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.     

Pareto-improving congestion pricing and revenue refunding with multiple user classes

This study investigates Pareto-improving congestion pricing and revenue refunding schemes in general transportation networks, which make every road user better off as compared with the situation without congestion pricing. We consider user heterogeneity in value of time (VOT) by adopting a multiclass user model with fixed origin–destination (OD) demands. We first prove that an OD and class-based Pareto-improving refunding scheme exists if and only if the total system monetary travel disutility is reduced. In view of the practical difficulty in identifying individual user’s VOT, we further investigate class-anonymous refunding schemes that give the same amount of refund to all user classes traveling between the same OD pair regardless of their VOTs. We establish a sufficient condition for the existence of such OD-specific but class-anonymous Pareto-improving refunding schemes, which needs information only on the average toll paid and average travel time for trips between each OD pair.     

The independence of volume-capacity ratio of private toll roads in general networks

In a general traffic network under some widely used assumptions, this paper proves that the level of service, represented by the volume-capacity (v/c) ratio, offered by a profit-maximizing private firm on a private toll road is independent of another competitor’s choice of capacity and toll rate for another private toll road. The v/c ratio will be the same as the one provided by a centralized welfare-maximizing traffic authority. Moreover, the ratio remains the same even in a regulated market where the authority imposes a cap for the generalized travel cost on the private toll road.     

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.     

Development and comparison of choice models and tolling schemes for high-occupancy/toll (HOT) facilities

A high-occupancy/toll (HOT) lane is an increasingly popular form of traffic management strategy which reserves a set of freeway lanes for HOVs and transit users, while allowing low-occupancy vehicles (LOVs) to enter for a fee. In turn, HOT lanes maintain a minimal level of service by regulating the volume of entering LOVs. The focus of this paper is how to model the choice process of individual drivers, which dictates the volume of LOVs that choose to pay and take the HOT lane. Such models and the insights they provide can be very helpful for the toll setting process. Two simple formulations (an all-or-nothing assignment and an additive logit model) are compared with a proposed formulation based on the population value of time (VOT) distribution. Both static and dynamic toll setting algorithms are studied based on the proposed lane choice model, and their performance is compared under deterministic traffic behavior.     

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.     

Minimizing CO2e emissions by setting a road toll

The main purpose of this paper is to develop a bi-level pricing model to minimize the CO₂e emissions and the total travel time in a small road network. In the lower level of the model, it is assumed that users of the road network find a dynamic user equilibrium which minimizes the total costs of those in the system. For the higher level of the model, different road toll strategies are applied in order to minimize the CO₂e emissions. The model has been applied to an illustrative example. It shows the effects on traffic flows, revenues, total time and CO₂e emissions for different numbers of servers collecting tolls and different pricing strategies over a morning peak traffic period. The results show that the CO₂e emissions produced can be significantly affected by the number of servers and the type of toll strategy employed. The model is also used to find the best toll strategy when there is a constraint on the revenue that is required to be raised from the toll and how this affects the emissions produced. Further runs compare strategies to minimize the CO₂e emissions with those that minimize total travel time in the road system. In the illustrative example, the results for minimizing CO₂e emissions are shown to be similar to the results obtained from minimizing the total travel time.     

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.     

The influence of (toll-related) travel costs in residential location decisions of households: A stated choice approach

In this paper, we investigate the impact of travel costs, in particular toll costs, on the residential location choice of households, using a stated choice survey. Within the stated choice experiment, car drivers that frequently face traffic congestion, traded-off several trip-related (including toll costs) and house/location-related factors in their decision where to locate. If we look at the influence of different variables, toll and fuel costs seem to be important. Respondents are more sensitive to travel costs (i.e. toll and fuel costs) than to equally high (monthly) housing costs. Travel time appears to play a less important role, as indicated by a low value of time (VOT). In addition, location-related factors, such as the type of location and the number of bedrooms, turn out to be important factors as well. It can be concluded that respondents generally speaking prefer to pay higher housing costs and accept longer travel times to avoid (high) travel costs. Finally, if we look at the difference in preferences in relation to toll and fuel cost, we can conclude that toll costs are valued more negatively than fuel costs, although the differences are small.     

