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.     

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.     

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.     

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.     

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.     

A novel permit scheme for managing parking competition and bottleneck congestion

Morning commuters may have to depart from home earlier to secure a parking space when parking supply in the city center is insufficient. Recent studies show that parking reservations can reduce highway congestion and deadweight loss of parking competition simultaneously. This study develops a novel tradable parking permit scheme to realize or implement parking reservations when commuters are either homogeneous or heterogeneous in their values of time. It is found that an expirable parking permit scheme with an infinite number of steps, i.e., the ideal-scheme, is superior to a time-varying pricing scheme in the sense that designing a permit scheme does not require commuters’ value of time information and the performance of the scheme is robust to the variation of commuters’ value of time. Although it is impractical to implement the ideal-scheme with an infinite number of steps, the efficiency loss of a permit scheme with finite steps can be bounded in both cases of homogeneous and heterogeneous commuters. Moreover, considering the permit scheme may lead to an undesirable benefit distribution among commuters, we propose an equal cost-reduction distribution of parking permits where auto commuters with higher value of time will receive fewer permits.     

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 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.     

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.     

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.     

On the morning commute problem with bottleneck congestion and parking space constraints

Morning commuters choose their departure times based on a combination of factors—the chances of running into bottleneck congestion, the likely schedule delays, and parking space availability. This study investigates the morning commute problem with both bottleneck congestion and parking space constraints. In particular, it considers the situation when some commuters have reserved parking spots while others have to compete for public ones on a first-come-first-served basis. Unlike the traditional pure bottleneck model, the rush-hour dynamic traffic pattern with a binding parking capacity constraint varies with the relative proportions of the two classes of commuters. It is found that an appropriate combination of reserved and unreserved parking spots can temporally relieve traffic congestion at the bottleneck and hence reduce the total system cost, because commuters without a reserved parking spot are compelled to leave home earlier in order to secure a public parking spot. System performance is quantified in terms of the relative proportions of the two classes of commuters and is compared with those in the extreme cases when all auto commuters have to compete for parking and when none of them have to compete for one.     

On the existence of pricing strategies in the discrete time heterogeneous single bottleneck model

In this paper, we study the pricing strategies in the discrete time single bottleneck model with general heterogeneous commuters. We first prove that in the system optimal assignment, the queue time must be zero for all the departures. Based on this result, the system optimal problem is formulated as a linear program. The solution existence and uniqueness are discussed. Applying linear programming duality, we then prove that the optimal dual variable values provide an optimal toll with which the system optimal solution is also an equilibrium solution. Extensive computational results are reported to demonstrate the insights gained from the formulations in this paper. These results confirm that a system optimal equilibrium can be found using the proposed approach.     

Expirable parking reservations for managing morning commute with parking space constraints

When total parking supply in an urban downtown area is insufficient, morning commuters would choose their departure times not only to trade off bottleneck congestion and schedule delays, but also to secure a parking space. Recent studies found that an appropriate combination of reserved and unreserved parking spaces can spread the departures of those morning commuters and hence reduce their total travel cost. To further mitigate both traffic congestion and social cost from competition for parking, this study considers a parking reservation scheme with expiration times, where commuters with a parking reservation have to arrive at parking spaces for the reservation before a predetermined expiration time. We first show that if all parking reservations have the same expiration time, it is socially preferable to set the reservations to be non-expirable, i.e., without expiration time. However, if differentiated expiration times are properly designed, the total travel cost can be further reduced as compared with the reservation scheme without expiration time, since the peak will be further smoothed out. We explore socially desirable equilibrium flow patterns under the parking reservation scheme with differentiated expiration times. Finally, efficiencies of the reservation schemes are examined.     

Improving travel efficiency by parking permits distribution and trading

In this paper, we study various parking management schemes in a many-to-one network, where each origin is connected to the destination by a highway with a bottleneck and a parallel transit line. First, we derive a model to compute the morning commuting pattern when the destination has inadequate parking space to accommodate potential private cars. Second, we propose and compare the following three schemes of distributing parking permits to commuters residing in different origins: uniform, Pareto improving, and system optimum distribution of parking permits. Third, free trading of parking permits among commuters in a free market is introduced to better cater for commuters’ parking needs. Numerical examples show that parking permits distribution and trading are very efficient in traffic management.     

An equilibrium analysis of commuter parking in the era of autonomous vehicles

This study is the first in the literature to model the joint equilibrium of departure time and parking location choices when commuters travel with autonomous vehicles (AVs). With AVs, walking from parking spaces to the work location is not needed. Instead, AVs will drop off the commuters at the workplace and then drive themselves to the parking spaces. In this context, the equilibrium departure/arrival profile is different from the literature with non-autonomous vehicles (non-AVs). Besides modeling the commuting equilibrium, this study further develops the first-best time-dependent congestion tolling scheme to achieve the system optimum. Also, a location-dependent parking pricing scheme is developed to replace the tolling scheme. Furthermore, this study discusses the optimal parking supply to minimize the total system cost (including both the travel cost and the social cost of parking supply) under either user equilibrium or system optimum traffic flow pattern. It is found that the optimal planning of parking can be different from the non-AV situation, since the vehicles can drive themselves to parking spaces that are further away from the city center and walking of commuters is avoided. This paper sheds light on future parking supply planning and traffic management.     

