Optimal distribution of financial incentives to foster off-hour deliveries in urban areas

The main objective of this paper is to develop mathematical formulations to gain insight into the best way to distribute financial incentives to receivers of urban deliveries to maximize participation in off-hour deliveries. The paper considers two different types of incentive budgets: exogenous, and endogenous. The exogenous case represents the condition in which an external decision maker determines the incentive budget that is to be distributed among potential participants in off-hour deliveries. In the case of an endogenous incentive budget, the entity distributing the incentives must raise the necessary funds using revenue generation mechanisms such as tolls and fines. The optimal incentives are obtained from the Karush–Kuhn–Tucker conditions of a mathematical program that maximizes the number of truck trips shifted to the off-hours as a function of the incentives. The mathematical models developed in this paper provide guidelines about how to optimally distribute financial incentives to foster off-hour deliveries.     

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.     

Marginal cost congestion pricing based on the network fundamental diagram

Congestion pricing schemes have been traditionally derived based on analytical representations of travel demand and traffic flows, such as in bottleneck models. A major limitation of these models, especially when applied to urban networks, is the inconsistency with traffic dynamics and related phenomena such as hysteresis and the capacity drop. In this study we propose a new method to derive time-varying tolling schemes using the concept of the Network Fundamental Diagram (NFD). The adopted method is based on marginal cost pricing, while it also enables to account realistically for the dynamics of large and heterogeneous traffic networks. We derive two alternative cordon tolls using network-aggregated traffic flow conditions: a step toll that neglects the spatial distribution of traffic by simply associating the marginal costs of any decrease in production within the NFD to the surplus of traffic; and a step toll that explicitly accounts for how network performance is also influenced by the spatial variance in a 3D-NFD. This pricing framework is implemented in the agent-based simulation model MATSim and applied to a case study of the city of Zurich. The tolling schemes are compared with a uniform toll, and they highlight how the inhomogeneous distribution of traffic may compromise the effectiveness of cordon tolls.     

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.     

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.     

Optimal distance- and time-dependent area-based pricing with the Network Fundamental Diagram

Given the efficiency and equity concerns of a cordon toll, this paper proposes a few alternative distance-dependent area-based pricing models for a large-scale dynamic traffic network. We use the Network Fundamental Diagram (NFD) to monitor the network traffic state over time and consider different trip lengths in the toll calculation. The first model is a distance toll that is linearly related to the distance traveled within the cordon. The second model is an improved joint distance and time toll (JDTT) whereby users are charged jointly in proportion to the distance traveled and time spent within the cordon. The third model is a further improved joint distance and delay toll (JDDT) which replaces the time toll in the JDTT with a delay toll component. To solve the optimal toll level problem, we develop a simulation-based optimization (SBO) framework. Specifically, we propose a simultaneous approach and a sequential approach, respectively, based on the proportional-integral (PI) feedback controller to iteratively adjust the JDTT and JDDT, and use a calibrated large-scale simulation-based dynamic traffic assignment (DTA) model of Melbourne, Australia to evaluate the network performance under different pricing scenarios. While the framework is developed for static pricing, we show that it can be easily extended to solve time-dependent pricing by using multiple PI controllers. Results show that although the distance toll keeps the network from entering the congested regime of the NFD, it naturally drives users into the shortest paths within the cordon resulting in an uneven distribution of congestion. This is reflected by a large clockwise hysteresis loop in the NFD. In contrast, both the JDTT and JDDT reduce the size of the hysteresis loop while achieving the same control objective. We further conduct multiple simulation runs with different random seed numbers to demonstrate the effectiveness of different pricing models against simulation stochasticity. However, we postulate that the feedback control is not applicable with guaranteed convergence if the periphery of the cordon area becomes highly congested or gridlocked.     

Differentiated congestion pricing of urban transportation networks with vehicle-tracking technologies

This paper explores a new type of congestion pricing that differentiates users with respect to their travel characteristics or attributes, and charges them different amounts of toll accordingly. The scheme can reduce the financial burden of travelers or lead to more substantial reduction of congestion. Given that the scheme requires tracking vehicles, an incentive program is designed to mitigate travelers’ privacy concerns and entice them to voluntarily disclose their location information.     

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.     

The impacts of time of day pricing on the behavior of freight carriers in a congested urban area: Implications to road pricing

