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.     

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.     

Robust optimization of distance-based tolls in a network considering stochastic day to day dynamics

This paper investigates the nonlinear distance-based congestion pricing in a network considering stochastic day-to-day dynamics. After an implementation/adjustment of a congestion pricing scheme, the network flows in a certain period of days are not on an equilibrium state, thus it is problematic to take the equilibrium-based indexes as the pricing objective. Therefore, the concept of robust optimization is taken for the congestion toll determination problem, which takes into account the network performance of each day. First, a minimax model which minimizes the maximum regret on each day is proposed. Taking as a constraint of the minimax model, a path-based day to day dynamics model under stochastic user equilibrium (SUE) constraints is discussed in this paper. It is difficult to solve this minimax model by exact algorithms because of the implicity of the flow map function. Hence, a two-phase artificial bee colony algorithm is developed to solve the proposed minimax regret model, of which the first phase solves the minimal expected total travel cost for each day and the second phase handles the minimax robust optimization problem. Finally, a numerical example is conducted to validate the proposed models and methods.     

A traffic-condition-based route guidance strategy for a single destination road network

Most of existing route guidance strategies achieves user optimal equilibrium by comparing travel time. Measuring travel time, however, might be uneasy on an urban road network. To contend with the issue, the paper mainly considers easily obtained inflow and outflow of a link and road capacity as input, and proposes a route guidance strategy for a single destination road network based on the determination of free-flow or congested conditions on alternative routes. An extended strategy for a complex network and a feedback approximation for avoiding forecast are further explored. Weaknesses of the strategy are also explicitly analyzed. To test the strategy, simulation investigations are conducted on two networks with multiple parallel routes. The results indicate that the strategy is able to provide stable splitting rates and to approximate user optimal equilibrium in different conditions, in particular when traffic demand is high. This strategy has potential to be applied in an urban road network due to its simplicity and easily obtained input data. The strategy is also applicable for single destination if some alternatives and similar routes are available.     

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.     

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.     

Simultaneous determination of the equilibrium market penetration and compliance rate of advanced traveler information systems

We consider a specific advanced traveler information systems (ATIS) whose objective is to reduce drivers’ travel time uncertainty with recurrent network congestion through provision of traffic information. Since the provided information is still partial or imperfect, drivers equipped with an ATIS cannot always find the shortest travel time route and thus may not always comply with the advice provided by ATIS. Thus, there are three classes of drivers on a specific day: drivers without ATIS, drivers with ATIS but without compliance with ATIS advice, drivers with ATIS and in compliance with ATIS advice. All three classes of drivers make route choice in a stochastic manner, but with different degree of uncertainty of travel time on the network. In this paper we investigate the interactions among the three classes of drivers in an ATIS environment using a multiple behavior stochastic user equilibrium model. By assuming that the market penetration of ATIS is an increasing function of the actual private gain (time saving minus the cost associated with system use) derived from ATIS service, and the ATIS compliance rate of equipped drivers is given as the probability of the actual travel time of complied drivers being less than that of non-complied drivers, we determine the equilibrium market penetration and compliance rate of ATIS and the resulting equilibrium network flow pattern using an iterative solution procedure.     

An advanced traveler general information system for Fresno,California

This study estimates the effects of an advanced traveler general information system (ATGIS), which includes fuel consumption and health-related emissions cost information on transportation network users’ travel choice behavior for recurrent congestion conditions. The effects are estimated using four different formulations based on four different behavioral assumptions. Incorporating stochastic features in link cost estimation rather than in route choice, we provide a novel modeling approach that enables us to use transportation planning models of major metropolitan areas without a need for major computationally-expensive changes in the existing models. We examined the effects of an ATGIS on the Fresno, CA, road network and found several interesting results. First, the ATGIS impact is closely related to pre-system (prior to the implementation of an ATGIS) perceived fuel and emissions costs. Total travel time in the city can be reduced by 17% (no pre-system perceived costs) to 1% (accurate pre-system perceived costs), and even increased by 1% (higher-than-actual pre-system perceived costs). Second, the addition of emissions costs, although negligible relative to fuel and time costs, can effectively reduce total system-wide travel time by up to 1% and fuel consumption by up to 0.6% during peak hours. Third, the ATGIS can reduce annual social costs by as much as $1053 million (high gas price, no pre-system perception) to $48 million (medium gas price, accurate pre-system perception), which are comparable to social cost savings by a congestion pricing (CP) scheme in the study area.     

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.     