Trading mechanisms for bottleneck permits with multiple purchase opportunities

This paper extends the theory of tradable bottleneck permits system to cases with multiple period markets and designs its implementation mechanism. The multiple period markets can achieve more efficient resource allocation than a single period market when users’ valuations of tradable permits change over time. To implement the multiple period trading markets, we propose an evolutionary mechanism that combines a dynamic auction with a capacity control rule that adjusts a number of permits issued for each market. Then, we prove that the proposed mechanism has the following desirable properties: (i) the dynamic auction is strategy-proof within each period and guarantees that the market choice of each user is optimal under a perfect information assumption of users and (ii) the mechanism maximizes the social surplus in a finite number of iterations. Finally, we show that the proposed mechanism may work well even for an incomplete information case.     

The evening commute with cars and transit: Duality results and user equilibrium for the combined morning and evening peaks

This paper extends Vickrey’s (1969) commute problem for commuters wishing to pass a bottleneck for both cars and transit that share finite road capacity. In addition to this more general framework considering two modes, the paper focuses on the evening rush, when commuters travel from work to home. Commuters choose which mode to use and when to travel in order to minimize the generalized cost of their own trips, including queueing delay and penalties for deviation from a preferred schedule of arrival and departure to and from work. The user equilibrium for the isolated morning and evening commutes are shown to be asymmetric because the schedule penalty in the morning is the difference between the departure and wished curves, and the schedule penalty in the evening is the difference between the arrival and wished curves. It is shown that the system optimum in the morning and evening peaks are symmetric because queueing delay is eliminated and the optimal arrival curves are the same as the departure curves.The paper then considers both the morning and evening peaks together for a single mode bottleneck (all cars) with identical travelers that share the same wished times. For a schedule penalty function of the morning departure and evening arrival times that is positive definite and has certain properties, a user equilibrium is shown to exist in which commuters travel in the same order in both peaks. The result is used to illustrate the user equilibrium for two cases: (i) commuters have decoupled schedule preferences in the morning and evening and (ii) commuters must work a fixed shift length but have flexibility when to start. Finally, a special case is considered with cars and transit: commuters have the same wished order in the morning and evening peaks. Commuters must use the same mode in both directions, and the complete user equilibrium solution reveals the number of commuters using cars and transit and the period in the middle of each rush when transit is used.     

Pareto-improving ramp metering strategies for reducing congestion in the morning commute

This paper presents an alternative approach to internalize congestion externality during the morning commute. We consider a linear freeway with multiple on-ramps and a downstream bottleneck and commuters accessing the freeway via different on-ramps try to arrive at work on time. Rather than charging congestion tolls as widely suggested by economists, we show that the old-fashioned engineering approach – ramp metering – can be a powerful tool to affect travelers’ departure time choice and thereby alter the congestion externality distribution among travelers. With carefully designed time-dependent metering plans, travelers from different origins can be channelized and will access the freeway bottleneck in different time periods, resulting in less total cost for the system compared to the no-metering case. The metering strategies are Pareto-improving, with travelers from the on-ramp with the highest priority having the smallest individual costs and travelers from the on-ramp with the lowest priority having their costs equal to those in the no-metering scenario. By changing the priority order of the ramps periodically, the benefit of the Pareto-improving metering strategies can be distributed evenly among all travelers. Numerical experiments show that the total user cost can be reduced by up to 40% with the proposed metering strategies. This study offers researchers and policy makers a different angle of looking at congestion externality, and the results provide an overview of the potential long term benefits that dynamic ramp metering strategies can achieve.     

Existence of self-financing and Pareto-improving congestion pricing: Impact of value of time distribution

This paper considers a static congestion pricing model in which travelers select a mode from either, driving on highway or taking public transit, to minimize a combination of travel time, operating cost and toll. The focus is to examine how travelers’ value of time (VOT), which is continuously distributed in a population, affects the existence of a pricing-refunding scheme that is both self-financing (i.e. requiring no external subsidy) and Pareto-improving (i.e. reducing system travel time while making nobody worse off). A condition that insures the existence of a self-financing and Pareto-improving (SFPI) toll scheme is derived. Our derivation reveals that the toll authority can select a proper SFPI scheme to distribute the benefits from congestion pricing through a credit-based pricing scheme. Under mild assumptions, we prove that an SFPI toll always exists for concave VOT functions, of which the linear function corresponding to the uniform distribution is a special case. Existence conditions are also established for a class of rational functions. These results can be used to analyze more realistic VOT distributions such as log-normal distribution. A useful implication of our analysis is that the existence of an SFPI scheme is not guaranteed for general functional forms. Thus, external subsidies may be required to ensure Pareto-improving, even if policy-makers are willing to return all toll revenues to road users.     

Discussing the “positive utilities” of autonomous vehicles: will travellers really use their time productively?

ABSTRACT

Autonomous vehicles (AVs) are expected to reshape travel behaviour and demand in part by enabling productive uses of travel time—a primary component of the “positive utility of travel” concept—thus reducing subjective values of travel time savings (VOT). Many studies from industry and academia have assumed significant increases in travel time use and reductions in VOT for AVs. In this position paper, I argue that AVs’ VOT impacts may be more modest than anticipated and derive from a different source. Vehicle designs and operations may limit activity engagement during travel, with AV users feeling more like car passengers than train riders. Furthermore, shared AVs may attenuate travel time use benefits, and productivity gains could be limited to long-distance trips. Although AV riders will likely have greater activity participation during travel, many in-vehicle activities today may be more about coping with commuting burdens than productively using travel time. Instead, VOT reductions may be more likely to arise from a different “positive utility”—subjective well-being improvements through reduced stresses of driving or the ability to relax and mentally transition. Given high uncertainty, further empirical research on the experiential, time use, and VOT impacts of AVs is needed.