The analysis of regulation on private highway investment under a build-operate-transfer scheme

The build-operate-transfer (BOT) approach has become an attractive instrument for public facility provision, especially for a project that faces difficulty with public finance. This study analyzes the regulation alternatives on private highway investment under a BOT scheme and their impacts on traffic flows, travel costs, toll, capacity, and social welfare (total user-benefit in the traffic system including congestion). For comparison, five cases are analyzed: (1) No BOT with maximizing welfare, (2) No BOT with breaking even on finance, (3) BOT without regulation, (4) BOT with a minimum flow constraint (the total users will not be less than those in Case 1), and (5) BOT with a maximum travel cost constraint (the travel cost for users on a non-tolled road will not exceed the maximum tolerance). After each case is modeled and simulated on some functional forms, we find that the case of BOT with regulations performs between the cases of maximizing welfare and that of maximizing profit. From the perspective of the government, regulation has less power in a project with low elastic demand. Furthermore, even when the regulation is strict, a high cost-efficient firm with BOT could result in a higher level of social welfare than that without a BOT scheme.     

Autonomous cars and dynamic bottleneck congestion: The effects on capacity,value of time and preference heterogeneity

‘Autonomous cars’ are cars that can drive themselves without human control. Autonomous cars can safely drive closer together than cars driven by humans, thereby possibly increasing road capacity. By allowing drivers to perform other activities in the vehicle, they may reduce the value of travel time losses (VOT). We investigate the effects of autonomous cars using a dynamic equilibrium model of congestion that captures three main elements: the resulting increase in capacity, the decrease in the VOT for those who acquire one and the implications of the resulting changes in the heterogeneity of VOTs. We do so for three market organizations: private monopoly, perfect competition and public supply. Even though an increased share of autonomous cars raises average capacity, it may hurt existing autonomous car users as those who switch to an autonomous car will impose increased congestion externalities due to their altered departure time behaviour. Depending on which effect dominates, switching to an autonomous vehicle may impose a net negative or positive externality. Often public supply leads to 100% autonomous cars, but it may be optimal to have a mix of car types, especially when there is a net negative externality. With a positive (negative) externality, perfect competition leads to an undersupply (oversupply) of autonomous cars, and a public supplier needs to subsidise (tax) autonomous cars to maximise welfare. A monopolist supplier ignores the capacity effect and adds a mark-up to its price.     

Characteristics of truck traffic in Singapore

This paper presents the results of a project conducted to study the characteristics of truck traffic in Singapore. Detailed traffic surveys recording counts of vehicles by axle-configuration were performed at 219 sites over a period of nearly two years. The surveys covered 5 different road classes, namely expressways, arterials, collectors, industrial roads and local roads. It was found that the time distribution of truck travel were not the same among the five road classes. The peaking characteristics of truck traffic were less pronounced compared to passenger car traffic. The peak hour truck volume varied from 67.0% to 9.7% of the daily truck traffic as compared to 13.8% for passenger car traffic. The lane distribution pattern of truck traffic was studied in detail by road class, and was found to be a function of total directional traffic volume, total directional truck volume and the number of traffic lanes. Composition analysis was also carried out to study the lane use characteristics of single- and multiple-unit trucks.     

Bayesian network-based formulation and analysis for toll road utilization supported by traffic information provision

