Modeling intermodal equilibrium for bimodal transportation system design problems in a linear monocentric city

This paper investigates the intermodal equilibrium, road toll pricing, and bus system design issues in a congested highway corridor with two alternative modes - auto and bus - which share the same roadway along this corridor. On the basis of an in-depth analysis of the demand and supply sides of the bimodal transportation system, the mode choice equilibrium of travelers along the continuum corridor is first presented and formulated as an equivalent variational inequality problem. The solution properties of the bimodal continuum equilibrium formulation are analytically explored. Two models, which account for different infrastructure/system regulatory regimes (public and private), are then proposed. In the public regulatory model, the road toll location and charge level are simultaneously optimized together with the bus service fare and frequency. In the private regulatory model, the fare and frequency of bus services, which are operated by a profit-driven private operator, are optimized for exogenously given toll pricing schemes. Finally, an illustrative example is given to demonstrate the application of the proposed models. Sensitivity analysis of residential/household distribution along the corridor is carried out together with a comparison of four different toll pricing schemes (no toll, first best, distance based, and location based). Insightful findings are reported on the interrelationships among modal competition, market regulatory regimes, toll pricing schemes, and urban configurations as well as their implications in practice.     

Modelling route choice behaviour in a tolled road network with a time surplus maximisation bi-objective user equilibrium model

In this paper, we propose a novel approach to model route choice behaviour in a tolled road network with a bi-objective approach, assuming that all users have two objectives: (1) minimise travel time; and (2) minimise toll cost. We assume further that users have different preferences in the sense that for any given path with a specific toll, there is a limit on the time that an individual would be willing to spend. Different users can have different preferences represented by this indifference curve between toll and time. Time surplus is defined as the maximum time minus the actual time. Given a set of paths, the one with the highest (or least negative) time surplus will be the preferred path for the individual. This will result in a bi-objective equilibrium solution satisfying the time surplus maximisation bi-objective user equilibrium (TSmaxBUE) condition. That is, for each O–D pair, all individuals are travelling on the path with the highest time surplus value among all the efficient paths between this O–D pair.We show that the TSmaxBUE condition is a proper generalisation of user equilibrium with generalised cost function, and that it is equivalent to bi-objective user equilibrium. We also present a multi-user class version of the TSmaxBUE condition and demonstrate our concepts with illustrative examples.     

The impact of speed limits on traffic equilibrium and system performance in networks

Speed limits are usually imposed on roads in an attempt to enhance safety and sometimes serve the purpose of reducing fuel consumption and vehicular emissions as well. Most previous studies up to date focus on investigation of the effects of speed limits from a local perspective, while network-wide traffic reallocation effects are overlooked. This paper makes the first attempt to investigate how a link-specific speed limit law reallocates traffic flow in an equilibrium manner at a macroscopic network level. We find that, although the link travel time–flow relationship is altered after a speed limit is imposed, the standard traffic assignment method still applies. With the commonly adopted assumptions, the uniqueness of link travel times at user equilibrium (UE) remains valid, and the UE flows on links with non-binding speed limits are still unique. The UE flows on other links with binding speed limits may not be unique but can be explicitly characterized by a polyhedron or a linear system of equalities and inequalities. Furthermore, taking into account the traffic reallocation effects of speed limits, we compare the capability of speed limits and road pricing for decentralizing desirable network flow patterns. Although from a different perspective for regulating traffic flows with a different mechanism, a speed limit law may play the same role as a toll charge scheme and perform better than some negative (rebate) toll schemes under certain conditions for network flow management.     

Modeling the impact of government guarantees on toll charge,road quality and capacity for Build-Operate-Transfer (BOT) road projects

Government guarantees are frequently used to attract private investors’ participation into Build-Operate-Transfer (BOT) road projects. In this paper, we investigate the impact of government guarantees on toll charge, road quality and road capacity by taking perspective of the private investor. The main results are: (1) Minimum traffic guarantee increases toll charge while decreasing road quality. Under a low guarantee level, minimum traffic guarantee has no impact on road capacity. However, it improves road capacity when a high guarantee level is performed. (2) Under minimum revenue guarantee, if the guarantee level is sufficiently high, the optimal toll charge will be sufficiently large, but road quality and road capacity will approach zero. (3) Price compensation guarantee decreases toll charge and increases both road quality and road capacity. This paper further investigates the impact of government guarantees when the contract is auctioned. We find that auction reduces the impact of government guarantees on toll charge while failing to affect the impact of government guarantees on road quality and capacity. Some policy implications are also derived from our model results.     

Viability of new road infrastructure with heterogeneous users

This paper explores the importance of heterogeneity in value of time and route choice when assessing the viability of new road infrastructure to alleviate congestion problems. The model incorporates strategic interaction between road operators in a cost-benefit framework and several competitive regimes are considered. It is then employed to establish the financial and socio-economic viability of a congestion pricing demonstration entering Madrid city centre, where road users have to choose between a free but highly congested road and a priced free-flowing road (semi-private regime). A logit estimation is undertaken with information from a questionnaire among road users in the Eastern Madrid area to obtain users’ value of time and of congestion.The tolls obtained generate a traffic reallocation towards the new roadway such that revenues suffice to render the infrastructure socio-economically viable. The private and the low toll regimes generate similar welfare gains that are close to the first best. Yet the former supposes large losses to users. The low toll and the semi-private regimes do not raise such distributional concerns. However, the low toll regime requires a sufficiently high traffic growth rate to make it financially viable; this does not happen for the other competitive regimes.     

