective to maximize the social surplus. This optimization problem is referred to as the toll location and level setting problem (TLLP) and is both non-convex, non-smooth and involves binary decision variables, and is therefore considered as a hard problem to solve. In this paper a solution approach is provided which instead of directly solving the TLLP, makes use of the first-best toll level solution, in which no restrictions are imposed on toll locations or levels. A first-best pricing scheme can be obtained by solving a convex program, and it has previously been shown that for the used routes in the network, the first-best toll levels on a route level are unique. By formulating an optimization problem, which instead of maximizing the social surplus, tries to find the link toll levels which minimize the deviation from first-best route tolls, a mixed integer linear program is obtained, and if the toll locations are predetermined the resulting optimization problem is a linear program. The approach of minimizing the deviation from first--best route tolls is applied for two different network models, and results are provided to show the applicability of the approach, as well as to compare with other approaches. Also, it is shown that for the Stockholm network, virtually the first-best level of social surplus can be obtained with a significantly reduced number of located tolls.

Coarse Tolling with Heterogeneous Preferences

This paper considers coarse tolling of congestion under heterogeneous preferences, and especially the distributional effects of such tolls. With coarse tolling, the toll equals a fixed value during the centre of the peak; outside this period, it is zero. This paper investigates three dimensions of heterogeneity. With the first, all values of time and schedule delay vary in fixed proportions, and this heterogeneity may stem from income differences. The second has differences in flexibility of users when to arrive. The third captures differences in willingness to arrive before or after the preferred arrival time. The paper uses three models of coarse tolling: the Laih, ADL, and Braking model. All three dimensions affect the welfare gain of coarse tolling. In the Laih model, the generalised price with coarse tolling is in between the no-toll and first-best one. In the other models this is not so, and distributional effects may be non-monotonic and very different from the first-best toll's effects. In the Braking model, the capacity goes unused for some time during the tolled period. Compared with in the Laih model, this raises total cost, and it is most harmful for users with low values and difficulty to arrive late: e.g. low-income users with a strict work start time or a trip to the doctor.

Reliability-Based Marginal Cost Pricing Problem Case with Both Demand Uncertainty and Travelers’ Perception Errors

Focusing on the first-best marginal cost pricing (MCP) in a stochastic network with both travel demand uncertainty and stochastic perception errors within the travelers’ route choice decision processes, this paper develops a perceived risk-based stochastic network marginal cost pricing (PRSN-MCP) model. Numerical examples based on an integrated method combining the moment analysis approach, the fitting distribution method, and the reliability measures are also provided to demonstrate the importance and properties of the proposed model. The main finding is that ignoring the effect of travel time reliability and travelers’ perception errors may significantly reduce the performance of the first-best MCP tolls, especially under high travelers’ confidence and network congestion levels. The analysis result could also enhance our understanding of (1) the effect of stochastic perception error (SPE) on the perceived travel time distribution and the components of road toll; (2) the effect of road toll on the actual travel time distribution and its reliability measures; (3) the effect of road toll on the total network travel time distribution and its statistics; and (4) the effect of travel demand level and the value of reliability (VoR) level on the components of road toll.

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.

Serviceability Based Park and Ride Choice Behaviors Influenced by Road Toll Policy for Metropolitan Commuting Corridors

Existing park and ride (P&R) facilities may enhance the serviceability of the transportation systems by redistributing travelers from vehicles mode to mass transit. As a tool in transportation demand management, road tolling policy will have an influence on the transportation system with P&R facilities. In this paper, impact of various road tolling policies on modal choice behaviors within context of commuting corridors with P&R services are investigated from the perspective of serviceability. The related road tolling schemes contains first-best toll, distance-based toll and cordon-based toll. The probability of commuters’ modal-choice is estimated using a stochastic equilibrium model. Innovatively, the serviceability concept is adopted to evaluate performances of different travel modes. Model results illustrate how transportation system performance is influenced by the different types of road tolling policies. Some of the results are concordant with empirical findings in the literature.