This paper describes the key findings from a major research project aimed at assessing the impacts of the Port Authority of New York and New Jersey’s time of day pricing initiative on the behavior of commercial carriers. The paper, believed by the authors to be the first comprehensive study on the subject, highlights key implications for road pricing policy.One of the most interesting findings is that carriers respond to time of day pricing by implementing multi-dimensional responses involving Productivity increases, Cost transfers, and Change in facility usage. This implies a more nuanced response than suggested by micro-economic theory, which would only predict a change in facility usage. In fact, no carrier was found to have responded by implementing only changes in facility usage, which leads to the authors to believe that this is a last resort alternative.In terms of numerical importance, three combinations of strategy groups represent almost 90% of the cases: Productivity increases (42.79%), followed by Changes in facility usage and Cost transfers (27.60%) and Productivity increases and Changes in facility usage and Cost transfers (19.32%). The fact that some of these responses impact only the carrier (i.e., Productivity increases) while others mostly impact the receivers (Changes in facility usage and Cost transfers) lead the authors to believe that the nature of the response is determined by the balance of power between carriers and receivers. If carriers dominate the relationship, then it is likely that policies that mostly impact receivers are implemented; otherwise, the carriers have no choice but implementing strategies that help them cope with the impacts of pricing without impacting their customers, i.e., productivity increases. In this context, the authors’ conjecture is that carriers consider changes in facility usage to be a very disruptive alternative that forces them—and more importantly their customers—to alter their shipping/delivery patterns. It should be pointed out that, although carriers stand to benefit from working during the off-peak hours, they could only do so if their customers are willing to work during the off-peak hours.The data indicate that 36 carriers (20.2%) changed behavior because of the time of day pricing initiative. This number includes 17 carriers (9.0%) that reacted by increasing shipping charges to receivers, which illustrates the need to find out more about how receivers reacted to the time of day pricing initiative. If the carriers that only increased shipment charges are excluded, 15.3% of carriers changed behavior because of time of day pricing.     

Advanced pricing and rationing policies for large scale multimodal networks

The applying of simplified schemes, such as cordon pricing, as second-best solution to the toll network design problem is investigated here in the context of multiclass traffic assignment on multimodal networks. To this end a suitable equilibrium model has been developed, together with an efficient algorithm capable of simulating large scale networks in quite reasonable computer time. This model implements the theoretical framework proposed in a previous work on the toll optimization problem, where the validity of marginal cost pricing for the context at hand is stated. Application of the model to the real case of Rome shows us, not only that on multimodal networks a relevant share (up to 20%) of the maximum improvements in terms of social welfare achievable with marginal cost pricing can in fact be obtained through cordon pricing, but also that in practical terms rationing is a valid alternative to pricing, thus getting around some of the relevant questions (theoretical, technical, social) the latter raises. As a result we propose a practical method to analyze advanced pricing and rationing policies differentiated for user categories, which enables us to compare alternative operative solutions with an upper bound on social welfare based on a solid theoretical background.     

Distributional impacts of road pricing: The truth behind the myth

This paper shows that road pricing can be regressive, progressive or neutral, and refutes the generalised idea that road pricing is always regressive. The potential distributional impacts of a road pricing scheme are assessed in three English towns. It is found that impacts are town specific and depend on where people live, where people work and what mode of transport they use to go to work. Initial impacts may be progressive even before any compensation scheme for losers is taken into account. When the situation before the scheme is implemented is such that majority of drivers entering the area where the scheme would operate come from households with incomes above the average, it can be expected that, once the scheme is implemented, these drivers coming from rich households will continue to cross the cordon and will be prepared to pay the charge. In such a case the overall effect will be that on average, rich people will pay the toll and poor people will not.     

Toll pricing framework under logit‐based stochastic user equilibrium constraints

This paper addresses the toll pricing framework for the first‐best pricing with logit‐based stochastic user equilibrium (SUE) constraints. The first‐best pricing is usually known as marginal‐cost toll, which can be obtained by solving a traffic assignment problem based on the marginal cost functions. The marginal‐cost toll, however, has rarely been implemented in practice, because it requires every specific link on the network to be charged. Thus, it is necessary to search for a substitute of the marginal cost pricing scheme, which can reduce the toll locations but still minimize the total travel time. The toll pricing framework is the set of all the substitute toll patterns of the marginal cost pricing. Assuming the users' route choice behavior following the logit‐based SUE principle, this paper has first derived a mathematical expression for the toll pricing framework. Then, by proposing an origin‐based variational inequality model for the logit‐based SUE problem, another toll pricing framework is built, which avoids path enumeration/storage. Finally, the numerical test shows that many alternative pricing patterns can inherently reduce the charging locations and total toll collected, while achieving the same equilibrium link flow pattern. Copyright © 2013 John Wiley & Sons, Ltd.     

Introducing congestion pricing on a new toll road

This paper proposes a demonstration project to test the effectiveness of congestion pricing in an urban area. It reviews the general theoretical case for such pricing and summarizes recent international interest in congestion pricing. Next, it sets forth the reasons why demonstration projects are needed, both to add to our knowledge about how effective congestion pricing may prove to be, and to address political and other public-acceptance barriers to implementation of the concept. The paper then defines a specific proposed test site for congestion pricing: a new toll road being planned for Orange County, California. It is proposed that instead of charging flat-rate tolls, the transportation agency could charge peak and off-peak tolls, increasing the level of the peak charge each year over a period of up to 10 years unless or until toll revenues decline below the levels forecast under the flat-rate toll alternative. Measurements of traffic flow and ride-sharing behavior would be made, as well as calculations of emission-reduction effects. The paper concludes with a brief discussion of marketing and political considerations involved in conducting such a demonstration.Abbreviations ARB Air Resources Board - AVI Automatic Vehicle Identification - CDMG Corridor Design Management Group - HOV High-occupancy vehicle - SJHTC San Joaquin Hills Transportation Corridor - TCA Transportation Corridor Agency - VMT Vehicle miles traveled     

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.     