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.     

Highway pricing and capacity choice in a road network under a build–operate–transfer scheme

It is often argued lately that the private sector should be allowed to build and operate roads in a transportation network at its own expense, in return it should receive the revenue from road toll charge within some years, and then these roads will be transferred to the government. This type of build–operate–transfer (B–O–T) projects is currently fashionable worldwide, especially for developing countries short of funds for road construction. One of the important issues concerning a highway B–O–T project is the selection of the capacity and toll charge of the new road and the evaluation of the relevant benefits to the private investor, the road users and the whole society under various market conditions. This paper deals with the selection and evaluation of a highway project under such a B–O–T scheme. For a given road network with elastic demand, mathematical models are proposed to investigate the feasibility of a candidate project and ascertain the optimal capacity and level of toll charge of the new highway. The response of road users to the new B–O–T project is explicitly considered. The characteristic of the problem is illustrated graphically with a numerical example.     

Profit maximization by a private toll road with cars and trucks

This paper examines the profit maximizing behavior of a private firm which operates a toll road competing against a free alternative in presence of cars and trucks. Trucks differ from cars in value of time (VOT), congestion externality, pavement damage, and link travel time function. We find that the firm takes either a car-strategy or a truck-strategy for profit maximization. For a traffic mix with relatively large car volume and small truck volume, the car-strategy results in no trucks using the toll road, while the truck-strategy results in all trucks using the toll road. We derive the equilibrium flow pattern under any combination of car-toll and truck-toll, based on which we identify a profit-maximizing frontier and a strategy-switching frontier in the car-toll and truck-toll two-dimensional space. By geometrically comparing the two frontiers, we establish general conditions under which each strategy will be taken, which suggest that the truck-to-car VOT ratio, the total traffic demand, and the difference in travel distance between the two roads are critical in shaping the firm's strategy.     

Toll pricing framework under logit‐based stochastic user equilibrium constraints

This paper addresses the toll pricing framework for the first‐best pricing with logit‐based stochastic user equilibrium (SUE) constraints. The first‐best pricing is usually known as marginal‐cost toll, which can be obtained by solving a traffic assignment problem based on the marginal cost functions. The marginal‐cost toll, however, has rarely been implemented in practice, because it requires every specific link on the network to be charged. Thus, it is necessary to search for a substitute of the marginal cost pricing scheme, which can reduce the toll locations but still minimize the total travel time. The toll pricing framework is the set of all the substitute toll patterns of the marginal cost pricing. Assuming the users' route choice behavior following the logit‐based SUE principle, this paper has first derived a mathematical expression for the toll pricing framework. Then, by proposing an origin‐based variational inequality model for the logit‐based SUE problem, another toll pricing framework is built, which avoids path enumeration/storage. Finally, the numerical test shows that many alternative pricing patterns can inherently reduce the charging locations and total toll collected, while achieving the same equilibrium link flow pattern. Copyright © 2013 John Wiley & Sons, Ltd.     

New models for financing and managing highways: asset-based road corporations in China

The China International Engineering Consulting Corporation undertook, in 1997, the study of Viability of Asset Based Road Corporations in China as part of the World Bank's transport sector program review. The purpose was to investigate, in a case study format, road administration in China with two specific objectives: to compare (toll) road management in different provinces and to investigate the financial viability of China's toll roads.This paper shows that the three case projects studied, each having different management structures, are all financially viable given the present financing arrangements. However, should the projects be immediately subject to market interest rates and loan maturities prevailing in China today, their financial viability would be uncertain.In a broader context, the World Bank's lending program has enabled China to experiment with different kinds of toll road management structures. These models have both advantages and disadvantages and seem to fit that province's political economic environment in which they are employed. The toll roads and, especially, the impacts of the toll road management and financing arrangements on road administration present challenges to road administration rarely faced even in the developed countries. The challenges involve questions of the congruence of public good and private interest, as well as the role of planning and public accountability – all serious questions as China moves forward in development. These questions are raised in the context of the case studies.     

