Network reliability‐based optimal toll design

Optimal toll design from a network reliability point of view is addressed in this paper. Improving network reliability is proposed as a policy objective of road pricing. A reliability‐based optimal toll design model, where on the upper level network performance including travel time reliability is optimized, while on the lower level a dynamic user‐equilibrium is achieved, is presented. Road authorities aim to optimize network travel time reliability by setting tolls in a network design problem. Travelers are influenced by these tolls and make route and trip decisions by considering travel times and tolls. Network performance reliability is analyzed for a degradable network with elastic and fluctuated travel demand, which integrates reliability and uncertainty, dynamic network equilibrium models, and Monte Carlo methods. The proposed model is applied to a small hypothesized network for which optimal tolls are derived. The network travel time reliability is indeed improved after implementing optimal tolling system. Trips may have a somewhat higher, but more reliable, travel time.     

Effect of advanced traveler information systems and road pricing in a network with non-recurrent congestion

The effect of the application of advanced transport information system (ATIS) and road pricing is studied in a transportation system under non-recurrent congestion. A stochastic network deterministic user equilibrium model (SNDUE) with elastic demand is formulated and used to evaluate the welfare and private impacts of different market penetrations of ATIS, together with road pricing for a simple network. Both marginal first-best road pricing and a second-best fixed road pricing are considered. The incentives of private users to use ATIS are analyzed and the characteristics of optimum tolls as a function of ATIS market penetration are shown. We conclude that ATIS is an efficient and necessary tool to reduce the effects of non-recurrent incidents in a transportation network, especially when non-recurrent congestion causes a significant deterioration of operational conditions of the network. If the impact of non-recurrent incidents on free flow costs is small or is reduced only to congestion effects, the use of road pricing would be more efficient. Social benefits obtained when jointly implementing ATIS and road pricing are practically the same whether first-best or second-best road pricing is used. Considering the private costs perceived by the network users, and the benefits experienced by equipped users, the maximum level of market penetration achieved could be limited because private benefits disappear after certain market penetration is obtained.     

Step-tolling with price-sensitive demand: Why more steps in the toll make the consumer better off

Most dynamic models of congestion pricing use fully time-variant tolls. However, in practice, tolls are uniform over the day, or at most have just a few steps. Such uniform and step tolls have received surprisingly little attention from the literature. Moreover, most models that do study them assume that demand is insensitive to the price. This seems an empirically questionable assumption that, as this paper finds, strongly affects the implications of step tolling for the consumer. In the bottleneck model, first-best tolling has no effect on the generalised price, and thus consumer surplus remains the same as without tolling. Conversely, under price-sensitive demand, step tolling increases the price, making the consumer worse off. The more steps the toll has, the closer it approximates the first-best toll, thereby increasing the welfare gain and making consumers better off. This indicates the importance for real-world tolls to have as many steps as possible: this not only raises welfare, but may also increase the political acceptability of the scheme by making consumers better off.     

Anticipating new-highway impacts: Opportunities for welfare analysis and credit-based congestion pricing

Pricing of roadways opens doors for infrastructure financing, and congestion pricing seeks to address inefficiencies in roadway operations. This paper emphasizes the revenue-generation opportunities and welfare impacts of flat-tolling schemes, standard congestion pricing, and credit-based congestion pricing policies. While most roadway investment decisions focus on travel time savings for existing trips, this work turns to logsum differences (which quantify changes in consumer surplus) for nested logit specifications across two traveler types, two destinations, three modes and three times of day, in order to arrive at welfare- and revenue-maximizing solutions. This behavioral specification is quite flexible, and facilitates benefit-cost calculations (as well as equity analysis), as demonstrated in this paper.The various cases examined suggest significant opportunities for financing new roadway investment while addressing congestion and equity issues, with net gains for both traveler types. Application results illustrate how, even after roadway construction and maintenance costs are covered, receipts may remain to distribute to eligible travelers so that typical travelers can be made better off than if a new, non-tolled road had been constructed. Moreover, tolling both routes (new and old) results in substantially shorter payback periods (5 versus 20 years) and higher welfare outcomes (in the case of welfare-maximizing tolls with credit distributions to all travelers). The tools and techniques highlighted here illustrate practical methods for identifying welfare-enhancing and cost-recovering investment opportunities, while recognizing multiple user classes and appropriate demand elasticity across times of day, destinations, modes and routes.     

