Second-best Congestion Pricing Research Articles

Code and Data Repository for Penalty Decomposition Methods for Second-Best Congestion Pricing Problems on Large-Scale Networks

he second-best congestion pricing (SBCP) problem is one of the most challenging problems in transportation due to its two-level hierarchical structure. In spite of various intriguing attempts for solving SBCP, existing solution methods are either heuristic without convergence guarantee or suitable for solving SBCP on small networks only. In this paper, we first reveal some convexity-based structural properties of the marginal value function reformation of SBCP and then, by effectively exploiting these structural properties, we propose two dedicated decomposition methods for solving SBCP on large-scale networks which are different from existing methods in that they avoid linearizing nonconvex functions. We establish the convergence of the two decomposition methods under commonly used conditions and provide the maximum number of iterations for deriving an approximate stationary solution. The computational experiments based on a collection of real road networks show that in comparison with three existing popular methods, the two proposed methods are capable of solving SBCP on larger-scale networks; and for instances that can be solved by existing methods, the two proposed methods are substantially faster.

Contextual Bayesian optimization of congestion pricing with day-to-day dynamics

Congestion pricing is a common approach to alleviate urban traffic congestion. The design of second-best congestion pricing schemes is typically formulated as non-linear programming and bi-level optimization problems, where the lower-level problem involves either a static or dynamic network equilibrium model. The complexity of these bi-level toll optimization problems increases considerably when incorporating day-to-day dynamic models of travel behavior and dynamic models of network congestion. These models are often operationalized using simulation, and consequently, the toll design problem is a computationally challenging simulation-based optimization problem where the evaluation of a single candidate pricing scheme involves simulating the day-to-day model until convergence. In order to circumvent this issue, we propose a contextual Bayesian optimization (BO) framework, where the BO scheme is embedded within the day-to-day dynamic model by using temporal contextual information. The framework implicitly incorporates the relationship between the objective function across days and uses past days’ observations (function evaluations) as weak priors when constructing the Gaussian process underlying the BO algorithm for the current day’s toll optimization problem, resulting in gains in computational efficiency.The contextual BO approach is applied to the design of distance-based pricing schemes for the morning commute problem. We demonstrate numerically that the scheme converges to the system optimum, and moreover, utilizes a significantly smaller number of simulation evaluations (ten-fold reduction) than the standard approach wherein each function evaluation involves simulating the day-to-day model until convergence. From a policy perspective, we find that the distance-based schemes yield significant welfare gains relative to area-based schemes and show that the design of the distance-based tariff scheme can significantly affect distributional impacts. A suitably designed two-part tariff structure can partially offset the relatively large welfare losses of travelers with longer commute distances while maintaining overall welfare. The proposed contextual BO scheme is also extended to incorporate context specific demand and supply information, which can be of value to policy-makers when evaluating optimal toll design schemes under a wide range of scenarios in a computational tractable manner.

Second-best urban tolls in a monocentric city with housing market regulations

This paper investigates second-best congestion pricing in a monocentric city characterized by distortionary regulations in the housing market (building height restrictions, no-development areas and property taxation). We demonstrate that the welfare gain of a Pigouvian tax may first fall and then increase as building height restrictions become more stringent. For example, a Pigouvian toll imposed in a city without restrictions may produce up to 40% larger welfare gains than Pigouvian tolling in a city with a mild, uniform in space, floor-to-area ratio restriction. In the presence of a tax-induced distortion, deviations of the Pigouvian toll can lead to non-negligible welfare gains. We discuss the important policy implications of the above findings.

Preference heterogeneity and congestion pricing: The two route case revisited

This paper studies first-best and second-best congestion pricing in the presence of unobserved and observed preference heterogeneity using a stylised stochastic user equilibrium choice model. Travellers choose between multiple alternatives, have heterogeneous values of travel times, and may differ in their valuation of variety. We derive first-best and second-best tolls taking into account how the overall network demand responds to expected generalized prices, including tolls. For second-best pricing, we show that with homogeneous values of times the welfare losses of second-best pricing are smaller when route choice is probabilistic than when route choice is deterministic. Furthermore, we find that with heterogeneous values of times and benefits of variety, uniform second-best tolls and group-differentiated tolls can be very close, implying potentially low welfare losses from the inability to differentiate tolls. Finally, we show that there are cases where all groups benefit from second-best congestion pricing, but that these cases are likely to be politically unacceptable because tolls are then higher for low income groups.

Impact of congestion pricing schemes on emissions and temporal shift of freight transport

This paper examines the freight transport temporal shift and the vehicular pollutants emissions in an urban transport network with congestion pricing schemes, specifically when only freight transportation is tolled in the peak period. The equivalent minimization models of no-toll, first-best, and second-best congestion pricing scenarios are presented with an excess-demand approach based on user equilibrium analysis, in which the different pricing schemes include multiple time periods and mixed traffic. We established results for the equivalent conditions and the uniqueness conditions of the models. The findings and policy insights are discussed using simulation and sensitivity analysis of the key parameters.

