Transaction costs and tradable mobility credits

Artificial markets for mobility credits have been proposed as an alternative to conventional congestion pricing schemes. This paper examines the effects of transaction costs on two types of markets: an auction market and a negotiated market. In an auction market, users purchase all of the needed mobility credits through a competitive bidding process. In a negotiated market, the users initially receive certain amount of mobility credits from the government and trade with each other through negotiation to fulfill their needs. We assume that a brokerage service is built in both markets to facilitate transactions and accordingly, the users have to pay a commission fee proportional to the value of trade. The users are also given the option to purchase credits from the government if for some reasons they cannot use or wish to avoid the markets. Our analyses suggest that the auction market can achieve the desired equilibrium allocation of mobility credits as long as the government sets its price properly and the unit transaction cost is lower than the price that the market would reach in absence of transaction costs. However, in the negotiated market, transaction costs could divert the system from the desired equilibrium regardless of their magnitude. More importantly, the initial allocation of mobility credits may affect the final equilibrium even when marginal transaction costs are constant.     

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.     

Continuous price and flow dynamics of tradable mobility credits

This study examines the price and flow dynamics under a tradable credit scheme, when the credits can be traded in a free market. A continuous dynamic model in a finite time horizon is proposed to describe the travelers’ learning behavior and the evolution of network flows and credit price, and then the existence and uniqueness of the equilibria are established. The conditions for stability and convergence of the dynamic system as the time horizon extends to infinity and the impact of limited implementation time horizon on the system behavior are investigated.     

Tradable credits for managing car travel: a review of empirical research and relevant behavioural approaches

Recently, there has been a surge of interest in Tradable Credits (TC) as an alternative measure to manage the growth of personal car use. This paper summarises the results and methodologies of studies that have sought to anticipate the behavioural responses to several proposed TC schemes that target personal travel. In a critical reflection on this work and in an attempt to inspire future research, we argue that future empirical studies on TC behaviours can greatly benefit from insights from the fields of behavioural economics and cognitive psychology. Therefore, in the second part of the paper, we bring together behavioural concepts from these fields that are relevant in a TC decision-making context. Based on observations from current TC studies and the behavioural mechanisms identified in the second part of the paper, we propose promising directions for future research on understanding the impact of TC on personal car travel.     

Tradable credits scheme and transit investment optimization for a two‐mode traffic network

This paper proposes an optimization model to minimize the “system costs” and guide travelers' behavior by exploring the optimal bus investment and tradable credits scheme design in a bimodal transportation system. Travelers' transport mode choice behavior (car or bus) and the modal equilibrium conditions between these two forms of transport are studied in the tradable credits scheme. Public transport priority is highlighted by charging car travelers credits only. The economies of scale presented by the transit system under the tradable credit scheme are analyzed by comparing the marginal cost and average cost. Numerical examples are presented to demonstrate the model. Furthermore, the effects of tradable credits schemes on bus investment and travelers' modal choice behavior are explored based on scenario discussions. Copyright © 2016 John Wiley & Sons, Ltd.     

Tradable credit schemes on networks with mixed equilibrium behaviors

This paper analyzes and designs tradable credit schemes on networks with two types of players, namely, a finite number of Cournot–Nash (CN) players and an infinite number of (infinitesimal) Wardrop-equilibrium (WE) players. We first show that there are nonnegative anonymous credit schemes that yield system optimum, when transaction costs are not considered. We then analyze how transaction costs would affect the trading and route-choice behaviors of both CN and WE players, and discuss the equilibrium conditions on the coupled credit market and transportation network in the presence of transaction costs. A variational inequality is formulated to describe the equilibrium and is subsequently applied to a numerical example to assess the impacts of transaction costs on a tradable credit system. As expected, transaction costs reduce the trading volume of credits and change their market price. They also change the way how players respond to credit charges in their route choices and cause efficiency losses to the credit schemes that are previously designed without considering transaction costs. With transaction costs, travel costs of WE players will likely increase while those of CN players may decrease due to their higher adaptability in routing strategies.     