Congestion pricing under operational,supply-side uncertainty

This paper is concerned with finding first-best tolls in static transportation networks with day-to-day variation in network capacity, as accounted for by changes in the volume-delay function. The key question in addressing this problem is that of information, namely, which agents have access to what information when making decisions. In this work, travelers are assumed to be either fully informed about network conditions before embarking on travel, or having no information except the probability distributions; likewise, the network manager (toll-setter) is either able to vary tolls in response to realized network conditions, or must apply the same tolls every day. Further, travelers’ preference for reliable travel is accounted for, representing risk aversion in the face of uncertainty. For each of the scenarios implied by combinations of these assumptions, we present methods to determine system-optimal link prices. A demonstration is provided, using the Sioux Falls test network, suggesting that attempts to incorporate uncertainty into nonresponsive tolls involve significantly higher prices.     

Capturing value of reliability through road pricing in congested traffic under uncertainty

Empirical studies showed that travel time reliability, usually measured by travel time variance, is strongly correlated with travel time itself. Travel time is highly volatile when the demand approaches or exceeds the capacity. Travel time variability is associated with the level of congestion, and could represent additional costs for travelers who prefer punctual arrivals. Although many studies propose to use road pricing as a tool to capture the value of travel time (VOT) savings and to induce better road usage patterns, the role of the value of reliability (VOR) in designing road pricing schemes has rarely been studied. By using road pricing as a tool to spread out the peak demand, traffic management agencies could improve the utility of travelers who prefer punctual arrivals under traffic congestion and stochastic network conditions. Therefore, we could capture the value of travel time reliability using road pricing, which is rarely discussed in the literature. To quantify the value of travel time reliability (or reliability improvement), we need to integrate trip scheduling, endogenous traffic congestion, travel time uncertainty, and pricing strategies in one modeling framework. This paper developed such a model to capture the impact of pricing on various costs components that affect travel choices, and the role of travel time reliability in shaping departure patterns, queuing process, and the choice of optimal pricing. The model also shows the benefits of improving travel time reliability in various ways. Findings from this paper could help to expand the scope of road pricing, and to develop more comprehensive travel demand management schemes.     

Peak period tolls: Precepts and prospects

This article presents the economic rationale for road pricing and provides some scale on the magnitude of peak period tolls that might be justified. It discusses the impacts of such tolls on congestion, air quality and economic development and suggests a long term strategy towards areawide implementation of peak period pricing. It discusses current trends which are increasing the likelihood for implementation of congestion pricing and toll roads in the future. In particular, it discusses some aspects of the 1991 Intermodal Surface Transportation Efficiency Act (ISTEA) which will eliminate some of the current restraints on congestion pricing and toll highways.Abbreviations ETC Electronic toll collection - FHWA Federal Highway Administration - HOV High occupancy vehicle - ISTEA Intermodal Surface Transportation Efficiency Act - LOS Level of service - TCM Transportation control measure - V/C Volume-to-capacity ratio - VMT Vehicle mile(s) of travel - vphpl Vehicles per hour per lane     

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.     

Accounting for travel time variability in the optimal pricing of cars and buses

A number of studies have shown that in addition to travel time and cost as the common influences on mode, route and departure time choices, travel time variability plays an increasingly important role, especially in the presence of traffic congestion on roads and crowding on public transport. The dominant focus of modelling and implementation of optimal pricing that incorporates trip time variability has been in the context of road pricing for cars. The main objective of this paper is to introduce a non-trivial extension to the existing literature on optimal pricing in a multimodal setting, building in the role of travel time variability as a source of disutility for car and bus users. We estimate the effect of variability in travel time and bus headway on optimal prices (i.e., tolls for cars and fares for buses) and optimal bus capacity (i.e., frequencies and size) accounting for crowding on buses, under a social welfare maximisation framework. Travel time variability is included by adopting the well-known mean–variance model, using an empirical relationship between the mean and standard deviation of travel times. We illustrate our model with an application to a highly congested corridor with cars, buses and walking as travel alternatives in Sydney, Australia. There are three main findings that have immediate policy implications: (i) including travel time variability results in higher optimal car tolls and substantial increases in toll revenue, while optimal bus fares remain almost unchanged; (ii) when bus headways are variable, the inclusion of travel time variability as a source of disutility for users yields higher optimal bus frequencies; and (iii) including both travel time variability and crowding discomfort leads to higher optimal bus sizes.     