Reducing traffic externalities by multiple-cordon pricing

The second-best congestion pricing schemes including common optimum, one cordon, and multiple cordons schemes are compared with the first-best optimum pricing scheme. A cross-subsidy effect exists in these second-best pricing models. However, the scheme with more cordons will diminish the cross-subsidy and approach an efficient and equitable outcome. The relative efficiency of a cordon pricing scheme for the case of Taipei metropolis is very high. One single cordon yields excellent performance of 93% relative efficiency. There might be some factors causing the good results: the uncongested traffic condition, the linear unit distance cost in traffic flow forming a nonlinear cost function, and the trip demands with continuous space and the same destination (the central business district) in the network.

On revenue recycling and the welfare effects of second-best congestion pricing in a monocentric city

This paper examines congestion taxes in a monocentric city with pre-existing labor taxation. When road toll revenue is used to finance labor tax cuts, 35% of the optimal road tax in our numerical model does not reflect marginal external congestion costs, but rather functions as a Ramsey–Mirrlees tax, i.e. an efficiency enhancing mechanism allowing for an indirect spatial differentiation of the labor tax. This adds a quite different motivation to road pricing, since welfare gains can be produced even in absence of congestion. We find that the optimal road tax is non-monotonic across space, reflecting the different impacts of labor supply elasticity and marginal utility of income, which both vary over space. The relative efficiencies of some archetype second-best pricing schemes (cordon toll, flat kilometer tax) are high (84% and 70% respectively). When road toll revenue is recycled lump-sum, the optimal toll lies below its Pigouvian level. Extensions in a bimodal framework show that the optimality of using road toll revenue to subsidize public transport depends on the initial inefficiency in public transport pricing.

Tolled multi-class traffic equilibria and toll sensitivities

We review properties of tolled equilibria in road networks, with users differing in their time values, and study corresponding sensitivities of equilibrium link flows w.r.t. tolls. Possible applications include modeling of individual travellers that have different trip purposes (e.g. work, business, leisure, etc.) and therefore perceive the relation between travel time and monetary cost in dissimilar ways. The typical objective is to reduce the total value of travel time (TVT) over all users. For first best congestion pricing, where all links in the network can be tolled, the solution can be internalized through marginal social cost (MSC) pricing. The MSC equilibrium typically has to be implemented through fixed tolls. The MSC as well as the fixed-toll equilibrium problems can be stated as optimization problems, which in general are convex in the fixed-toll case and non-convex in the MSC case. Thus, there may be several MSC equilibria. Second-best congestion pricing, where one only tolls a subset of the links, is much more complex, and equilibrium flows, times and TVT are not in general differentiable w.r.t. tolls in sub-routes used by several classes. For generic tolls, where the sets of shortest paths are stable, we show how to compute Jacobians (w.r.t positive tolls) of link flows and times as well as of the TVT. This can be used in descent schemes to find tolls that minimize the TVT at least locally. We further show that a condition of independent equilibrium cycles, together with a natural extension of the single class regularity condition of strict complementarity, leads to genericity, and hence existence of said Jacobians.

Probabilistic Choice and Congestion Pricing with Heterogeneous Travellers and Price-Sensitive Demand

This paper deals with first-best and second-best congestion pricing of a stylised two-link network with probabilistic route choice of travellers. Travellers may have heterogeneous values of travel times and may differ in their idiosyncratic route preferences. We derive first-best and second-best tolls taking into account how the overall network demand responds to generalized costs including the tolls that are levied. We show that with homogeneous values of times the welfare losses of second-best pricing, of one link only, may be smaller if route choice is probabilistic. Furthermore, we show that with heterogeneous values of times, common second-best tolls and group-differentiated tolls can be very close when route choice is governed by random utility maximisation, leading to low welfare losses from the inability to differentiate tolls.

Traffic reallocation impacts and automobile toxic pollutants emission for a general network in urban highway system: a second-best congestion pricing analysis

This paper examines temporal, spatial and modal effects of second-best congestion pricing schemes in traffic volume reallocation, traffic mode shifting and automobiles toxic pollutants emission control in urban road systems. A problem in two time periods (peak and off-peak) and two travel modes (private car and bus) on one-way network is analysed, and a second-best congestion pricing model with multiple time periods and travel modes is constructed using an excess-demand approach. The paper provides a thorough empirical study of second-best scenario and two extreme regimes: no-toll problem and first-best problem. The main findings are: congestion pricing policies have major impacts: 1) diversion of tolled route to the free route; 2) shift of peak period traffic to the off-peak period; 3) shift of traffic volume by private car to bus; 4) reduction in total traffic volume and increase in total passenger volume (private car and bus); 5) reduction in the total emission amount of automobiles’ toxic pollutants.