Optimal biofuel supply chain design under consumption mandates with renewable identification numbers

The Renewable Identification Number (RIN) system is a tracking mechanism that enforces the U.S. Renewable Fuel Standard by monitoring obligated parties’ compliance with the biofuel consumption mandates. This paper incorporates the RIN system into the design of a biofuel supply chain that addresses independent decisions of non-cooperative farmers, biofuel manufacturers, and blenders. Game-theoretic models are developed to examine the impacts of the RIN system on individual stakeholders’ decisions (e.g., on farmland use, bio-refinery investment, biofuel production) and the competition between food and biofuel industries, in both a perfectly competitive scenario and a monopoly scenario. For the perfectly competitive scenario, Nash equilibrium can be obtained by solving a convex optimization problem. For the monopoly scenario, a bi-level Stackelberg leader–follower model is developed, from which we found that a rigid mandate on blenders may suppress the total biofuel production. To avoid such unintended consequences, a relaxed unit-RIN based penalty scheme is proposed and shown to improve the overall biofuel supply chain performance. Managerial insights are drawn from a numerical case study for the state of Illinois.     

Real-time congestion pricing strategies for toll facilities

This paper analyzes the dynamic traffic assignment problem on a two-alternative network with one alternative subject to a dynamic pricing that responds to real-time arrivals in a system optimal way. Analytical expressions for the assignment, revenue and total delay in each alternative are derived as a function of the pricing strategy. It is found that minimum total system delay can be achieved with many different pricing strategies. This gives flexibility to operators to allocate congestion to either alternative according to their specific objective while maintaining the same minimum total system delay. Given a specific objective, the optimal pricing strategy can be determined by finding a single parameter value in the case of HOT lanes. Maximum revenue is achieved by keeping the toll facility at capacity with no queues for as long as possible. Guidelines for implementation are discussed.     

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.     

Can Hong Kong price-manage its cross-harbor-tunnel congestion?

Hong Kong drivers face daily congestion, especially at the Cross Harbor Tunnel (CHT) whose tolls are substantially lower than those of the drivers’ other two tunnel options: the Eastern Harbor Crossing (EHC) and the Western Harbor Crossing (WHC). In 2013, the Hong Kong Special Administrative Region (HKSAR) Government issued a consultation paper, seeking public comments on three toll-change proposals that would raise the CHT’s tolls and lower the EHC’s tolls. The WHC’s tolls would remain unchanged due to its congested connecting roads. Using monthly crossing data available from the HKSAR’s Transport Department for 2000–2012, this paper uses a Generalized Leontief demand system to document that the usage patterns of the three tunnels is price-responsive. Hence, we conclude that the proposed toll changes are likely to be effective in transportation demand management, by shifting a portion of the CHT’s usage to the EHC and WHC, thereby relieving the CHT’s congestion.     

Trial and error method for optimal tradable credit schemes: The network case

Recent studies on the new congestion reduction method―tradable credit scheme rely on the full information of speed‐flow relationship, demand function, and generalized cost. As analytical travel demand, functions are difficult to establish in practice. This paper develops a trial and error method for selecting optimal credit schemes for general networks in the absence of demand functions. After each trial of tradable credit scheme, the credit charging scheme and total amount of credits to be distributed are updated by both observed link flows at traffic equilibrium and revealed credit price at market equilibrium. The updating strategy is based on the method of successive averages and its convergence is established theoretically. Our numerical experiments demonstrate that the method of successive averages based trial and error method for tradable credit schemes has a lower convergence speed in comparison with its counterpart for congestion pricing and could be enhanced by exploring more efficient methods that make full use of credit price information. Copyright © 2013 John Wiley & Sons, Ltd.     

Dynamic user equilibrium with side constraints for a traffic network: Theoretical development and numerical solution algorithm

