The Role of Tradable Credit Schemes in Road Traffic Congestion Management

Abstract

Road traffic congestion is not yet reflected in current market prices within the sector and has given rise to a number of instruments to mitigate the resulting negative impacts. The focus of this paper is the tradable credit scheme — an incentive-based economic measure — in order to address traffic congestion. The research questions are (1) whether the state-of-the-art in the literature suggests that tradable credit schemes could be feasibly introduced to mitigate congestion, and (2) whether a tradable credit scheme could have advantages over other instruments. A brief outline of congestion mitigation approaches is provided first to position this type of economic instrument with respect to other measures. The broad issues in the design of a tradable credit scheme are then presented. Most research to date has focused on the use of tradable credits to manage related pollution, but it is clear there is potential to design a scheme for traffic congestion management. To date this is a novel review of tradable credit schemes that has focused specifically on their role in road traffic congestion management.     

Road pricing for congestion control with unknown demand and cost functions

It is widely recognized that precise estimation of road tolls for various pricing schemes requires a few pieces of information such as origin–destination demand functions, link travel time functions and users’ valuations of travel time savings, which are, however, not all readily available in practice. To circumvent this difficulty, we develop a convergent trial-and-error implementation method for a particular pricing scheme for effective congestion control when both the link travel time functions and demand functions are unknown. The congestion control problem of interest is also known as the traffic restraint and road pricing problem, which aims at finding a set of effective link toll patterns to reduce link flows to below a desirable target level. For the generalized traffic equilibrium problem formulated as variational inequalities, we propose an iterative two-stage approach with a self-adaptive step size to update the link toll pattern based on the observed link flows and given flow restraint levels. Link travel time and demand functions and users’ value of time are not needed. The convergence of the iterative toll adjustment algorithm is established theoretically and demonstrated on a set of numerical examples.     

Managing network mobility with tradable credits

A system of tradable travel credits is explored in a general network with homogeneous travelers. A social planner is assumed to initially distribute a certain number of travel credits to all eligible travelers, and then there are link-specific charges to travelers using that link. Free trading of credits among travelers is assumed. For a given credit distribution and credit charging scheme, the existence of a unique equilibrium link flow pattern is demonstrated with either fixed or elastic demand. It can be obtained by solving a standard traffic equilibrium model subject to a total credit consumption constraint. The credit price at equilibrium in the trading market is also conditionally unique. The appropriate distribution of credits among travelers and correct selection of link-specific rates is shown to lead to the most desirable network flow patterns in a revenue-neutral manner. Social optimum, Pareto-improving and revenue-neutral, and side-constrained traffic flow patterns are investigated.     

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.     

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.     

Taxis in road pricing zone: should they pay the congestion charge?

This study aims at investigating the impact and feasibility of charging taxis with toll fee in the pricing zone when designing congestion pricing scheme. A bi‐level programming model is developed to compare the maximum social welfares before and after the congestion charge is imposed on taxis. The lower level is a combined network equilibrium model formulated as a variational inequality program, which considers the logit‐based mode split, route choice, elastic demand, and vacant taxi distributions. The upper level is to maximize the social welfare when toll rates vary. The bi‐level problem can be solved by the genetic algorithm, whereas the lower level is solved by the block Gauss–Seidel decomposition approach together with the method of successive averages and diagonalization algorithm. An application with numerical examples is conducted to demonstrate the effectiveness of the proposed model and algorithm and to reveal some interesting findings. Copyright © 2014 John Wiley & Sons, Ltd.     