Congestion pricing has been proposed and investigated as an effective means of optimizing traffic assignment, alleviating congestion, and enhancing traffic operation efficiencies. Meanwhile, advanced traffic information dissemination systems, such as Advanced Traveler Information System (ATIS), have been developed and deployed to provide real-time, accurate, and complete network-wide traffic information to facilitate travelers’ trip plans and routing selections. Recent advances in ATIS technologies, especially telecommunication technology, allow dynamic, personalized, and multimodal traffic information to be disseminated and impact travelers’ choices of departure times, alternative routes, and travel modes in the context of congestion pricing. However, few studies were conducted to determine the impact of traffic information dissemination on toll road utilizations. In this study, the effects of the provisions of traffic information on toll road usage are investigated and analyzed based on a stated preference survey conducted in Texas. A Bayesian Network (BN)-based approach is developed to discover travelers’ opinions and preferences for toll road utilization supported by network-wide traffic information provisions. The probabilistic interdependencies among various attributes, including routing choice, departure time, traffic information dissemination mode, content, coverage, commuter demographic information, and travel patterns, are identified and their impacts on toll road usage are quantified. The results indicate that the BN model performs reasonably well in travelers’ preference classifications for toll road utilization and knowledge extraction. The BN Most Probable Explanation (MPE) measurement, probability inference and variable influence analysis results illustrate travelers using highway advisory radio and internet as their primary mode of receiving traffic information are more likely to comply with routing recommendations and use toll roads. Traffic information regarding congested roads, road hazard warnings, and accident locations is of great interest to travelers, who tend to acquire such information and use toll roads more frequently. Travel time formation for home-based trips can considerably enhance travelers’ preferences for toll road usage. Female travelers tend to seek traffic information and utilize toll roads more frequently. As expected, the information provided at both pre-trip and en-route stages can positively influence travelers’ preferences for toll road usage. The proposed methodology and research findings advance our previous study and provide insight into travelers’ behavioral tendencies concerning toll road utilization in support of traffic information dissemination.     

Enhanced traffic information dissemination to facilitate toll road utilization: a nested logit model of a stated preference survey in Texas

This paper investigates the effects of the provision of traffic information on toll road usage based on a stated preference survey conducted in central Texas. Although many researchers have studied congestion pricing and traffic information dissemination extensively, most of them focused on the effects that these instruments individually produce on transportation system performance. Few studies have been conducted to elaborate on the impacts of traffic information dissemination on toll road utilization. In this study, 716 individuals completed a survey to measure representative public opinions and preferences for toll road usage in support of various traffic information dissemination classified by different modes, contents, and timeliness categories. A nested logit model was developed and estimated to identify the significant attributes of traffic information dissemination, traveler commuting patterns, routing behavior, and demographic characteristics, and analyze their impacts on toll road utilization. The results revealed that the travelers using dynamic message sign systems as their primary mode of receiving traffic information are more likely to choose toll roads. The potential toll road users also indicated their desire to obtain traffic information via internet. Information regarding accident locations, road hazard warnings, and congested roads is frequently sought by travelers. Furthermore, high-quality congested road information dissemination can significantly enhance travelers’ preferences of toll road usage. Specifically the study found that travelers anticipated an average travel time saving of about 11.3 min from better information; this is about 30 % of travelers’ average one-way commuting time. The mean value of the time savings was found to be about $11.82 per hour, close to ½ of the average Austin wage rate. The model specifications and result analyses provide in-depth insights in interpreting travelers’ behavioral tendencies of toll road utilization in support of traffic information. The results are also helpful to shape and develop future transportation toll system and transportation policy.     

Private road competition and equilibrium with traffic equilibrium constraints

Toll road competition is one of the important issues under a build-operate-transfer (BOT) scheme, which is being encountered nowadays in many cities. When there are two or more competing firms and each firm operates a competitive toll road, their profits are interrelated due to the competitors' choices and demand inter-dependence in the network. In this paper we develop game-theoretic approaches to the study of the road network, on which multiple toll roads are operated by competitive private firms. The strategic interactions and market equilibria among the private firms are analyzed both in determining their supply (road capacity) and price (toll level) over the network. The toll road competition problems in general traffic equilibrium networks are formulated as an equilibrium program with equilibrium constraints or bi-level variational inequalities. Heuristic solution methods are proposed and their convergences are demonstrated with simple network examples. It is shown that private pricing and competition can be both profitable and welfare-improving.     