This paper investigates a traffic volume control scheme for a dynamic traffic network model which aims to ensure that traffic volumes on specified links do not exceed preferred levels. The problem is formulated as a dynamic user equilibrium problem with side constraints (DUE-SC) in which the side constraints represent the restrictions on the traffic volumes. Travelers choose their departure times and routes to minimize their generalized travel costs, which include early/late arrival penalties. An infinite-dimensional variational inequality (VI) is formulated to model the DUE-SC. Based on this VI formulation, we establish an existence result for the DUE-SC by showing that the VI admits at least one solution. To analyze the necessary condition for the DUE-SC, we restate the VI as an equivalent optimal control problem. The Lagrange multipliers associated with the side constraints as derived from the optimality condition of the DUE-SC provide the traffic volume control scheme. The control scheme can be interpreted as additional travel delays (either tolls or access delays) imposed upon drivers for using the controlled links. This additional delay term derived from the Lagrange multiplier is compared with its counterpart in a static user equilibrium assignment model. If the side constraint is chosen as the storage capacity of a link, the additional delay can be viewed as the effort needed to prevent the link from spillback. Under this circumstance, it is found that the flow is incompressible when the link traffic volume is equal to its storage capacity. An algorithm based on Euler’s discretization scheme and nonlinear programming is proposed to solve the DUE-SC. Numerical examples are presented to illustrate the mechanism of the proposed traffic volume control scheme.     

Intermodal and international freight network modeling

The authors describe the development and application of a single, integrated digital representation of a multimodal and transcontinental freight transportation network. The network was constructed to support the simulation of some five million origin to destination freight shipments reported as part of the 1997 United States Commodity Flow Survey. The paper focuses on the routing of the tens of thousands of intermodal freight movements reported in this survey. Routings involve different combinations of truck, rail and water transportation. Geographic information systems (GIS) technology was invaluable in the cost-effective construction and maintenance of this network and in the subsequent validation of mode sequences and route selections. However, computationally efficient routing of intermodal freight shipments was found to be most efficiently accomplished outside the GIS. Selection of appropriate intermodal routes required procedures for linking freight origins and destinations to the transportation network, procedures for modeling intermodal terminal transfers and inter-carrier interlining practices, and a procedure for generating multimodal impedance functions to reflect the relative costs of alternative, survey reported mode sequences.     

Integrating congestion pricing and transit investment planning

This paper develops a mathematical model and solution procedure to identify an optimal zonal pricing scheme for automobile traffic to incentivize the expanded use of transit as a mechanism to stem congestion and the social costs that arise from that congestion. The optimization model assumes that there is a homogenous collection of users whose behavior can be described as utility maximizers and for which their utility function is driven by monetary costs. These monetary costs are assumed to be the tolls in place, the per mile cost to drive, and the value of their time. We assume that there is a system owner who sets the toll prices, collects the proceeds from the tolls, and invests those funds in transit system improvements in the form of headway reductions. This yields a bi-level optimization model which we solve using an iterative procedure that is an integration of a genetic algorithm and the Frank–Wolfe method. The method and solution procedure is applied to an illustrative example.     

Robust optimization of distance-based tolls in a network considering stochastic day to day dynamics

This paper investigates the nonlinear distance-based congestion pricing in a network considering stochastic day-to-day dynamics. After an implementation/adjustment of a congestion pricing scheme, the network flows in a certain period of days are not on an equilibrium state, thus it is problematic to take the equilibrium-based indexes as the pricing objective. Therefore, the concept of robust optimization is taken for the congestion toll determination problem, which takes into account the network performance of each day. First, a minimax model which minimizes the maximum regret on each day is proposed. Taking as a constraint of the minimax model, a path-based day to day dynamics model under stochastic user equilibrium (SUE) constraints is discussed in this paper. It is difficult to solve this minimax model by exact algorithms because of the implicity of the flow map function. Hence, a two-phase artificial bee colony algorithm is developed to solve the proposed minimax regret model, of which the first phase solves the minimal expected total travel cost for each day and the second phase handles the minimax robust optimization problem. Finally, a numerical example is conducted to validate the proposed models and methods.     

Speed limits,speed selection and network equilibrium

This paper investigates the local and global impact of speed limits by considering road users’ non-obedient behavior in speed selection. Given a link-specific speed limit scheme, road users will take into account the subjective travel time cost, the perceived crash risk and the perceived ticket risk as determinant factors for their actual speed choice on each link. Homogeneous travelers’ perceived crash risk is positively related to their driving speed. When travelers are heterogeneous, the perceived crash risk is class-specific: different user classes interact with each other and choose their own optimal speed, resulting in a Nash equilibrium speed pattern. With the speed choices on particular roads, travelers make route choices, resulting in user equilibrium in a general network. An algorithm is proposed to solve the user equilibrium problem with heterogeneous users under link-specific speed limits. The models and algorithms are illustrated with numerical examples.     