State-dependent congestion pricing with reference-dependent preferences

Demand and capacity fluctuations are common for roads and other congestible facilities. With ongoing advances in pricing technology and ways of communicating information to prospective users, state-dependent congestion pricing is becoming practical. But it is still rare or nonexistent in many potential applications. One explanation is that people dislike uncertainty about how much they will pay. To explore this idea, a model of reference-dependent preferences is developed based on Köszegi and Rabin (2006). Using a facility yields an “intrinsic” utility and a “gain-loss” utility measured relative to the probability distribution over states of utility outcomes. Two types of preferences are analyzed: bundled preferences in which gains and losses are perceived for overall utility, and unbundled preferences in which gains and losses are perceived separately for the toll and other determinants of utility.Tolls are chosen to maximize total expected utility plus revenues. With bundled preferences the toll is set above the Pigouvian level when usage conditions are good, and below it when conditions are bad, in order to reduce fluctuations in utility. With unbundled preferences the direction of toll adjustment is less clear and depends on whether supply or demand is variable. For both types of preferences tolls are sensitive to the strength of gain-loss utility. If gain-loss utility is moderately strong, a state-independent toll can be optimal.     

Traffic congestion pricing methodologies and technologies

This paper reviews the methods and technologies for congestion pricing of roads. Congestion tolls can be implemented at scales ranging from individual lanes on single links to national road networks. Tolls can be differentiated by time of day, road type and vehicle characteristics, and even set in real time according to current traffic conditions. Conventional toll booths have largely given way to electronic toll collection technologies. The main technology categories are roadside-only systems employing digital photography, tag & beacon systems that use short-range microwave technology, and in-vehicle-only systems based on either satellite or cellular network communications. The best technology choice depends on the application. The rate at which congestion pricing is implemented, and its ultimate scope, will depend on what technology is used and on what other functions and services it can perform.     

Nonlinear pricing in linear cities with elastic demands

Nonlinear road pricing charges each traveler based on his/her trip’s corresponding particular attribute level. In order to help authorities in designing road pricing systems at a strategic level, this paper attempts to address two fundamental questions: (i) what is the value of pricing’s nonlinearity for mitigating traffic congestion? (ii) if a nonlinear toll function is implemented, should it be convex, concave or other shape? Specifically, we consider distance-based pricing in linear cities. For linear monocentric cities with heterogeneous travelers, we show that the system optimal distance-based pricing indeed exhibits nonlinearity. It is proved that: (i) the cost-based system optimal toll function is monotonically increasing and concave with respect to the traveled distance; (ii) the time-based system optimal toll function always exists and is unique. If the initial proportion of each traveler group is invariant along a corridor and the demand function is of exponential type, then the time-based system optimal toll function enables the travelers, living further away from a city center, to face a lower toll level per unit distance. For a linear polycentric city, we demonstrate: (i) there always exists the system optimal differentiated (in terms of city centers) toll functions; (ii) it is highly possible that the system optimal non-differentiated toll function does not exist. Hence, we further propose an optimal toll design model, prove the Lipschitz continuity of its objective and adopt a global-optimization algorithm to solve it.     

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.     

Optimal cordon pricing in a non-monocentric city

This paper examines the effect of cordon pricing based on an urban spatial model of a non-monocentric city where trips may occur between any pair of locations in the city. The model describes the spatial distribution of trip demand and traffic congestion under alternative pricing schemes. We evaluate the efficiency of resource allocation by comparing three schemes: no-toll equilibrium, first-best optimum, and optimal cordon pricing. Optimal cordon pricing is defined as a combination of cordon location and toll level that maximizes the social surplus in a city. Simulations show that cordon pricing is not always effective for congestion management: cordon pricing tends to be effective as the urban structure is more monocentric.     

Trial-and-error method for congestion pricing scheme under side-constrained probit-based stochastic user equilibrium conditions

A toll pattern that can restrict link flows on the tolled links to some predetermined thresholds is named as effective toll solution, which can be theoretically obtained by solving a side-constraint traffic assignment problem. Considering the practical implementation, this paper investigates availability of an engineering-oriented trial-and-error method for the effective toll pattern of cordon-based congestion pricing scheme, under side-constrained probit-based stochastic user equilibrium (SUE) conditions. The trial-and-error method merely requires the observed traffic counts on each entry of the cordon. A minimization model for the side-constrained probit-based SUE problem with elastic demand is first proposed and it is shown that the effective toll solution equals to the product of value of time and optimal Lagrangian multipliers with respect to the side constraints. Then, employing the Lagrangian dual formulation of the minimization method, this paper has built a convergent trial-and-error method. The trial-and-error method is finally tested by a numerical example developed from the cordon-based congestion pricing scheme in Singapore.