Morning commute problem considering route choice, user heterogeneity and alternative system optima

This paper extends the bottleneck model to study congestion behavior of morning commute and its implications to transportation economics. The proposed model considers simultaneous route and departure time choices of heterogenous users who are distinguished by their valuation of travel time and punctual arrival. Moreover, two dynamic system optima are considered: one minimizes system cost in the unit of monetary value (i.e., the conventional system optimum, or SO) and the other minimizes system cost in the unit of travel time (i.e., the time-based SO, or TSO). Analytical solutions of no-toll equilibrium, SO and TSO are provided and the welfare effects of the corresponding dynamic congestion pricing options are examined, with and without route choice. The analyses suggest that TSO provides a Pareto-improving solution to the social inequity issue associated with SO. Although a TSO toll is generally discriminatory, anonymous TSO tolls do exist under certain circumstances. Unlike in the case with homogenous users, an SO toll generally alters users’ route choices by tolling the poorer users off the more desirable road, which worsens social inequity. Numerical examples are presented to verify analytical results.     

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.     

First-best marginal cost toll for a traffic network with stochastic demand

First-best marginal cost pricing (MCP) in traffic networks has been extensively studied with the assumption of deterministic travel demand. However, this assumption may not be realistic as a transportation network is exposed to various uncertainties. This paper investigates MCP in a traffic network under stochastic travel demand. Cases of both fixed and elastic demand are considered. In the fixed demand case, travel demand is represented as a random variable, whereas in the elastic demand case, a pre-specified random variable is introduced into the demand function. The paper also considers a set of assumptions of traveler behavior. In the first case, it is assumed that the traveler considers only the mean travel time in the route choice decision (risk-neutral behavior), and in the second, both the mean and the variance of travel time are introduced into the route choice model (risk-averse behavior). A closed-form formulation of the true marginal cost toll for the stochastic network (SN-MCP) is derived from the variational inequality conditions of the system optimum and user equilibrium assignments. The key finding is that the calculation of the SN-MCP model cannot be made by simply substituting related terms in the original MCP model by their expected values. The paper provides a general function of SN-MCP and derives the closed-form SN-MCP formulation for specific cases with lognormal and normal stochastic travel demand. Four numerical examples are explored to compare network performance under the SN-MCP and other toll regimes.     

Predicting travel time reliability using mobile phone GPS data

Estimates of road speeds have become commonplace and central to route planning, but few systems in production provide information about the reliability of the prediction. Probabilistic forecasts of travel time capture reliability and can be used for risk-averse routing, for reporting travel time reliability to a user, or as a component of fleet vehicle decision-support systems. Many of these uses (such as those for mapping services like Bing or Google Maps) require predictions for routes in the road network, at arbitrary times; the highest-volume source of data for this purpose is GPS data from mobile phones. We introduce a method (TRIP) to predict the probability distribution of travel time on an arbitrary route in a road network at an arbitrary time, using GPS data from mobile phones or other probe vehicles. TRIP captures weekly cycles in congestion levels, gives informed predictions for parts of the road network with little data, and is computationally efficient, even for very large road networks and datasets. We apply TRIP to predict travel time on the road network of the Seattle metropolitan region, based on large volumes of GPS data from Windows phones. TRIP provides improved interval predictions (forecast ranges for travel time) relative to Microsoft’s engine for travel time prediction as used in Bing Maps. It also provides deterministic predictions that are as accurate as Bing Maps predictions, despite using fewer explanatory variables, and differing from the observed travel times by only 10.1% on average over 35,190 test trips. To our knowledge TRIP is the first method to provide accurate predictions of travel time reliability for complete, large-scale road networks.     

Equity effects of congestion pricing: Quantitative methodology and a case study for Stockholm

It is widely recognised that congestion pricing could be an effective measure to solve environmental and congestion problems in urban areas—a reform that normally also would generate a net welfare surplus. Despite this the implementation of congestion pricing has been very slow. One reason for a low public and political acceptance could be that equity impacts have not been given enough concern. In studies of distributional impacts of congestion pricing it has often been claimed that the reform is regressive rather than progressive even if there are studies claiming the opposite. We develop a method for detailed, quantitative assessment of equity effects of road pricing and apply it to a real-world example, namely a proposed congestion-charging scheme for Stockholm. The method simultaneously takes into account differences in travel behaviour, in preferences (such as values of time) and in supply of travel possibilities (car ownership, public transport level-of-service etc.). We conclude that the two most important factors for the net impact of congestion pricing are the initial travel patterns and how revenues are used. Differences in these respects dwarf differences in other factors such as values of time. This is accentuated by the fact that the total collected charges are more than three times as large as the net benefits. With respect to different groups, we find that men, high-income groups and residents in the central parts of the city will be affected the most. If revenues are used for improving public transport, this will benefit women and low-income groups the most. If revenues are used for tax cuts, the net benefits will be about equal for men and women on the average, while it naturally will benefit high-income groups. Given that it is likely that the revenues will be used to some extent to improve the public transport system, we conclude that the proposed congestion-charging scheme for Stockholm is progressive rather than regressive.     