Dynamic congestion pricing with day-to-day flow evolution and user heterogeneity

This paper investigates evolutionary implementation of congestion pricing schemes to minimize the system cost and time, measured in monetary and time units, respectively, with the travelers’ day-to-day route adjustment behavior and their heterogeneity. The travelers’ heterogeneity is captured by their value-of-times. First, the multi-class flow dynamical system is proposed to model the travelers’ route adjustment behavior in a tolled transportation network with multiple user classes. Then, the stability condition and properties of equilibrium is examined. We further investigate the trajectory control problem via dynamic congestion pricing scheme to derive the system cost, time optimum, and generally, Pareto optimum in the sense of simultaneous minimization of system cost and time. The trajectory control problem is modeled by a differential–algebraic system with the differential sub-system capturing the flow dynamics and the algebraic one capturing the pricing constraint. The explicit Runge–Kutta method is proposed to calculate the dynamic flow trajectories and anonymous link tolls. The method allows the link tolls to be updated with any predetermined periods and forces the system cost and/or time to approach the optimum levels. Both analytical and numerical examples are adopted to examine the efficiency of the method.     

Urban delivery industry response to cordon pricing, time-distance pricing, and carrier-receiver policies in competitive markets

The paper develops a set of analytical formulations to study the behavior of the urban delivery industry in response to cordon time-of-day pricing, time-distance pricing, and comprehensive financial policies targeting carriers and receivers. This is accomplished by modeling the behavior of receivers in response to financial incentives, and the ensuing behavior of the carrier in response to both pricing and the receivers’ decisions concerning off-hour deliveries. The analytical formulations consider both the base case condition, and a mixed operation with both regular hour and off-hour deliveries; two pricing schemes: cordon time of day, and time-distance pricing; two types of operations: single-tour, and multi-tour carriers; and three different scenarios in terms of profitability of the carrier operation, which include an approximation to the best case, the expected value, and the worst case. The analyses, both theoretical and numerical, highlight the limitations of pricing-only approaches. In the case of cordon time of day pricing, the chief conclusion is that it is of limited use as a freight demand management tool because: (1) in a competitive market the cordon toll cannot be transferred to the receivers as it is a fixed cost and (2) the structure of the cost function, that only provides an incentive to the carrier to switch to the off-hours when all the receivers in the tour switch to the off-hours. The analyses of time-distance pricing clearly indicate that, though its tolls could be transferred to the receivers and provide an incentive for behavior change, the magnitude of the expected toll transfers under real life conditions are too small to have any meaningful impact on receivers choice of delivery times. In essence, the key policy implication is that in order to change the joint behavior of carrier and receivers, financial incentives—or programs that foster unassisted off-hour deliveries—should be made available to receivers in exchange for their commitment to do off-hour deliveries. As the paper proves, if a meaningful number of receivers switch to the off-hours, the carriers are likely to follow suit.     

Link-based day-to-day network traffic dynamics and equilibria

A general dynamical system model with link-based variables is formulated to characterize the processes of achieving equilibria from a non-equilibrium state in traffic networks. Several desirable properties of the dynamical system model are established, including the equivalence between its stationary state and user equilibrium, the invariance of its evolutionary trajectories, and the uniqueness and stability of its stationary points. Moreover, it is shown that not only a link-based version of two existing day-to-day traffic dynamics models but also two existing link-based dynamical system models of traffic flow are the special cases of the proposed model. The stabilities of stationary states of these special cases are also analyzed and discussed. In addition, an extension is made to the case with elastic demand. The study is helpful for better understanding the day-to-day adjustment mechanism of traffic flows in networks.     

Nonlinear pricing on private roads with congestion and toll collection costs

Nonlinear pricing (a form of second-degree price discrimination) is widely used in transportation and other industries but it has been largely overlooked in the road-pricing literature. This paper explores the incentives for a profit-maximizing toll-road operator to adopt some simple nonlinear pricing schemes when there is congestion and collecting tolls is costly. Users are assumed to differ in their demands to use the road. Regardless of the severity of congestion, an access fee is always profitable to implement either as part of a two-part tariff or as an alternative to paying a toll. Use of access fees for profit maximization can increase or decrease welfare relative to usage-only pricing for profit maximization. Hence a ban on access fees could reduce welfare.