Pareto-improving toll and subsidy scheme on transportation networks

This paper presents an original study on the economics of a link-based Toll and Subsidy Scheme (TSS) on a general transportation network. Different from a traditional congestion pricing scheme, the combination of toll and subsidy is found to be able to serve more planning purposes simultaneously, such as efficiency, fairness, and public acceptance. We first demonstrate that on a one-origin or one-destination network, a pareto-improving, system-optimal and revenue-neutral TSS always exists and can be obtained by solving a set of linear equations. Recognizing that such a scheme may not always exist for a multi-origin network, we then define the maximum-revenue problem with pareto-improving constrains to find the maximum possible revenue collected by the toll and subsidy scheme with optimal arc flows and non-increasing origin-destination travel costs. We discover that the problem is actually the dual problem of a balanced transportation problem, which can thus be solved efficiently by existing algorithms. At the end of the paper, a numerical example with a small synthetic network is provided for the comparison of toll and subsidy scheme with other existing toll schemes in terms of OD travel disutilities

OPTIMAL CONGESTION CHARGES IN GENERAL EQUILIBRIUM

This paper deals with pricing and investment decision problems of multi-route and multi-period highway systems in which the congestion is a significant factor in the assessment of system costs. This study approaches this congestion pricing scheme with two different social welfare maximization problems, both of which search for the optimal solutions through general equilibrium analysis. These two optimization problems have an identical structure except financial constraints that reflect different decision environments. One welfare maximization problem involves estimating the first-best social optimal solution. This problem yields the optimal solution for the implementation scheme to impose the differentiated congestion charge for each trip alternative in terms of travel route and trip period. The optimal congestion charge for this problem has the expression similar to that derived in previous studies dealing with congestion pricing. Another maximization problem involves characterizing the second-best optimal solution. In this problem, it is assumed to impose the congestion toll only on a single highway link. This problem yields the second-best congestion toll different from the first-best one. This second-best optimal congestion toll has the structure to reflect its impact on other highway links exempt from the congestion charge program. Document type: Articl

Road Pricing for Congestion Management and Infrastructure Financing

Road pricing has two distinct objectives, to alleviate the congestion problem, and to generate revenue for transportation infrastructure financing. Accordingly, road pricing studies can be roughly classified into two branches with overlapping, one on congestion pricing and the other on toll roads. This dissertation contributes to both branches of road pricing studies. Three topics are discussed. The first two are related with congestion pricing and the third one is related with infrastructure financing. The first topic is that we study the optimal single-step coarse toll design problem for the bottleneck model where the toll level and toll window length have maximum acceptable upper bounds and the unconstrained optimal solution exceeds the upper bounds. We consider proportional user heterogeneity where users’ values of time and schedule delay vary in fixed proportions. Three classic coarse tolling models are studied, the ADL, Laih and braking models. In the ADL model, toll non-payers form a mass arrival at the bottleneck following the last toll payer. In the Laih model, there is a separated waiting facility for toll non-payers to wait until the toll ends. In the braking model, toll non-payers can choose to defer their arrival at the bottleneck to avoid paying the toll. We find that, in the ADL and the Laih models, the optimal solution chooses the maximum acceptable toll level and toll window length. The ADL model further requires the tolling period to be started as late as possible to eliminate the queue at the toll ending moment. In the braking model, if the upper bound of the toll window length is too small, no toll should be charged. Otherwise the optimal solution chooses the maximum acceptable toll window length and may choose a toll price less than the maximum acceptable level. The second topic is that we develop a new coarse tolling model to address the coarse tolling problem during morning peak hour. An “overtaking model” is proposed by considering that toll payers could overtake those braking commuters (toll non-payers) to pay toll to pass the bottleneck. This would allow commuters to brake and in the meanwhile can make the bottleneck fully utilized during the tolling period, i.e., eliminate the somewhat unrealistic unused tolling period in the braking model. The overtaking model systematically combines the Laih model and the braking model together, capturing both of their properties. Specifically, the overtaking model reduces to the Laih model when the unit overtaking cost approaches zero, and reduces to the braking model when the unit overtaking cost is too high. An unconstrained optimal tolling scheme is developed, and we find out that, unlike the ADL and the Laih models, in the overtaking model, the tolling scheme causing capacity waste could be better than tolling scheme without capacity waste. It is found that, the optimal tolling scheme is affected by the unit overtaking cost. One critical unit overtaking cost is defined. For a small unit overtaking cost, the optimal tolling scheme is similar to that of the Laih model, i.e., featured by no queue exists at the toll starting and ending moments and no capacity waste exists; for a large unit overtaking cost, the optimal tolling scheme is to set the toll high enough to prevent users from overtaking and thereby make the model reduce to the braking model. In the latter case, although the unused tolling period (as in the braking model) can be fully utilized through lowering the toll to make commuters overtake, the system cost will be increased by doing so. The third topic is that we investigate the profit maximizing behavior of a private firm which operates a toll road competing against a free alternative in presence of cars and trucks. Trucks differ from cars in value of time (VOT), congestion externality, pavement damage, and link travel time function. We consider mixed travel behaviors of cars and trucks in that trucks choose routes deterministically, while cars follow stochastic user equilibrium in route choice. We derive the equilibrium flow pattern under any combination of car-toll and truck-toll, and identify an integrated equilibrium range within which each road is used by both cars and trucks. We find that, depending on the per-truck pavement damage cost, the firm may take a car-strategy, a truck-strategy, or a car-truck mixed strategy. The perception error of car users, the VOTs and traffic demands of cars and trucks are critical in shaping the firm’s strategy