Optimal joint distance and time toll for cordon-based congestion pricing

This paper addresses the optimal toll design problem for the cordon-based congestion pricing scheme, where both a time-toll and a nonlinear distance-toll (i.e., joint distance and time toll) are levied for each network user’s trip in a pricing cordon. The users’ route choice behaviour is assumed to follow the Logit-based stochastic user equilibrium (SUE). We first propose a link-based convex programming model for the Logit-based SUE problem with a joint distance and time toll pattern. A mathematical program with equilibrium constraints (MPEC) is developed to formulate the optimal joint distance and time toll design problem. The developed MPEC model is equivalently transformed into a semi-infinite programming (SIP) model. A global optimization method named Incremental Constraint Method (ICM) is designed for solving the SIP model. Finally, two numerical examples are used to assess the proposed methodology.     

Multimodal,multiclass stochastic dynamic traffic assignment for evaluating information provision strategies

A multimodal, multiclass stochastic dynamic traffic assignment model was developed to evaluate pre‐trip and enroute travel information provision strategies. Three different information strategies were examined: user optimum [UO], system optimum [SO] and mixed optimum [MO]. These information provision strategies were analyzed based on the levels of traffic congestion and market penetration rate for the information equipment. Only two modes, bus and car, were used for evaluating and calculating the modal split ratio. Several scenarios were analyzed using day‐to‐day and within day dynamic models. From the results analyzed, it was found that when a traffic manager provides information for drivers using the UO strategy and drivers follow the provided information absolutely, the total travel time may increases over the case with no information. Such worsening occurs when drivers switch their routes and face traffic congestion on the alternative route. This phenomenon is the 'Braess Paradox'.     

Network user equilibrium of battery electric vehicles considering flow-dependent electricity consumption

This paper addresses the equilibrium traffic assignment problem involving battery electric vehicles (BEVs) with flow-dependent electricity consumption. Due to the limited driving range and the costly/time-consuming recharging process required by current BEVs, as well as the scarce availability of battery charging/swapping stations, BEV drivers usually experience fear that their batteries may run out of power en route. Therefore, when choosing routes, BEV drivers not only try to minimize their travel costs, but also have to consider the feasibility of their routes. Moreover, considering the potential impact of traffic congestion on the electricity consumption of BEVs, the feasibility of routes may be determined endogenously rather than exogenously. A set of user equilibrium (UE) conditions from the literature is first presented to describe the route choice behaviors of BEV drivers considering flow-dependent electricity consumption. The UE conditions are then formulated as a nonlinear complementarity model. The model is further formulated as a variational inequality (VI) model and is solved using an iterative solution procedure. Numerical examples are provided to demonstrate the proposed models and solution algorithms. Discussions of how to evaluate and improve the system performance with non-unique link flow distribution are offered. A robust congestion pricing model is formulated to obtain a pricing scheme that minimizes the system travel cost under the worst-case tolled flow distribution. Finally, a further extension of the mathematical formulation for the UE conditions is provided.     

Impact analysis of cordon-based congestion pricing on mode-split for a bimodal transportation network

This paper investigates the impact of cordon-based congestion pricing scheme on the mode-split of a bimodal transportation network with auto and rail travel modes. For any given toll-charge pattern, its impact on the mode-split can be estimated by solving a combined mode-split and traffic-assignment problem. Using a binary logit model for the mode-split, the combined problem is converted into a traffic-assignment problem with elastic demand. Probit-based stochastic user equilibrium (SUE) principle is adopted for this traffic-assignment problem, and a continuously distributed value of time (VOT) is assumed to convert the toll charges and transit fares into time-units. This combined mode-split and traffic-assignment problem is then formulated as a fixed-point model, which can be solved by a convergent Cost Averaging method. The combined mode-split and traffic-assignment problem is then used to analyze a multimodal toll design problem for cordon-based congestion pricing scheme, with the aim of increasing the mode-share of public transport system to a targeted level. Taking the fixed-point model as a constraint, the multimodal toll design problem is thus formulated as a mathematical programming with equilibrium constraints (MPEC) model. A genetic algorithm (GA) is employed to solve this MPEC model, which is then numerical validated by a network example.     

Evaluating commuter opinion of congestion pricing in metropolitan Seattle

Continued growth and development in the Puget Sound region combined with existing geographic limitations have resulted in a transportation network that is at or near capacity for many hours during every weekday. Single‐occupancy vehicles (SOVs) remain the predominant mode of travel, despite a network of high‐occupancy vehicle lanes and regional transit. Given this situation, considering alternative methods to regulate traffic flow is necessary, and the implementation of a regional congestion pricing system is one such option. Although widespread throughout the world, congestion pricing has only recently been implemented in the United States.     

Optimization of transport investment and pricing policies: the role of transport pricing in network design

This paper investigates the role of transport pricing in network design and describes two facts about flow pattern in a transportation system. The first, illustrated by an example of Braess paradox, is that adding a new link to the network does not necessarily minimize the total travel time. The second is that introducing of appropriate toll pricing may reduce not only the total network time but also the travel time for each individual traveller. It follows with the investigations of different system objectives and different pricing policies (only toll pricing and distance‐based pricing are considered), and shows how they affect the system performance and flow pattern. Lastly, a systematic optimization process is proposed for integrated planning of transport network and pricing policies.