Managing rush hour travel choices with tradable credit scheme

This paper Analyzes a new tradable credit scheme (TCS) for managing commuters’ travel choices, which seeks to persuade commuters to spread evenly within the rush hour and between primary and alternative routes so that excessive traffic congestion can be alleviated. The scheme defines a peak time window and charges those who use the primary route within that window in the form of mobility credits. Those who avoid the peak-time window, by either traveling outside the peak time window or switching to the alternative route, may be rewarded credits. A market is created such that those who need to pay credits can purchase them from those who acquire them from their rewarding travel choices. A general analytical framework is proposed for a system of two parallel routes. The framework (1) considers a variety of assumptions about commuters’ behavior in response to the discontinuous credit charge introduced at the boundary of the peak-time window, (2) allows modeling congestion effects (or demand elasticity) on the alternative route, and (3) enables both the design of system optimal TCS and the analysis of the efficiency of any given TCS. Our analyses indicate that the proposed TCS not only achieves up to 33% efficiency gains in the base scenario, but also distributes the benefits among all the commuters directly through the credit trading. The results also suggest that very simple TCS schemes could provide substantial efficiency gains for a wide range of scenarios. Such simplicity and robustness are important to practicability of the proposed scheme. Numerical experiments are conducted to examine the sensitivity of TCS designs to various system parameters.     

Tradable network permits: A new scheme for the most efficient use of network capacity

Akamatsu et al. (2006) proposed a new transportation demand management scheme called “tradable bottleneck permits” (TBP), and proved its efficiency properties for a single bottleneck model. This paper explores the properties of a TBP system for general networks. An equilibrium model is first constructed to describe the states under the TBP system with a single OD pair. It is proved that equilibrium resource allocation is efficient in the sense that the total transportation cost in a network is minimized. It is also shown that the “self-financing principle” holds for the TBP system. Furthermore, theoretical relationships between TBP and congestion pricing (CP) are discussed. It is demonstrated that TBP has definite advantages over CP when demand information is not perfect, whereas both TBP and CP are equivalent for the perfect information case. Finally, it is shown that the efficiency result also holds for more general demand conditions.     

Surrogate‐based optimization of cordon toll levels in congested traffic networks

The benefit, in terms of social surplus, from introducing congestion charging schemes in urban networks is depending on the design of the charging scheme. The literature on optimal design of congestion pricing schemes is to a large extent based on static traffic assignment, which is known for its deficiency in correctly predict travel times in networks with severe congestion. Dynamic traffic assignment can better predict travel times in a road network, but are more computational expensive. Thus, previously developed methods for the static case cannot be applied straightforward. Surrogate‐based optimization is commonly used for optimization problems with expensive‐to‐evaluate objective functions. In this paper, we evaluate the performance of a surrogate‐based optimization method, when the number of pricing schemes, which we can afford to evaluate (because of the computational time), are limited to between 20 and 40. A static traffic assignment model of Stockholm is used for evaluating a large number of different configurations of the surrogate‐based optimization method. Final evaluation is performed with the dynamic traffic assignment tool VisumDUE, coupled with the demand model Regent, for a Stockholm network including 1240 demand zones and 17 000 links. Our results show that the surrogate‐based optimization method can indeed be used for designing a congestion charging scheme, which return a high social surplus. Copyright © 2016 John Wiley & Sons, Ltd.     

Network equilibrium for congested multi‐mode networks with elastic demand

This paper proposes an elastic demand network equilibrium model for networks with transit and walking modes. In Hong Kong, the multi‐mode transit system services over 90% of the total journeys and the demand on it is continuously increasing. Transit and walking modes are related to each other as transit passengers have to walk to and from transit stops. In this paper, the multi‐mode elastic‐demand network equilibrium problem is formulated as a variational inequality problem where the combined mode and route choices are modeled in a hierarchical logit structures and the total travel demand for each origin‐destination pair is explicitly given by an elastic demand function. In addition, the capacity constraint for transit vehicles and the effects of bi‐directional flows on walkways are considered in the proposed model. All these congestion effects are taken into account for modeling the travel choices. A solution algorithm is developed to solve the multi‐mode elastic‐demand network equilibrium model. It is based on a Block Gauss‐Seidel decomposition approach coupled with the method of successive averages. A numerical example is used to illustrate the application of the proposed model and solution algorithm.     