A multi‐class mean‐excess traffic equilibrium model with elastic demand

Recent empirical studies have revealed that travel time variability plays an important role in travelers' route choice decisions. To simultaneously account for both reliability and unreliability aspects of travel time variability, the concept of mean‐excess travel time (METT) was recently proposed as a new risk‐averse route choice criterion. In this paper, we extend the mean‐excess traffic equilibrium model to include heterogeneous risk‐aversion attitudes and elastic demand. Specifically, this model explicitly considers (1) multiple user classes with different risk‐aversions toward travel time variability when making route choice decisions under uncertainty and (2) the elasticity of travel demand as a function of METT when making travel choice decisions under uncertainty. This model is thus capable of modeling travelers' heterogeneous risk‐averse behaviors with both travel choice and route choice considerations. The proposed model is formulated as a variational inequality problem and solved via a route‐based algorithm using the modified alternating direction method. Numerical analyses are also provided to illustrate the features of the proposed model and the applicability of the solution algorithm. Copyright © 2012 John Wiley & Sons, Ltd.     

Optimal tolls for multi-class traffic: Analytical formulations and policy implications

This paper puts together an analytical formulation to compute optimal tolls for multi-class traffic. The formulation is comprised of two major modules. The first one is an optimization component aimed at computing optimal tolls assuming a Stackelberg game in which the toll agency sets the tolls, and the equilibrating traffic plays the role of the followers. The optimization component is supported by a set of cost models that estimate the externalities as a function of a multivariate vector of traffic flows. These models were estimated using Taylor series expansions of the output obtained from traffic simulations of a hypothetical test case. Of importance to the paper is the total travel time function estimated using this approach that expresses total travel time as a multivariate function of the traffic volumes. The formulation presented in the paper is then applied to a variety of scenarios to gain insight into the optimality of current toll policies. The optimal tolls are computed for two different cases: independent tolls, and tolls proportional to passenger car equivalencies (PCE).The numerical results clearly show that setting tolls proportional to PCEs leads to lower values of welfare that are on average 15% lower than when using independent tolls, though, in some cases the total welfare could be up to 33% lower. This is a consequence of two factors. First, the case of independent tolls has more degrees of freedom than the case of tolls proportional to PCEs. Second, tolls proportional to PCEs do not account for externalities other than congestion, which is likely to lead to lower welfare values.The analytical formulations and numerical results indicate that, because the total travel time is a non-linear function of the traffic volumes, the marginal social costs and thus the optimal congestion tolls also depend on the traffic volumes for each vehicle class. As a result of this, for the relatively low volumes of truck traffic observed in real life, the optimal congestion tolls for trucks could indeed be either lower or about the same as for passenger cars. This stand in sharp contrast with what is implied in the use of PCEs, i.e., that the contribution to congestion are constant. This latter assumption leads to optimal truck congestion tolls that are always proportional to the PCE values.The comparison of the toll ratios (truck tolls divided by passenger car tolls) for both observed and optimal conditions suggests that the tolls for small trucks are about the right level, maybe a slightly lower than optimal. However, the analysis of the toll ratio for large trucks seems to indicate a significant overcharge. The estimates show that the average observed toll ratio for large trucks is even higher than the maximum optimal toll ratio found in the numerical experiments. This suggests that the tolls for large trucks are set on the basis of revenue generation principles while the passenger car tolls are being set based on a mild form of welfare maximization. This leads to a suboptimal cross-subsidization of passenger car traffic in detriment of an important sector of the economy.     