Tollroads are only part of the overall trip: the error of our ways in past willingness to pay studies

With rare exception, actual tollroad traffic in many countries has failed to reproduce forecast traffic levels, regardless of whether the assessment is made after an initial year of operation or as long as 10 years after opening. Pundits have offered many reasons for this divergence, including optimism bias, strategic misrepresentation, the promise to equity investors of early returns on investment, errors in land use forecasts, and specific assumptions underlying the traffic assignment models used to develop traffic forecasts. One such assumption is the selection of a behaviourally meaningful value of travel time savings (VTTS) for use in a generalised cost or generalised time user benefit expression that is the main behavioural feature of the traffic assignment (route choice) model. Numerous empirical studies using stated choice experiments have designed choice sets of alternatives as if users choose a tolled route or a free route under the (implied) assumption that the tolled route is tolled for the entire trip. Reality is often very different, with a high incidence of use of a non-tolled road leading into and connecting out of a tolled link. In this paper we recognise this feature of route choice and redesign the stated choice experiment to account for it. Furthermore, this study is a follow up to a previous study undertaken before a new toll road was in place, and it benefits from real exposure to the new toll road. We find that the VTTS is noticeably reduced, and if the VTTS is a significant contributing influence on errors on traffic forecasts, then the lower estimates make sense behaviourally.     

Fatal crash involvement by multiple-trailer trucks

Considerable uncertainty surrounds the relative safety of combination trucks with two or three trailers, compared to those pulling single trailers. This article uses data on conditions present in 5889 fatal crashes involving combination trucks to examine the extent to which these conditions vary for the two configurations. Using two complementary techniques, multiple classification analysis and automatic interaction detector, we evaluate the additive and interactive effects of these conditions. We conclude that multiple-trailer trucks are more likely to be involved in fatal crashes in the following conditions: darkness; snow, slush, or ice on the road surface; involvement of three or more vehicles, indicating at least moderate traffic volume; and higher-speed facilities with 65 to 75 mph limits.     

The effect of the competition between cars and trucks on the evolution of the motorway transport system

Motorways, which were devised at the beginning of their history as dedicated roads intended to be traveled by cars only, are at present also traveled by considerable flows of trucks. This fact has deeply changed the motorway transport system with respect to its original conception, owing to the interactions between two categories of vehicles whose characteristics are very different. These interactions greatly increase the transport cost perceived by car drivers with respect to truck drivers. This paper studies the consequences of this cost asymmetry on the evolution of the transport system when the geometric characteristics of a motorway remain unchanged in time, while transport demand increases. By using a theoretical model of competition between cars and trucks, it is shown that, if both the geometric characteristics of a motorway and the increase rate of the activities that feed the transport demand remain unchanged over time, the competition between cars and trucks, as well as the fact that in general passengers have better transport alternatives than freight, make the increase rate of truck traffic greater than that of cars, causing a progressive increase in the proportion of trucks in the time periods in which a motorway is traveled by both the vehicle categories. Since truck traffic on motorways, at least in Europe, is very scarce on weekends and in holiday periods, in which motorways are traveled almost only by cars, these results seem to indicate a tendency to the specialization of motorways, which are likely to be used in the future mostly by only one category of vehicles in different periods of time.     

An econometric analysis of motorway renewal costs in Germany

The analysis of motorway renewal costs presented in this paper was driven by two research questions: First, to analyse the economic process of motorway renewal work and to identify whether there exist economies of scale; and second to identify the influence of traffic volume on renewal costs and to derive an estimate of marginal infrastructure costs as part of optimal road user charges. The analysis is based on cross-sectional data for motorway renewal costs and traffic volume in Germany during the period 1980–1999. Two translog models were estimated, each of them including the factor input prices for labour, material and capital, and a set of regional dummy variables as well as dummy variables for the type of material used for renewal. The first model includes in addition to these variables the sqm of renewed road as explanatory variable. The second model was constructed to analyse the relationship between traffic volume and renewal costs and contains the average annual daily traffic volume of trucks and passenger cars as independent variables. Two main results were derived from the models: First, motorway renewal work is characterised by substantial economies of scale. Second, the relationship between renewal costs and traffic volume is expressed by a cost elasticity, i.e., the ratio between marginal and average costs, which ranges from 0.05 up to 1.17 with a digressive increase of marginal costs.