Optimal congestion taxes in a time allocation model

The purpose of this paper is to study optimal congestion taxes in a time-allocation framework. This makes it possible to distinguish taxes on inputs in the production of car trips and taxes on transport as an activity. Moreover, the model allows us to consider the implications of treating transport as a demand, derived from other activities. We extend several well known tax rules from the public finance literature and carefully interpret the implications for the optimal tax treatment of passenger transport services. The main findings of the paper are the following. First, if governments are limited to taxing market inputs into transport trip production, the time-allocation framework: (i) provides an argument for taxing congestion below marginal external cost, (ii) implies a favourable tax treatment for time-saving devices such as GPS, and (iii) provides a previously unnoticed argument for public transport subsidies. Second, if the government has access to perfect road pricing that directly taxes transport as an activity, all previous results disappear. Third, in the absence of perfect road pricing, the activity-specific congestion attracted by employment centres, by shopping centres or by large sports and cultural events should be corrected via higher taxes on market inputs in these activities (e.g., entry tickets, parking fees, etc.).     

Congestion-aware system optimal route choice for shared autonomous vehicles

We study the shared autonomous vehicle (SAV) routing problem while considering congestion. SAVs essentially provide a dial-a-ride service to travelers, but the large number of vehicles involved (tens of thousands of SAVs to replace personal vehicles) results in SAV routing causing significant congestion. We combine the dial-a-ride service constraints with the linear program for system optimal dynamic traffic assignment, resulting in a congestion-aware formulation of the SAV routing problem. Traffic flow is modeled through the link transmission model, an approximate solution to the kinematic wave theory of traffic flow. SAVs interact with travelers at origins and destinations. Due to the large number of vehicles involved, we use a continuous approximation of flow to formulate a linear program. Optimal solutions demonstrate that peak hour demand is likely to have greater waiting and in-vehicle travel times than off-peak demand due to congestion. SAV travel times were only slightly greater than system optimal personal vehicle route choice. In addition, solutions can determine the optimal fleet size to minimize congestion or maximize service.     

The tax treatment of company cars, commuting and optimal congestion taxes

In Europe, the preferential tax treatment of company cars implies that many employees receive a company car as part of their compensation package. In this paper, we consider a model in which wages and the decision whether or not to provide a company car are the result of direct negotiation between employer and employee. Using this framework, we theoretically and numerically study first- and second-best optimal tax policies on labour and transport markets, focusing on the role of the tax treatment of company cars. We obtain the following results. First, higher labour taxes and a more favourable tax treatment of company cars raise the fraction employees that receives a company car; congestion and congestion tolls reduce it. Second, in countries that provide large implicit subsidies to company cars, eliminating the preferential tax treatment of company cars may be an imperfect but quite effective substitute for currently unavailable congestion tolls. The numerical illustration, calibrated using Belgian data, suggests that it yields about half the welfare gain attainable through optimal congestion taxes. Third, the favourable tax treatment of company cars justifies large public transport subsidies; the numerical results are consistent with zero public transport fares. Finally, we find that earlier models that ignored the preferential tax treatment of company cars may have substantially underestimated optimal congestion tolls in Europe. The numerical illustration suggests that about one third of the optimal congestion toll we obtain can be attributed to the current tax treatment of company cars.     

E-commerce and traffic congestion: An economic and policy analysis

E-commerce, due to its ability to re-direct consumers from physical stores to online, can potentially alleviate traffic congestion. In this paper, we set up a theoretic model to analyze interactions between a firm’s distribution strategy and traffic congestion. In an unregulated economy, we first characterize the private firm’s optimal strategy concerning e-commerce under the influence of traffic congestion. We then examine a centralized economy where the firm is publicly owned and derive the distribution strategy that maximizes social welfare. Comparing the two cases, we show that the private firm’s incentives may deviate from the socially optimal decisions, which leads to inefficiency. We identify two effects, i.e., monopoly effect and congestion externality effect, which drive the private firm to deviate from the social optimum. Based on our analysis, we propose a differentiated tolls/rebates policy to achieve maximum social welfare. Under such a policy, the firm will not only adopt the socially optimal distribution strategy but offer the socially optimal quantities.     