Rationing and pricing strategies for congestion mitigation: Behavioral theory,econometric model,and application in Beijing

Some travel demand management policies such as road pricing have been widely studied in literature. Rationing policies, including vehicle ownership quota and vehicle usage restrictions, have been implemented in several megaregions to address congestion and other negative transportation externalities, but not well explored in literature. Other strategies such as Vehicle Mileage Fee have not been well accepted by policy makers, but attract growing research interest. As policy makers face an increasing number of policy tools, a theoretical framework is needed to analyze these policies and provide a direct comparison of their welfare implications such as efficiency and equity. However, such a comprehensive framework does not exist in literature. To bridge this gap, this study develops an analytical framework for analyzing and comparing travel demand management policies, which consists of a mathematical model of joint household vehicle ownership and usage decisions and welfare analysis methods based on compensating variation and consumer surplus. Under the assumptions of homogenous users and single time period, this study finds that vehicle usage rationing performs better when relatively small percentages of users (i.e. low rationing ratio) are rationed off the roads and when induced demand elasticity resulting from congestion mitigation is low. When the amount of induced demand exceeds a certain level, it is shown analytically that vehicle usage restrictions will always cause welfare losses. When the policy goal is to reduce vehicle travel by a fixed portion, road pricing provides a larger welfare gain. The performance of different policies is influenced by network congestion and congestibility. This paper further generalizes the model to consider heterogenous users and demonstrates how it can be applied for policy analysis on a real network after careful calibration.     

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.     

Drivers’ willingness-to-pay to reduce travel time: evidence from the San Diego I-15 congestion pricing project

The adoption of congestion pricing depends fundamentally upon drivers’ willingness to pay to reduce travel time during the congested morning peak period. Using revealed preference data from a congestion pricing demonstration project in San Diego, we estimate that willingness to pay to reduce congested travel time is higher than previous stated preference results. Our estimate of median willingness to pay to reduce commute time is roughly $30 per hour, although this may be biased upward by drivers’ perception that the toll facility provides safer driving conditions. Drivers also use the posted toll as an indicator of abnormal congestion and increase their usage of the toll facility when tolls are higher than normal.     

Equilibrium at a bottleneck when long-run and short-run scheduling preferences diverge

We consider the use of a Vickrey road bottleneck in the context of repetitive scheduling choices, distinguishing between long-run and short-run scheduling preferences. The preference structure reflects that there is a distinction between the (exogenous) ‘long-run preferred arrival time’, which would be relevant if consumers were unconstrained in the scheduling of their activities, and the ‘short-run preferred arrival time’, which is the result of an adaptation of travel routines in the face of constraints caused by, in particular, time-varying congestion levels. We characterize the unpriced equilibrium, the social optimum as well as second-best situations where the availability of the pricing instruments is restricted. All of them entail a dispersed distribution of short-run preferred arrival times. We obtain the intriguing results that the dispersion is lower in the social optimum than in the unpriced equilibrium, and that the application of first-best short-run tolls does not induce efficient long-run choices of travel routines.     

A dynamic cordon pricing scheme combining the Macroscopic Fundamental Diagram and an agent-based traffic model

