How much is too much for tolled road users: Toll saturation and the implications for car commuting value of travel time savings?

The current practice of forecasting the demand for new tolled roads typically assumes that car users are prepared to pay a higher toll for a shorter journey, and they will keep doing so as long as the toll cost is not higher than their current value of travel time savings. Practice ignores the possibility that there could be a point when motorists stop driving on toll roads due to a toll budget constraint. The unconstrained toll budget assumption may be valid in networks where the addition of a new toll road does not result in a binding budget constraint that car users may have for using toll roads (although it could also be invoked for existing tolled routes through a reduction in use of a tolled route). In a road network like Sydney which offers a growing number of (linked) tolled roads, the binding budget constraint may be invoked, and hence including additional toll links might in turn reduce the car users’ willingness to pay for toll roads to save the same amount of travel time. When this occurs, car users are said to reach a toll saturation point (or threshold) and begin to consider avoiding one or more toll roads. Whilst toll saturation has important implications for demand forecasting and planning of toll roads, this type of behaviour has not been explored in the literature. We investigate the influence that increasing toll outlays has on preferences of car commuters to use one or more tolled roads as the number of tolled roads increases. The Sydney metropolitan area offers a unique laboratory to test this phenomenon, with nine tolled roads currently in place and another five in planning. The evidence supports the hypothesis that the value of travel time savings decreases as a consequence of toll saturation.     

Dynamic congestion pricing with day-to-day flow evolution and user heterogeneity

This paper investigates evolutionary implementation of congestion pricing schemes to minimize the system cost and time, measured in monetary and time units, respectively, with the travelers’ day-to-day route adjustment behavior and their heterogeneity. The travelers’ heterogeneity is captured by their value-of-times. First, the multi-class flow dynamical system is proposed to model the travelers’ route adjustment behavior in a tolled transportation network with multiple user classes. Then, the stability condition and properties of equilibrium is examined. We further investigate the trajectory control problem via dynamic congestion pricing scheme to derive the system cost, time optimum, and generally, Pareto optimum in the sense of simultaneous minimization of system cost and time. The trajectory control problem is modeled by a differential–algebraic system with the differential sub-system capturing the flow dynamics and the algebraic one capturing the pricing constraint. The explicit Runge–Kutta method is proposed to calculate the dynamic flow trajectories and anonymous link tolls. The method allows the link tolls to be updated with any predetermined periods and forces the system cost and/or time to approach the optimum levels. Both analytical and numerical examples are adopted to examine the efficiency of the method.     

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.     

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.     

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

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

A discrete dynamical system of formulating traffic assignment: Revisiting Smith’s model

Through relaxing the behavior assumption adopted in Smith’s model (Smith, 1984), we propose a discrete dynamical system to formulate the day-to-day evolution process of traffic flows from a non-equilibrium state to an equilibrium state. Depending on certain preconditions, the equilibrium state can be equivalent to a Wardrop user equilibrium (UE), Logit-based stochastic user equilibrium (SUE), or boundedly rational user equilibrium (BRUE). These equivalence properties indicate that, to make day-to-day flows evolve to equilibrium flows, it is not necessary for travelers to choose their routes based on actual travel costs of the previous day. Day-to-day flows can still evolve to equilibrium flows provided that travelers choose their routes based on estimated travel costs which satisfy these preconditions. We also show that, under a more general assumption than the monotonicity of route cost function, the trajectory of the dynamical system converges to a set of equilibrium flows by reasonably setting these parameters in the dynamical system. Finally, numerical examples are presented to demonstrate the application and properties of the dynamical system. The study is helpful for understanding various processes of forming traffic jam and designing an algorithm for calculating equilibrium flows.     

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.     

Value of time – A citizen perspective

The dominant empirical approach to infer Value of Time is based on experiments in which respondents are typically asked to make hypothetical travel choices as if they were paying travel costs from their own budget, in exchange for personal travel time gains. However, many scholars have argued that such travel choice decisions of individuals in their role of consumer of mobility are likely to be a poor proxy of how they in their role of citizen believe government should spend tax money to generate travel time gains for large numbers of travelers. So far, this possible deviation between what we call ‘consumer VoT’ and ‘citizen VoT’ has not been studied empirically. In this paper, we fill this gap, by designing a Stated Choice experiment with eight different frames; some representing a typical consumer choice situation, others gradually approaching a citizen perspective. We find that individuals’ willingness to pay from previously collected tax money for travel time gains created by a government policy, is significantly higher than their willingness to pay, from their after tax income, for time gains obtained by choosing a different route. This result implies that citizen VoT is higher than consumer VoT. This difference does not stem from a stronger willingness to spend previously collected tax money compared to spending one’s own income, but from a difference in the value attached to travel gains: a travel time gain resulting from government action is valued more than the same travel time gain obtained by one’s own route choices. This and a range of other empirical results are discussed in depth, in light of the conceptual differences between preferences of individuals in a role of consumer or citizen.     

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).     