On the degradation of performance for traffic networks with oblivious users

We consider the problem of characterizing user equilibria and optimal solutions for routing in a given network. We extend the known models by considering users oblivious to congestion in the following sense: While in the typical user equilibrium setting the users follow a strategy that minimizes their individual cost by taking into account the (dynamic) congestion due to the current routing pattern, an oblivious user ignores congestion altogether; instead, he or she decides his routing on the basis of cheapest routes on a network without any flow whatsoever. These cheapest routes can be, for example, the shortest paths in the network without any flow. This model tries to capture the fact that a certain percentage of travelers base their route simply on the distances they observe on a map, without thinking (or knowing, or caring) about the delays experienced on this route due to their fellow travelers. In this work we study the effect of such users using as the measure of network performance its price of anarchy, i.e., the ratio of the total latency experienced by the users (oblivious or not) at equilibrium over the social optimum.     

A framework to evaluate policy options for supporting electric vehicles in urban freight transport

Electric vehicles (EVs) are considered as a feasible alternative to traditional vehicles. Few studies have addressed the impacts of policies supporting EVs in urban freight transport. To cast light on this topic, we established a framework combining an optimization model with economic analysis to determine the optimal behavior of an individual delivery service provider company and social impacts (e.g., externalities and welfare) in response to policies designed to support EVs, such as purchase subsidy, limited access (zone fee) to congestion/low-emission zones with exemptions for EVs, and vehicle taxes with exemptions for EVs. Numerical experiments showed that the zone fee can increase the company’s total logistics costs but improve the social welfare. It greatly reduced the external cost inside the congestion/low-emission zone with a high population, dense pollution, and heavy traffic. The vehicle taxes and subsidy were found to have the same influence on the company and society, although they have different effects with low tax/subsidy rates because their different effects on vehicle routing plans. Finally, we performed a sensitivity analysis. Local factors at the company and city levels (e.g., types of vehicle and transport network) are also important to designing efficient policies for urban logistics that support EVs.     

No entry for congestion taxes?

This paper reviews some of the recent thinking on the theory of congestion taxes and considers some of the reasons why little practical interest has been shown in them despite the existence of an extensive academic literature. Recent developments in the theory suggest that the concept of an optimal congestion tax may be a somewhat utopian one, but if some measure of traffic restriction is desired, it is argued that congestion taxes have advantages over possible alternative non-pricing approaches. The costs of developing and operating congestion tax schemes are seen as a substantial deterrent to their use in practice, but it is argued that the political costs involved are perhaps of more fundamental significance.     

Using the revenues from congestion pricing

The economic theory behind congestion pricing relies on using the revenues to help compensate highway users. But can practical methods of using revenues come close to achieving this compensation, and still have salient appeal to important political groups? This paper investigates the possibilities for designing a package of revenue uses that can achieve these twin goals. The suggested approach returns two-thirds of the revenues to travelers through travel allowances and tax reductions, and uses the rest to improve transportation throughout the area, including affected business centers. By replacing regressive sales and fuel taxes, this approach offsets the tendency of the prices alone to have a regressive distributional impact. By lowering taxes, funding new highways, improving transit, and upgrading business centers, the package provides inducements for support from several key interest groups. The potential amounts of money involved are discussed using nationwide data, and in more detail using a case study of ubiquitous facility pricing throughout the Los Angeles region. Illustrative calculations of the effects on various individuals confirm that such a package can create net benefits for a wide spectrum of people and interest groups.     