On Revenue Recycling and the Welfare Effects of Second-Best Congestion Pricing in a Monocentric City

This paper explores the interactions between congestion pricing and a tax-distorted labor market within a monocentric urban equilibrium model. We compute the efficiency gains of various second-best policies, i.e. combinations of toll schemes and revenue recycling programs, with a predetermined level of public revenue. We find that 35% of the space-varying road tax does not reflect marginal external congestion costs, but rather functions as a Ramsey-Mirrlees tax, i.e. an efficiency enhancing mechanism allowing space differentiation of the labor tax. Such a space-varying tax adds a quite different motivation to road pricing, since it can produce large welfare gains even in the absence of congestion. We show that both a cordon toll and a flat kilometer tax achieve over 80% of these gains when combined with specific types of revenue recycling, such as labor tax cuts or public transport subsidies. Sensitivity analysis shows that the optimal type of revenue recycling depends on the level of inefficiency in the provision of public transport prior to the introduction of congestion pricing.

Second-best congestion pricing schemes in the monocentric city

This paper considers second-best congestion pricing in the monocentric city, with endogenous residential density and endogenous labour supply. A spatial general equilibrium model is developed that allows consideration of the three-way interactions between urban density, traffic congestion and labour supply. Congestion pricing schemes are analysed that are second-best ‘by design’ (and not because distortions exist elsewhere in the spatial economy), like cordon charging and flat kilometre charges. Both for Cobb–Douglas utility and for CES utility, the analyses suggest that the relative welfare losses from second-best pricing, compared to first-best pricing, are surprisingly small.

Second-Best Congestion Pricing Schemes in the Monocentric City

This paper considers second-best congestion pricing in the monocentric city, with endogenous residential density and endogenous labour supply. A spatial general equilibrium model is developed that allows consideration of the three-way interactions between urban density, traffic congestion and labour supply. Congestion pricing schemes are analyzed that are second-best 'by design' (and not because distortions exist elsewhere in the spatial economy), like cordon charging and flat kilometre charges. Both for Cobb-Douglas utility and for CES utility, the analyses suggest that the relative welfare losses from second-best pricing, compared to first-best pricing, are surprisingly small.

Second-Best Congestion Pricing in Urban Space: Cordon Pricing and Its Alternatives

This paper examines the effects of alternative congestion pricing systems, cordon pricing and congestion pricing for existing toll roads, using the network equilibrium model developed for the Osaka Metropolitan Area, Japan. Cordon pricing is more effective in reducing the total efficiency loss from traffic congestion, but produces relatively large amounts of toll revenue. On the other hand, pricing for existing toll roads keeps the loss in consumer surplus (and toll revenue) relatively low to attain the same level of efficiency gain as the cordon pricing.

Second-best congestion pricing in general static transportation networks with elastic demands

This paper studies the second-best problem where not all links of a congested transportation network can be tolled. The second-best tax rule for this problem is derived for general static networks, so that the solution presented is valid for any graph of the network and any set of tolling points available. A number of known second-best tax rules are shown to be special cases of the general solution presented. It is further demonstrated that, for instance by using the concept of ‘virtual links’, the same method can be applied to a broader class of second-best problems in static networks. Finally, a small network is used to demonstrate numerically that an interior second-best optimum need not always be unique, and need not always exist. However, both examples require extreme differences in marginal external costs across links, and a non-optimal toll-point to be used, which casts doubt on the practical relevance of this complication.

Second-best congestion pricing in general networks. Heuristic algorithms for finding second-best optimal toll levels and toll points

This paper considers the second-best problem where not all links of a congested transportation network can be tolled. This paper builds on earlier work, in which the second-best tax rule for this problem was derived for general static networks, so that the solution presented is valid for any graph of the network, and for any set of tolling points available on that network. An algorithm is presented for finding second-best tolls, based on this general solution. A simulation model is used for studying its performance for various archetype pricing schemes: a toll-cordon, area licences, parking policies in the city centre, pricing of a single major highway, and pay-lanes and `free-lanes' on major highways. Furthermore, an exploratory analysis is given of a method for selecting the optimal location of toll points when not all links can be tolled.

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.

Urban highway congestion: An economic analysis of second-best congestion pricing schemes : Liu, Nan, Ph.D University of Illinois at Chicago, 1995. 102 pp.

Urban highway congestion: An economic analysis of second-best congestion pricing schemes : Liu, Nan, Ph.D University of Illinois at Chicago, 1995. 102 pp.

Second-Best Congestion Pricing: The Case of an Untolled Alternative

This paper deals with second-best one-route congestion pricing in case of an untolled alternative. Using a two-link network simulation model, the effects of various demand and cost parameters on the relative efficiency of one-route tolling are analyzed. It is investigated whether the existence of costs of congestion charging may be a reason for one-route tolling to be more “overall efficient” than two-route tolling. Finally, the efficiency of revenue-maximizing one-route and two-route tolling is discussed.