Optimal locations and travel time display for variable message signs

This paper first develops a network equilibrium model with the travel time information displayed via variable message signs (VMS). Specifically, the equilibrium considers the impact of the displayed travel time information on travelers’ route choices under the recurrent congestion, with the endogenous utilization rates of displayed information by travelers. The existence of the equilibrium is proved and an iterative solution procedure is provided. Then, we conduct the sensitivity analyses of the network equilibrium and further propose a paradox, i.e., providing travel time information via VMS to travelers may degrade the network performance under some poor designs. Therefore, we investigate the problem of designing the VMS locations and travel time display within a given budget, and formulate it as a mixed integer nonlinear program, solved by an active-set algorithm. Lastly, numerical examples are presented to offer insights on the equilibrium results and optimal designs of VMS.     

Comparative analysis of three user equilibrium models under stochastic demand

Recent empirical studies on the value of time and reliability reveal that travel time variability plays an important role on travelers' route choice decision process. It can be considered as a risk to travelers making a trip. Therefore, travelers are not only interested in saving their travel time but also in reducing their risk. Typically, risk can be represented by two different aspects: acceptable risk and unacceptable risk. Acceptable risk refers to the reliability aspect of acceptable travel time, which is defined as the average travel time plus the acceptable additional time (or buffer time) needed to ensure more frequent on‐time arrivals, while unacceptable risk refers to the unreliability aspect of unacceptable late arrivals (though infrequent) that have a travel time excessively higher than the acceptable travel time. Most research in the network equilibrium based approach to modeling travel time variability ignores the unreliability aspect of unacceptable late arrivals. This paper examines the effects of both reliability and unreliability aspects in a network equilibrium framework. Specifically, the traditional user equilibrium model, the demand driven travel time reliability‐based user equilibrium model, and the α‐reliable mean‐excess travel time user equilibrium model are considered in the investigation under an uncertain environment due to stochastic travel demand. Numerical results are presented to examine how these models handle risk under travel time variability.     

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.     

Multi-class percentile user equilibrium with flow-dependent stochasticity

Travelers often reserve a buffer time for trips sensitive to arrival time in order to hedge against the uncertainties in a transportation system. To model the effects of such behavior, travelers are assumed to choose routes to minimize the percentile travel time, i.e. the travel time budget that ensures their preferred probability of on-time arrival; in doing so, they drive the system to a percentile user equilibrium (UE), which can be viewed as an extension of the classic Wardrop equilibrium. The stochasticity in the supply of transportation are incorporated by modeling the service flow rate of each road segment as a random variable. Such stochasticity is flow-dependent in the sense that the probability density functions of these random variables, from which the distribution of link travel time are constructed, are specified endogenously with flow-dependent parameters. The percentile route travel time, obtained by directly convolving the link travel time distributions in this paper, is not available in closed form in general and has to be numerically evaluated. To reveal their structural properties, percentile UE solutions are examined in special cases and verified with numerical results. For the general multi-class percentile UE traffic assignment problem, a variational inequality formulation is given and solved using a route-based algorithm. The algorithm makes use of the diagonal elements in the Jacobian of percentile route travel time, which is approximated through recursive convolution. Preliminary numerical experiments indicate that the algorithm is able to achieve highly precise equilibrium solutions.     

Traveler route choice: Travel time implications of improved information and adaptive decisions

The Wardrop user equilibrium model states that travelers choose the fastest available route and always choose the same route on repeated trips. However, travelers are not always capable of choosing the fastest route, and if travel time is uncertain, they may acquire information on the day of travel that helps to select a better route. Thus, travelers can reduce their travel time over the Wardrop “optimum” by selecting routes adaptively. The focus of this paper is to find the most promising approach for improving actual transit route choice through providing better traveler information. Actual and ideal travel time were estimated for each of six information scenarios, ranging from one where travelers use transit maps, to one where travelers use adaptive route choice, and to the hypothetical situation referred to as perfect information. Travelers using maps and travelers using maps and schedules took significantly longer than ideally possible on an experimental trip (24% longer with maps, 42% longer with maps and schedules). Ideal travel time under perfect information was 49% less than actual travel time with no information, and 6% less than that of the best non-adaptive decision rule. Time adaptive route choice resulted in no travel time reduction. The potential travel time improvement from giving travelers more information was not as great as that from making information more understandable. Adaptive route choice did not offer great potential on the studied trip. To be effective there must be several nearly equal route options, and trips must involve transfers, which excludes most travel on transit today.     