The characteristics of congested flow on a freeway across lanes,space, and time

For the most part, previous studies of freeway flow kinematics and dynamics (especially relating to schock wave propagation and to the fundamental diagram) have looked only at flow within a single lane. However, the perturbations in flow which make the dynamics interesting—and of practical importance—normally arise in multiple lane settings. This study examines flow-occupancy dynamics at the onset of congestion by taking into consideration the flows across all the lanes, individually. The results show that just prior to the onset of congestion, flow rates in the shoulder lane are only about 50% of the flows in the median and middle lanes. As the congestion moves upstream through a data collection station, flow rates in the two fast lanes decrease, but flow rates in the shoulder lane invariably increase. After the onset of congested operations, all three tend toward the same average occupancy and speed. These results provide support for an earlier suggestion that discontinuous flow-concentration functions are not necessary, and also help to resolve some of the questions raised by that earlier suggestion.     

How much should gasoline be taxed when electric vehicles conquer the market? An analysis of the mismatch between efficient and existing gasoline taxes under emerging electric mobility

The taxation of gasoline is characterized by large variability across countries and recent research has analyzed existing gasoline tax levels from an economic efficiency point of view focusing on conventional internal combustion engine vehicles. Most studies find that existing fuel tax rates do not coincide with economically efficient levels. As long as policymakers do not take action to reduce the resulting efficiency gap, there will be an ongoing welfare loss to the economy. However, the composition of passenger car fleets will probably be subject to fundamental changes in the (near) future due to the emergence of electric mobility. This raises the question of whether the mismatch between current and efficient fuel taxation will persist, shrink, or even exacerbate under emerging electric mobility. This paper aims at answering this question by determining the structure and level of optimal gasoline taxes in the presence of electric vehicles (EVs). First, the optimal (nationwide) gasoline tax is analytically derived employing a general equilibrium approach. It is shown that differences in traffic related marginal external costs among fuel powered cars and EVs affect the corrective Pigouvian component of the optimal gasoline tax while a differential tax treatment influences the fiscal rational of the tax. Second, the model is applied to Germany using differentiated data on e.g. external costs and behavioral responses. Under a wide range of scenarios, the present analyses indicate a strong relationship between optimal gasoline taxes and electric mobility, calling for a downward adjustment of efficient gasoline taxes. The effect is mainly driven by financial incentives for purchasing and using EVs. Since fuel is likely to be undertaxed in many countries, the emergence of electric mobility will therefore close the gap between gasoline taxes in place and economically efficient taxes. On the other side, it will increase the efficiency gap in those countries where gasoline is overtaxed. This also has important implications for policy concerned with environmental objectives. Pushing electric mobility seriously and at the same time taxing gasoline efficiently could actually prevent sufficient CO₂ emission savings. However, at least in the case of Germany, even a downward adjusted optimal gasoline tax under electric mobility is likely to be higher than the current (non-optimal) tax.     

How to road price in a world with electric vehicles and government budget constraints

In this paper we examine what characterizes second-best road prices targeting external costs from driving electric (EV) and conventional (ICEV) vehicles when there are distortionary labor taxes and binding government budget constraints. Further, we examine how this second-best pricing fits with government set goals of reducing CO₂ emissions. The paper further develops an analytical framework for assessing first- and second-best road prices on vehicle kilometers, extending it to include EVs and externalities that vary geographically and by time of day. We find that optimal road prices largely vary with external cost, but are also significantly affected by the interactions with the rest of the fiscal system. Not surprisingly, the highest road prices should be for ICEVs in large cities during peak hours due to high external costs. More surprisingly, we find that the road price for ICEVs in rural areas should be lower than that for EVs due to large fiscal interaction effects. These road prices give large welfare gains, but they lead to no reduction in carbon emissions when applying the currently recommended social cost of carbon.     