Pricing scheme design of ridesharing program in morning commute problem

This paper examines the dynamic user equilibrium of the morning commute problem in the presence of ridesharing program. Commuters simultaneously choose departure time from home and commute mode among three roles: solo driver, ridesharing driver, and ridesharing rider. Considering the congestion evolution over time, we propose a time-varying compensation scheme to maintain a positive ridesharing ridership at user equilibrium. To match the demand and the supply of ridesharing service over time, the compensation scheme should be set according to the inconvenience cost functions and the out-of-pocket cost functions. When the price charged per time unit is higher than the inconvenience cost per time unit perceived by the ridesharing drivers, the ridesharing participants will travel at the center of peak hours and solo drivers will commute at the two tails. Within the feasible region with positive ridership, the ridesharing program can reduce the congestion and all the commuters will be better off. To support system optimum (SO), we derive a time-varying toll combined with a flat ridesharing price from eliminating queuing delay. Under SO toll, the ridesharing program can attract more participants and have an enlarged feasible region. This reveals that the commuters are more tolerant to the inconvenience caused by sharing a ride at SO because of the lower travel time. Compared with no-toll equilibrium, both overall congestion and individual travel cost are further reduced at SO.     

Congestion mechanism and demand adjustment strategies for double-cell system with bottlenecks

In this paper, ramp systems on the Beijing 3rd ring road are described as double-cell ramp systems with a bottleneck. By analyzing empirical data for the Beijing 3rd ring road, we found that the initial states have an important impact on the final convergence states of the ramp systems. Then, we studied the dynamic process of the ramp systems, determined the congestion mechanism, and then designed a ramp control method based on the obtained mechanism. Under a feasible demand, double-cell ramp systems exhibit two typical cases, including an upstream-bottleneck system (in which the bottleneck cell is upstream) and a downstream-bottleneck system (in which the bottleneck cell is downstream). Then, a cell transmission model is used to analyze the dynamic evolution processes, starting from different initial states, and determine the congestion mechanism for each case. It is proven that the two systems have different possible equilibrium sets and congestion mechanisms. In an upstream-bottleneck system, the downstream always converges to the uncongested equilibrium, while the upstream bottleneck cell may experience congestion under certain initial states. In a downstream-bottleneck system, the congestion starts downstream, and then gradually propagates upstream. Furthermore, based on the different congestion mechanisms, two demand adjustment strategies are proposed, which redistribute the stationary feasible demand. The simulation results indicate that both systems can converge to uncongested equilibriums after demand adjustment. The ramp demand adjustment methods provide a scientific basis for urban traffic system management.     

Optimization method of alternate traffic restriction scheme based on elastic demand and mode choice behavior

As a countermeasure to urban traffic congestion, alternate traffic restriction (ATR) involves a certain proportion of automobiles being prohibited from entering pre-determined ATR districts during specific time periods. The present study introduces an optimization method for ATR schemes in terms of both their restriction districts and the proportion of restricted automobiles. As a Stackelberg game between traffic policy makers and road users, the ATR scheme optimization problem is established using a bi-level programming model, with the upper-level examining an ATR scheme aimed at consumers’ surplus maximization under the condition of overload flow minimization, and the lower-level synthetically optimizing elastic demand, mode choice (private car, public transit and park-and-ride) and multi-class user equilibrium assignment. A genetic algorithm based on the graph theory is also proposed to solve the bi-level programming model with a gradient project algorithm for solving the lower-level model. To our knowledge, this study represents the first attempt to theoretically optimize an ATR scheme using a systematic approach with mathematical model specification.     