Commercially managed road funds: managing roads like a business,not like a bureaucracy

Nearly all countries are seriously short of revenues for investment and maintenance of roads. Improving utilization of the existing road budget has helped to narrow, but not eliminate, this financing gap. Requests for additional resources from the government's budget have fallen on deaf ears, because the road sector has grown too large to be fully-financed through general tax revenues. Government tax systems were not designed to finance major economic sectors like roads. Faced with an acute shortage of funds, many road agencies have introduced tolls on high-volume roads and have invited the private sector to build and operate such roads under concession agreements. Although this has narrowed the financing gap, tolling is only economic on a small part of the road network. Tolls have thus had a relatively small impact on the financing gap. Against this background, and mindful of the fact that roads are now 'big business' on the scale of the Fortune Global 500, a growing number of countries have started to 'bring roads into the market place, put them on a fee-for-service basis and manage them like a business.' The fee-for-service concept, though superficially like the user-pay principle and the associated road funds which became popular during the 1950s, differs from user-pay in a number of important respects. The key differences are that: (i) only road user charges go into the road fund (i.e., there are no earmarked taxes); (ii) the fund is managed by a representative board with half or more members representing road users and the business community; (iii) members are nominated by the constituencies they represent and there is an independent chairperson; (iv) financing arrangements are designed to ensure that money is not diverted from other sectors; (v) funds are managed pro-actively by a small secretariat; (vi) there are published financial regulations governing the way funds are managed; (vii) charges are adjusted regularly to meet agreed expenditure targets; and (viii) there are regular technical and financial audits. Other important characteristics are that most commercially managed road funds are managed through a separate road fund administration, funds are channeled to all roads (sometimes even to unclassified roads) and they are introduced as part of a wider agenda to commercialize road management. Some of these road funds have been set up as road public utilities under a board with powers to set their own tariffs.     

Evaluation of exclusive bus lanes in a bi-modal degradable road network

In this paper, we proposed an evaluation method of exclusive bus lanes (EBLs) in a bi-modal degradable road network with car and bus transit modes. Link travel time with and without EBLs for two modes is analyzed with link stochastic degradation. Furthermore, route general travel costs are formulated with the uncertainty of link travel time for both modes and the uncertainty of waiting time at a bus stop and in-vehicle congestion costs for the bus mode. The uncertainty of bus waiting time is considered to be relevant to the degradation of the front links of the bus line. A bi-modal user equilibrium model incorporating travelers’ risk adverse behavior is proposed for evaluating EBLs. Finally, two numerical examples are used to illustrate how the road degradation level, travelers’ risk aversion level and the front link’s correlation level with the uncertainty of the bus waiting time affect the results of the user equilibrium model with and without EBLs and how the road degradation level affects the optimal EBLs setting scheme. A paradox of EBLs setting is also illustrated where adding one exclusive bus lane may decrease share of bus.     

Users’ perceptions and willingness to pay in interurban toll roads: identifying differences across regions from a nationwide survey in Spain

Users’ acceptability is considered one of the key drivers for the successful implementation of transport policy measures. This is especially crucial in the case of toll roads since they are financed through drivers’ contributions. Previous literature in this field has mainly focused on measuring users’ attitudes towards urban congestion pricing strategies. However limited research has been developed concerning interurban toll roads. Previous research shows that socioeconomic variables are not conclusive to explain users’ perceptions towards tolls. By contrast, other drivers such as regional differences seem to play a more important role, especially when charging conditions within the same nation greatly vary across regions. This paper analyzes regional differences in users’ attitudes within an asymmetrical distribution of the toll road network across regions. Based on a nationwide survey conducted to road users in interurban toll roads in Spain, we develop both a binomial logit and a censored regression (tobit) model to explore drivers’ perceptions and willingness to pay. The research concludes that users from regions with a more extensive tolled network generally show a more negative attitude towards charges, but not necessarily a lower willingness to pay. The paper also points out that an asymmetrical distribution of toll roads across regions may result in negative perceptions among those users perceiving to be unfairly treated when compared to citizens in other regions.     

Design of income-equitable toll prices for high occupancy toll lanes in a single toll facility

Income inequity potentially exists under high occupancy toll (HOT) lanes whereby higher-income travelers may reap the benefits of the facility. An income-based multi-toll pricing approach is proposed for a single HOT lane facility in a network to maximize simultaneously the toll revenue and address the income equity concern, while ensuring a minimum level-of-service on the HOT lanes and that the toll prices do not exceed pre-specified thresholds. The problem is modeled as a bi-level optimization formulation. The upper level model maximizes revenue for the tolling authority subject to pre-specified upper bounds on tolls. The lower level model solves the stochastic user equilibrium problem. An agent-based solution approach is used to determine the toll prices by considering the tolling authority and commuters as agents. Results from numerical experiments indicate that a multi-toll pricing scheme is more equitable and can yield higher revenues compared to a single toll price scheme across travelers.     

Solving the Pareto-improving toll problem via manifold suboptimization

Congestion tolls are considered to be Pareto-improving if they reduce travel delay or improve social benefit and ensure that, when compared to the situation without any tolling intervention, no user is worse off in terms of travel cost measured, e.g., in units of time. The problem of finding Pareto-improving tolls can be formulated as a mathematical program with complementarity constraints, a class of optimization problems difficult to solve. Using concepts from manifold suboptimization, we propose a new algorithm that converges to a strongly stationary solution in a finite number of iterations. The algorithm is also applicable to the problem of finding approximate Pareto-improving tolls and can address the cases where demands are either fixed or elastic. Numerical results using networks from the literature are also given.