Convexity and robustness of dynamic traffic assignment and freeway network control

We study the use of the System Optimum (SO) Dynamic Traffic Assignment (DTA) problem to design optimal traffic flow controls for freeway networks as modeled by the Cell Transmission Model, using variable speed limit, ramp metering, and routing. We consider two optimal control problems: the DTA problem, where turning ratios are part of the control inputs, and the Freeway Network Control (FNC), where turning ratios are instead assigned exogenous parameters. It is known that relaxation of the supply and demand constraints in the cell-based formulations of the DTA problem results in a linear program. However, solutions to the relaxed problem can be infeasible with respect to traffic dynamics. Previous work has shown that such solutions can be made feasible by proper choice of ramp metering and variable speed limit control for specific traffic networks. We extend this procedure to arbitrary networks and provide insight into the structure and robustness of the proposed optimal controllers. For a network consisting only of ordinary, merge, and diverge junctions, where the cells have linear demand functions and affine supply functions with identical slopes, and the cost is the total traffic volume, we show, using the Pontryagin maximum principle, that variable speed limits are not needed in order to achieve optimality in the FNC problem, and ramp metering is sufficient. We also prove bounds on perturbation of the controlled system trajectory in terms of perturbations in initial traffic volume and exogenous inflows. These bounds, which leverage monotonicity properties of the controlled trajectory, are shown to be in close agreement with numerical simulation results.     

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

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

A traffic assignment model for a ridesharing transportation market

A nascent ridesharing industry is being enabled by new communication technologies and motivated by the many possible benefits, such as reduction in travel cost, pollution, and congestion. Understanding the complex relations between ridesharing and traffic congestion is a critical step in the evaluation of a ridesharing enterprise or of the convenience of regulatory policies or incentives to promote ridesharing. In this work, we propose a new traffic assignment model that explicitly represents ridesharing as a mode of transportation. The objective is to analyze how ridesharing impacts traffic congestion, how people can be motivated to participate in ridesharing, and, conversely, how congestion influences ridesharing, including ridesharing prices and the number of drivers and passengers. This model is built by combining a ridesharing market model with a classic elastic demand Wardrop traffic equilibrium model. Our computational results show that (i) the ridesharing base price influences the congestion level, (ii) within a certain price range, an increase in price may reduce the traffic congestion, and (iii) the utilization of ridesharing increases as the congestion increases. Copyright © 2014 John Wiley & Sons, Ltd.     

The time-dependent pollution-routing problem

The Time-Dependent Pollution-Routing Problem (TDPRP) consists of routing a fleet of vehicles in order to serve a set of customers and determining the speeds on each leg of the routes. The cost function includes emissions and driver costs, taking into account traffic congestion which, at peak periods, significantly restricts vehicle speeds and increases emissions. We describe an integer linear programming formulation of the TDPRP and provide illustrative examples to motivate the problem and give insights about the tradeoffs it involves. We also provide an analytical characterization of the optimal solutions for a single-arc version of the problem, identifying conditions under which it is optimal to wait idly at certain locations in order to avoid congestion and to reduce the cost of emissions. Building on these analytical results we describe a novel departure time and speed optimization algorithm for the cases when the route is fixed. Finally, using benchmark instances, we present results on the computational performance of the proposed formulation and on the speed optimization procedure.     

Empirical analysis of heterogeneous traffic flow and calibration of porous flow model

Heterogeneous traffic flow, characterized by a free inter-lane exchange, has become an important issue in addressing congestion in urban areas. It is of particular interest in many developing countries, that experience a strong increase in motorcycle use. New approaches to the heterogeneous non-lane-based flow have been proposed. However insufficient empirical verification has been made to estimate vehicle interaction, that is necessary for an accurate representation of mixed-flow conditions. In this paper, we focus on the porous flow approach to capture the complex interactions. The parameters from this approach are estimated from empirical observations. Video data was recorded and processed to capture vehicle interactions at a number of road sections in Surabaya City, Indonesia. The specific behavior of each vehicle in the traffic flow was captured by developing the pore size–density distributions, analyzing the class-specific critical pore sizes, and producing the class specific speed–density and flow–density diagrams. The results reveal how critical pore sizes are based on pore size–density distributions, the flow diagram for each vehicle class, and how traffic flow relationships for motorcyclists and the other vehicles exhibit significant differences. It is concluded that the proposed approach can represent the specific behavior of the motorcyclist in heterogeneous traffic flow, in both the situations of with- and without an exclusive lane for motorcycles, can clarify motorcyclist’s behavior in terms of passenger car unit of motorcycle, and can therefore support policy making on the improvement of urban transport.     