Optimal regulation on building size and city boundary: An effective second-best remedy for traffic congestion externality

This paper numerically evaluates the efficiency of regulations on building size and city size in a congested closed city by comparing welfare gain with that achieved under a first-best toll regime. Results show that whereas the urban growth boundary (UGB) is a poor substitute for the toll regime as expected, an optimal regulation on building size in the presence of a suitably chosen UGB yields significant welfare gain, producing an effective substitute for a first-best toll regime. Moreover, the optimal regulation on the building size requires not only downward adjustment to the market population density at the boundary locations but also upward adjustment at the central locations.

Step Tolling with Price Sensitive Demand: Why More Steps in the Toll Makes 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 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 price. This seems an empirically questionable assumption that, as this paper finds, strongly affects the implications of step tolling for the consumer. First-best tolling has no effect on the generalized price, and thus leaves the consumer equally well off as without tolling. Conversely, under price-sensitive demand, step tolling increases the price and lowers the number of users, making consumers worse off. The more steps the step toll has, the closer it approximates the first-best toll, thereby increasing the welfare gain and making consumers better off. This makes it important for real-world tolls to have as many steps as possible: this not only raises welfare, but also increases the political acceptability of the scheme by making consumers better off.

Optimal Pricing of Flights and Passengers at Congested Airports: The Efficiency of Atomistic Charges

This paper investigates optimal airport pricing when airlines provide imperfect substitutes products, and make decisions on capacity, scheduling and pricing. We show that the first-best toll per flight may be higher than the simple market-shares formula that were recently derived for Cournot models, and approaches the atomistic toll (which ignores the airlines' internalization of self-imposed congestion) as products become closer substitutes. This increases the relevance of congestion pricing and does not require leadership behavior. We also find that an airport requires two pricing instruments to achieve the first-best outcome: per-passenger subsidies to counteract airlines' market power, and per-flight tolls to correct congestion externalities. We numerically analyze second-best policies of having only one tax instrument, as well as the performance of atomistic pricing, and find that the latter may offer a more attractive alternative than what is suggested by simpler Cournot models.

Congestion pricing under operational, supply-side uncertainty

This paper is concerned with finding first-best tolls in static transportation networks with day-to-day variation in network capacity, as accounted for by changes in the volume-delay function. The key question in addressing this problem is that of information, namely, which agents have access to what information when making decisions. In this work, travelers are assumed to be either fully informed about network conditions before embarking on travel, or having no information except the probability distributions; likewise, the network manager (toll-setter) is either able to vary tolls in response to realized network conditions, or must apply the same tolls every day. Further, travelers’ preference for reliable travel is accounted for, representing risk aversion in the face of uncertainty. For each of the scenarios implied by combinations of these assumptions, we present methods to determine system-optimal link prices. A demonstration is provided, using the Sioux Falls test network, suggesting that attempts to incorporate uncertainty into nonresponsive tolls involve significantly higher prices.

Urban growth boundaries: An effective second-best remedy for unpriced traffic congestion?

This paper evaluates the efficacy of the urban growth boundary (UGB) as a second-best substitute for a first-best toll regime in a congested city. Numerical results show that, while a UGB is welfare-improving, validating previous theoretical results, the utility gain it generates is a very small fraction of that achieved under a toll regime. Thus, the paper suggests that a UGB may not be a useful instrument for attacking the distortions caused by unpriced traffic congestion.

Economic efficiency of second-best congestion pricing schemes in urban highway systems

This paper 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 paper uses economic theory of the second best and a simulation model to compare first-best, second-best and no-toll solutions for a model with two routes and two time periods (peak and pre-peak). The main findings from the simulation results are: (1) the second-best scheme is effective but less efficient than the first-best scheme in reallocating traffic volumes; (2) the second-best tolls are appreciably smaller than the first-best tolls; (3) the welfare gains from the second-best policy are much smaller than the welfare gains that are possible with a complete set of first-best tolls. It is also shown that the nature of the simulation results is not sensitive to reasonable cost and demand parameters.