Pricing is considered an effective management policy to reduce traffic congestion in transportation networks. In this paper we combine a macroscopic model of traffic congestion in urban networks with an agent-based simulator to study congestion pricing schemes. The macroscopic model, which has been tested with real data in previous studies, represents an accurate and robust approach to model the dynamics of congestion. The agent-based simulator can reproduce the complexity of travel behavior in terms of travelers’ choices and heterogeneity. This integrated approach is superior to traditional pricing schemes. On one hand, traffic simulators (including car-following, lane-changing and route choice models) consider travel behavior, i.e. departure time choice, inelastic to the level of congestion. On the other hand, most congestion pricing models utilize supply models insensitive to demand fluctuations and non-stationary conditions. This is not consistent with the physics of traffic and the dynamics of congestion. Furthermore, works that integrate the above features in pricing models are assuming deterministic and homogeneous population characteristics. In this paper, we first demonstrate by case studies in Zurich urban road network, that the output of a agent-based simulator is consistent with the physics of traffic flow dynamics, as defined by a Macroscopic Fundamental Diagram (MFD). We then develop and apply a dynamic cordon-based congestion pricing scheme, in which tolls are controlled by an MFD. And we investigate the effectiveness of the proposed pricing scheme. Results show that by applying such a congestion pricing, (i) the savings of travel time at both aggregated and disaggregated level outweigh the costs of tolling, (ii) the congestion inside the cordon area is eased while no extra congestion is generated in the neighbor area outside the cordon, (iii) tolling has stronger impact on leisure-related activities than on work-related activities, as fewer agents who perform work-related activities changed their time plans. Future work can apply the same methodology to other network-based pricing schemes, such as area-based or distance-traveled-based pricing. Equity issues can be investigated more carefully, if provided with data such as income of agents. Value-of-time-dependent pricing schemes then can also be determined.     

Quantifying the benefit of responsive pricing and travel information in the stochastic congestion pricing problem

This paper is concerned with roadway pricing amidst the uncertainty which characterizes long-term transportation planning. Uncertainty is considered both on the supply-side (e.g., the effect of incidents on habitual route choice behavior) and on the demand-side (e.g., due to prediction errors in demand forecasting). The framework developed in this paper also allows the benefits of real-time travel information to be compared directly against the benefits of responsive pricing, allowing planning agencies to identify the value of these policy options or contract terms in publicly-operated toll roads. Specifically, six scenarios reflect different combinations of policy options, and correspond to different solution methods for optimal tolls. Demonstrations are provided on both the Sioux falls and Anaheim networks. Results indicate that providing information to drivers implemented alongside responsive tolling may reduce expected total system travel time by over 9%, though more than 8% of the improvement is due to providing information, with the remaining 1% improvement gained from responsive tolling.     

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.     

Estimating commuter mode choice: A discrete choice analysis of the impact of road pricing and parking charges

Automobile use leads to external costs associated with emissions, congestion, noise and other impacts. One option for minimizing these costs is to introduce road pricing and parking charges to reduce demand for single occupant vehicle (SOV) use, while providing improvements to alternatives to encourage mode switching. However, the impact of these policies on urban mode choice is uncertain, and results reported from regions where charging has been introduced may not be transferable. In particular, revealed preference data associated with cost recovery tolls on single facilities may not provide a clear picture of driver response to tolls for demand management. To estimate commuter mode choice behaviour in response to such policies, 548 commuters from a Greater Vancouver suburb who presently drive alone to work completed an individually customized discrete choice experiment (DCE) in which they chose between driving alone, carpooling or taking a hypothetical express bus service when choices varied in terms of time and cost attributes. Attribute coefficients identified with the DCE were used in a predictive model to estimate commuter response to various policy oriented combinations of charges and incentives. Model results suggest that increases in drive alone costs will bring about greater reductions in SOV demand than increases in SOV travel time or improvements in the times and costs of alternatives beyond a base level of service. The methods described here provide an effective and efficient way for policy makers to develop an initial assessment of driver reactions to the introduction of pricing policies in their particular regions.     

Effects of alternative road pricing systems on network performance

Four road pricing systems, with charges based on cordons crossed, distance travelled, time spent travelling and time spent in congestion, have been tested using the congested assignment network model SATURN and its elastic assignment demand response routine, SATEASY. All tests have been based on a SATURN application of the city of Cambridge, with charges imposed inside an appropriate ring of bypasses. While initial results showed that congestion pricing achieved the greatest increase in average speed in the charged area, later analysis cast doubt on its superiority. Congestion pricing is able to distinguish more effectively the extent to which different types of journey contribute to congestion and achieves given reductions in travel at lower levels of charge. However, it is much less effective in reducing distance travelled and, by encouraging use of minor roads, may achieve far smaller environmental benefits. Time-based pricing performs better than the other systems on most indicators. Generally, the results suggest that when rerouting effects are included in the predictive modelling process the benefits of road pricing may be significantly smaller than previously expected.