Activity-based market equilibrium for capacitated multimodal transport systems

Empirical studies have shown that demand for multimodal transport systems is highly correlated with activity schedules of individuals. Nonetheless, existing analytical equilibrium models of multimodal systems have only considered trip-based demand. We propose a new market equilibrium model that is sensitive to traveler activity schedules and system capacities. The model is based on a constrained mixed logit model of activity schedule choice, where each schedule in the choice set is generated with a multimodal extension of the household activity pattern problem. The extension explicitly accounts for both passenger choices of activity participation and multimodal choices like public transit, walking, and vehicle parking. The market equilibrium is achieved with Lagrangian relaxation to determine the optimal dual price of the capacity constraint, and a method of successive averages with column generation finds an efficient choice set of activity schedules to assign flows over the dynamic network load capacities. An example illustrates the model and algorithm, effects similar to Vickrey’s morning commute model can be observed as a special case. A case study of the Oakville Go Transit station access “last mile” problem in the Greater Toronto Area is conducted with 166 survey samples reflecting 3680 individuals. Results suggest that a $10 fixed parking fee at Oakville station would lead to a reduction of access auto share from 54.8% to 49.5%, an increase in access transit share from 20.7% to 25.9%, and a disutility increase of 11% for the of single-activity residents of Oakville.     

Price of anarchy for non-atomic congestion games with stochastic demands

We generalize the notions of user equilibrium, system optimum and price of anarchy to non-atomic congestion games with stochastic demands. In this generalized model, we extend the two bounding methods from Roughgarden and Tardos (2004) and Correa et al. (2008) to bound the price of anarchy, and compare the upper bounds we have obtained. Our results show that the price of anarchy depends not only on the class of cost functions but also demand distributions and, to some extent, the network topology. The upper bounds are tight in some special cases, including the case of deterministic demands.     

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.     

Global convergence of the trial-and-error method for the traffic-restraint congestion-pricing scheme with day-to-day flow dynamics

The traffic-restraint congestion-pricing scheme (TRCPS) aims to maintain traffic flow within a desirable threshold for some target links by levying the appropriate link tolls. In this study, we propose a trial-and-error method using observed link flows to implement the TRCPS with the day-to-day flow dynamics. Without resorting to the origin–destination (O–D) demand functions, link travel time functions and value of time (VOT), the proposed trial-and-error method works as follows: tolls for the traffic-restraint links are first implemented each time (trial) and they are subsequently updated using observed link flows in a disequilibrium state at any arbitrary time interval. The trial-and-error method has the practical significance because it is necessary only to observe traffic flows on those tolled links and it does not require to wait for the network flow pattern achieving the user equilibrium (UE) state. The global convergence of the trial-and-error method is rigorously demonstrated under mild conditions. We theoretically show the viability of the proposed trial-and-error method, and numerical experiments are conducted to evaluate its performance. The result of this study, without doubt, enhances the confidence of practitioners to adopt this method.     

Interactions between driver information,route choice,and optimal signal timing on a simple network

The interaction between driver information, route choice, and optimal traffic signal settings was investigated using a simple two-route system with a single “T” intersection and a fixed O-D demand. The logit model and the method of successive averages (MSA) were used to calculate the route choice probabilities and the stochastic equilibrium assignment. Given an assignment, signal settings which minimized average intersection delay were calculated; flow reassignment and new optimal signal settings were then obtained and this iterative process continued until convergence. The calculations were performed either directly in a combined assignment/signal optimization model or in stages using the output flows of an assignment model as inputs to TRANSYT-7F and iterating between the two models. Results show that a unique joint signal timing/assignment equilibrium is reached in all cases provided that a certain precision in drivers' perceptions is not reached. If driver information increases to this precision (bifurcation point) and beyond, results show clearly that the unique joint signal timing/assignment equilibrium no longer exists. In fact, three joint equilibria points exist after the bifurcation point. Two of these points are stable and one is not. It was found that the system yields the lowest total intersection delay when the joint equilibrium is such that all traffic and hence the major part of green time is assigned to only one of the two routes. Although this may not be feasible to implement in practice, the results indicate clearly for this simple example that there is a trade-off between a system with minimum total delay but no unique joint signal-settings/assignment equilibrium (achieved when drivers have nearly perfect information about the system) and a system with a unique joint equilibrium but with higher total delay (achieved when drivers have reasonably good but somewhat limited information). In most cases the second system seems appropriate for a number of practical reasons.