Integrating congestion pricing,transit subsidies and mode choice

We model and analyze optimal (welfare maximizing) prices and design of transport services in a bimodal context. Car congestion and transit design are simultaneously introduced and consumers choose based on the full price they perceive. The optimization variables are the congestion toll, the transit fare (and hence the level of subsidies) and transit frequency. We obtain six main results: (i) the optimal car-transit split is generally different from the total cost minimizing one; (ii) optimal congestion and transit price are interdependent and have an optimal frequency attached; (iii) the optimal money price difference together with the optimal frequency yield the optimal modal split; (iv) if this modal split is used in traditional stand-alone formulations – where each mode is priced independently–resulting congestion tolls and transit subsidies and fares are consistent with the optimal money price difference; (v) self-financing of the transport sector is feasible; and (vi) investment in car infrastructure induces an increase in generalized cost for all public transport users.     

Optimal dynamic parking pricing for morning commute considering expected cruising time

This paper investigates how recurrent parking demand can be managed by dynamic parking pricing and information provision in the morning commute. Travelers are aware of time-varying pricing information and time-varying expected occupancy, through either their day-to-day experience or online information provision, to make their recurrent parking choices. We first formulate the parking choices under the User Equilibrium (UE) conditions using the Variational Inequality (VI) approach. More importantly, the System Optimal (SO) parking flow pattern and SO parking prices are also derived and solved efficiently using Linear Programming. Under SO, any two parking clusters cannot be used at the same time by travelers between more than one Origin–Destination (O–D) pairs. The SO parking flow pattern is not unique, which offers sufficient flexibility for operators to achieve different management objectives while keeping the flow pattern optimal. We show that any optimal flow pattern can be achieved by charging parking prices in each area that only depend on the time or occupancy, regardless of origins and destinations of users of this area. In the two numerical experiments, the best system performance is usually achieved by pricing the more preferred (convenient) area such that it is used up to a terminal occupancy of around 85–95%. Optimal pricing essentially balances the parking congestion (namely cruising time) and the level of convenience.     

The key principles of optimal train control—Part 2: Existence of an optimal strategy,the local energy minimization principle,uniqueness, computational techniques

We discuss the problem of finding an energy-efficient driving strategy for a train journey on an undulating track with steep grades subject to a maximum prescribed journey time. In Part 1 of this paper we reviewed the state-of-the-art and established the key principles of optimal train control for a general model with continuous control. We assumed only that the tractive and braking control forces were bounded by non-increasing speed-dependent magnitude constraints and that the rate of energy dissipation from frictional resistance was given by a non-negative strictly convex function of speed. Partial cost recovery from regenerative braking was allowed. Our aim was to minimize the mechanical energy required to drive the train. We examined the characteristic optimal control modes, studied allowable control transitions and established the existence of optimal switching points. We found algebraic formulae for the adjoint variables in terms of speed on track with piecewise-constant gradient and drew phase plots of the associated optimal evolutionary lines for the state and adjoint variables. In Part 2 we will establish integral forms of the necessary conditions for optimal switching, find general bounds on the positions of the optimal switching points, justify an extended local energy minimization principle and show how these ideas can be used to calculate the optimal strategy. We prove that an optimal strategy always exists and use a perturbation analysis to show that the optimal strategy is unique. Finally we discuss computation of optimal switching points in two realistic examples with steep grades and describe the optimal control strategies and corresponding speed profiles for a complete journey with several different allowed journey times. In practice the strategies described here have been shown to reduce the costs of energy used by as much as 20%.