Toll Roads in Australia: An Overview of Characteristics and Accuracy of Demand Forecasts

Abstract

A primary motivation of this paper is to draw together, in one source, information on the nature, extent and performance of Australia's evolving toll road network which is currently spread across many disparate published and unpublished sources. This paper provides key information (e.g. length, toll rates, year opened, operator(s) and payment alternatives) on all of the fully interoperable toll roads in Australia that are present in Sydney (e.g. the M2, M4, M5, etc.), Melbourne (CityLink and EastLink) and Brisbane (the Gateway Bridge, the Logan Motorway and the Gateway Extension). Where available, we compare and discuss actual traffic levels and forecasts, revealing the sizeable gap or ‘error’ in forecasts, especially during the first year of operation. Ordinary least squares regression and panel random effects regression models are developed to identify potential sources of explanation of differences in error forecasts between the Australian toll roads at various points post the opening date. A separate analysis of a sample of toll roads in the USA was also undertaken that supports the main findings from the Australian toll road network. Key influences on errors in forecasts are the capacity of a toll road, the elapsed time that the toll road has been in place, the specific period of time in which a tolled road is introduced into the network (which influences the complexity of route options including multiple tolled routes and hence toll saturation), the length of the tolled route, the presence of cash payment and the charging regime (i.e. fixed vs. distance‐based or variable user tolls).     

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.     

Optimal choice of capacity,toll and government guarantee for build-operate-transfer roads under asymmetric cost information

The private provision of public roads via the build-operate-transfer (BOT) mode has been increasingly used around the world. By viewing a BOT contract as a combination of road capacity, toll and government guarantee, this paper investigates optimal concession contract design under both symmetric and asymmetric information about the marginal maintenance cost of private investors. Under asymmetric information, the government guarantee serves as an instrument to induce a private investor to reveal his true cost information. Compared with the situation under symmetric information, the government will suffer a loss of social welfare; the private investor will charge a higher toll that increases in his reported marginal maintenance cost, and specify a lower capacity that decreases with the reported cost. The results also show that the private investor obtains extra information rent beyond the reservation level of return and the rent decreases with his reported cost. However, the resulting volume-capacity ratios of the BOT road under both information structures are the same.     

Joint road toll pricing and capacity development in discrete transport network design problem

The paper demonstrates a method to determine road network improvements that also involve the use of a road toll charge, taking the perspective of the government or authority. A general discrete network design problem with a road toll pricing scheme, to minimize the total travel time under a budget constraint, is proposed. This approach is taken in order to determine the appropriate level of road toll pricing whilst simultaneously addressing the need for capacity. The proposed approach is formulated as a bi-level programming problem. The optimal road capacity improvement and toll level scheme is investigated with respect to the available budget levels and toll revenues.     

Impact of congestion charging on the transit market: An inter-modal equilibrium model

An inter-modal equilibrium model links an urban road network subject to a congestion charge to a parallel urban transit market, with a view to finding the optimum congestion charge consistent with the commercial decisions of the transit operator(s). A congestion charge is set to maximise social surplus. Travel behaviour is assumed to conform to elastic-demand user equilibrium traffic assignment. The transit market is assumed to be either a profit maximising monopoly or a profit maximising duopoly competing non-cooperatively. The operator(s) set the fares to maximise profits and the supply of transit services are determined by the resulting demand. The problem has been formulated as a bi-level programme with the determination of the congestion charge on the upper level and the setting of transit fares on the lower level. In the case of non-cooperating operators, the Bertrand–Nash equilibrium fares are sought. The results of the model are analysed for a small example based loosely on Edinburgh. This reveals the importance of competition in the transit market for the trade off between the government, the transit provider(s) and the travellers.     

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.     

Speed limits,speed selection and network equilibrium

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

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.     

The strategic transportation research study — Its origins and purposes

The highway industry in the United States spends about $35 to $40 billion annually. Management of the industry is almost wholly decentralized. This decentralization plus diminishing fuel tax revenues used to finance road improvements have caused road research efforts to decline to a very low level. Comparisons between funds for highway research and those spent by private firms in similar industries show that private firms spend from 5 to 12 times the rate of highway agencies. The problem of how much to spend on research is difficult both for private-sector and for public-sector enterprises. The level of research spending is shown to correlate well with both profitability and growth in U.S. firms. Four methods used for making research decisions in the private sector are discussed. The goals of the Strategic Transportation Research Study (STRS), which is being conducted by the Transportation Research Board to examine highway and transportation needs, are described.     

Sensitivity analysis on stochastic equilibrium transportation networks using genetic algorithm

This study deals with the sensitivity analysis of an equilibrium transportation networks using genetic algorithm approach and uses the bi‐level iterative sensitivity algorithm. Therefore, integrated Genetic Algorithm‐TRANSYT and Path Flow Estimator (GATPFE) is developed for signalized road networks for various level of perceived travel time in order to test the sensitivity of perceived travel time error in an urban stochastic road networks. Level of information provided to drivers correspondingly affects the signal timing parameters and hence the Stochastic User Equilibrium (SUE) link flows. When the information on road system is increased, the road users try to avoid conflicting links. Therefore, the stochastic equilibrium assignment concept tends to be user equilibrium. The GATPFE is used to solve the bi‐level problem, where the Area Traffic Control (ATC) is the upper‐level and the SUE assignment is the lower‐level. The GATPFE is tested for six‐junction network taken from literature. The results show that the integrated GATPFE can be applied to carry out sensitivity analysis at the equilibrium network design problems for various level of information and it simultaneously optimize the signal timings (i.e. network common cycle time, signal stage and offsets between junctions).