Optimising Differentiated Tolls on Large Scale Networks, by using an Intellegent Search Algorithm

The design of an optimal road pricing scheme is not a trivial problem. Following the Dutch government’s kilometre charge plans, this paper focuses on the optimisation of link based toll levels differentiated in space and time. The optimal toll level design problem is formulated as a bi-level mathematical program. In the upper level we minimise an object function, e.g. the average travel time in the network, using a fixed number of price categories. At the lower level a dynamic traffic assignment model is used to determine the effects of differentiated road pricing schemes on the traffic system. Focus of the paper is on the upper-level where optimal toll levels are approximated. In the optimisation procedure different variants of a pattern search algorithm are tested in a case study. Inspection of the solution space shows that many local minima exist, so the selection of the initial solution becomes important. In the case study however it appears that in all local minima the value of the objective function is almost the same, indicating the fact that many different toll schemes result in the same average travel time. The case study is also used to test the performance of the different variants of the pattern search algorithm. It appears that it is beneficial to change more variables at a time and to use a memory to remember where improvement of the objective function has been made. First tests on a medium scale network showed that it is possible to apply the framework on this network, though further computational improvements are needed to apply the framework to large scale networks, for example by parallel processing

Credit-based Pricing for Multi-user Class Transportation Facilities

This paper proposes an innovative arc-based credit (ABC) congestion pricing scheme to improve the system performance in a transportation network. By associating each arc with apositive or negative credit rate, the strategy can accomplish multiple planning goals, such as efficiency, fairness, and public acceptance simultaneously. We first demonstrate that on a one-origin or one-destination network, a pareto-improving, system-optimal and revenue-neutral credit scheme always exists and can be obtained by solving a set of linear equations. Recognizing that such a credit scheme may not exist in a multi-origin network, we then define the maximum-revenue problem with pareto-improving constrains (MRPI): find the maximum possible revenue collected by the credit scheme with optimal arc flows and non-increasing origin-destination (OD) travel costs. We discover that the dual of MRPI is equivalent to a typical Transportation Problem which, therefore, provides a simple way to calculate the revenue by just examining the dual problem. At the end of the paper, a numerical example with a small synthetic network is provided for the comparison of the credit scheme with other existing toll schemes in terms of OD travel disutilities

Multi-concentric optimal charging cordon design

The performance of a road pricing scheme varies greatly by its actual design and implementation. The design of the scheme is also normally constrained by several practicality requirements. One of the practicality requirements which is tackled in this paper is the topology of the charging scheme. The cordon shape of the pricing scheme is preferred due to its user-friendliness (i.e. the scheme can be understood easily). This has been the design concept for several real world cases (e.g. the schemes in London, Singapore, and Norway). The paper develops a methodology for defining an optimal location of a multi-concentric charging cordons scheme using Genetic Algorithm (GA). The branch-tree structure is developed to represent a valid charging cordon scheme which can be coded using two strings of node numbers and number of descend nodes. This branch-tree structure for a single cordon is then extended to the case with multi-concentric charging cordons. GA is then used to evolve the design of a multi-concentric charging cordons scheme encapsulated in the twostring chromosome. The algorithm developed, called GA-AS, is then tested with the network of the Edinburgh city in UK. The results suggest substantial improvements of the benefit from the optimised charging cordon schemes as compared to the judgemental ones which illustrate the potential of this algorithm

Bounding the efficiency of road pricing

This paper deals with the following question associated with congestion pricing in a general network with either fixed or elastic travel demand: what is the maximum efficiency loss of a general second-best pricing scheme due to inexact marginal-cost pricing in comparison with the first-best pricing or system optimum case? A formal answer to this question is provided by establishing an inefficiency bound associated with a given road pricing scheme. An application of the methods is provided for the practical trial-and-error implementation of marginal-cost pricing with unknown demand functions

A Comparative Evaluation Of Fdsa,ga, And Sa Non-linear Programming Algorithms And Development Of System-optimal Methodology For Dynamic Pricing On I-95 Express

As urban population across the globe increases, the demand for adequate transportation grows. Several strategies have been suggested as a solution to the congestion which results from this high demand outpacing the existing supply of transportation facilities. High –Occupancy Toll (HOT) lanes have become increasingly more popular as a feature on today’s highway system. The I-95 Express HOT lane in Miami Florida, which is currently being expanded from a single Phase (Phase I) into two Phases, is one such HOT facility. With the growing abundance of such facilities comes the need for indepth study of demand patterns and development of an appropriate pricing scheme which reduces congestion. This research develops a method for dynamic pricing on the I-95 HOT facility such as to minimize total travel time and reduce congestion. We apply non-linear programming (NLP) techniques and the finite difference stochastic approximation (FDSA), genetic algorithm (GA) and simulated annealing (SA) stochastic algorithms to formulate and solve the problem within a cell transmission framework. The solution produced is the optimal flow and optimal toll required to minimize total travel time and thus is the system-optimal solution. We perform a comparative evaluation of FDSA, GA and SA non-linear programming algorithms used to solve the NLP and the ANOVA results show that there are differences in the performance of the NLP algorithms in solving this problem and reducing travel time. We then conclude by demonstrating that econometric iv forecasting methods utilizing vector autoregressive (VAR) techniques can be applied to successfully forecast demand for Phase 2 of the 95 Express which is planned for 201