Bottleneck Model

We analyze the welfare effects of part-day teleworking on road traffic congestion in the context of Vickrey's dynamic bottleneck model. Endogenous decisions to become equipped with a teleworkingenabling technology change the commuting pattern of equipped drivers and, due to congestion externalities, affect travel costs of all drivers. We show that even costless teleworking might be marginally welfare reducing, after reaching the optimal penetration level, as an equipped driver imposes a higher travel externality on other equipped drivers than unequipped drivers do. We find that private monopolistic supply of the technology might yield a higher social welfare than perfectly competitive supply.

This paper studies the optimal multi-step toll design problem for the bottleneck model with general user heterogeneity. The design model is formulated as a mathematical program with equilibrium constraints (MPEC), which is NP-hard due to non-convexity in both the objective function and the feasible set. An analytical method is proposed to solve the MPEC by decomposing it into smaller and easier quadratic programs, each corresponding to a unique departure order of different user classes. The quadratic programs are defined on a polyhedral set, which makes it easier to identify a local optimum. Importantly, each quadratic program is constrained by a set of linear feasibility cuts that define the presence of each user class in the arrival window. We prove that the proposed method ensures global optimality provided that each quadratic program can be solved globally. To obviate enumerating all departure orders, a heuristic method is developed to navigate through the solution space by using the multipliers associated with the feasibility cuts. Numerical experiments are conducted on several small examples to validate the proposed methodology. These experiments show that the proposed heuristic method is effective in finding near-optimal solution within a relatively small number of iterations.

Theoretical and empirical studies of consumer scheduling behavior usually ignore that consumers have more flexibility to adjust their schedule in the long run than in the short run. We are able to distinguish between long-run choices of travel routines and short-run choices of departure times due to an extensive panel dataset of commuters who participate in a real-life peak avoidance experiment. We find that the participants, who obtain a monetary reward for not traveling along a camera-observed highway link during the morning peak, value travel time higher in the long-run context compared to the short run, as changes in travel time are more permanent and can be exploited better through the adjustment of routines. Schedule delays are, in contrast, valued higher in the short-run model, reflecting that scheduling restrictions are typically more binding in the short run. Since the short-run and the long-run shadow prices differ by factors ranging from 2 to 5 in our basic model, our results may have substantial impacts on optimal choices for transport policies such as pricing and investment.

This paper studies first-best and second-best congestion pricing in the presence of unobserved and observed preference heterogeneity using a stylised stochastic user equilibrium choice model. Travellers choose between multiple alternatives, have heterogeneous values of travel times, and may differ in their valuation of variety. We derive first-best and second-best tolls taking into account how the overall network demand responds to expected generalized prices, including tolls. For second-best pricing, we show that with homogeneous values of times the welfare losses of second-best pricing are smaller when route choice is probabilistic than when route choice is deterministic. Furthermore, we find that with heterogeneous values of times and benefits of variety, uniform second-best tolls and group-differentiated tolls can be very close, implying potentially low welfare losses from the inability to differentiate tolls. Finally, we show that there are cases where all groups benefit from second-best congestion pricing, but that these cases are likely to be politically unacceptable because tolls are then higher for low income groups.

Individual users often control a significant share of total traffic flows. Examples include airlines, rail and maritime freight shippers, urban goods delivery companies and passenger transportation network companies. These users have an incentive to internalize the congestion delays their own vehicles impose on each other by adjusting the timing of their trips. We investigate simultaneous trip-timing decisions by large users and small users in a dynamic model of congestion. Unlike previous work, we allow for heterogeneity of trip-timing preferences and for the presence of small users such as individual commuters and fringe airlines. We derive the optimal fleet departure schedule for a large user as a best-response to the aggregate departure rate of other users. We show that when the vehicles in a large user's fleet have a sufficiently dispersed distribution of desired arrival times, there may exist a pure-strategy Nash-equilibrium (PSNE) in which the large user schedules vehicles when there is a queue. This resolves the problem of non-existence of a PSNE identified in Silva et al. (2017) for the case of symmetric large users. We also develop some examples to identify under what conditions a PSNE exists. The examples illustrate how self-internalization of congestion by a large user can affect the nature of equilibrium and the travel costs that it and other users incur.

The variability of travel time modifies the rush hour traffic and the cost of commuting. The bottleneck model of road congestion with fixed peak-load demand is augmented of an additive random delay. When individuals have (α--) preferences, there exists a unique Nash equilibrium. The variability of travel time leads to departure rates that are spread more evenly over the rush hour than when travel times are deterministic. This equilibrium mechanism mitigates both congestion and the cost of unreliability. This implies that "single-traveler models," which treat congestion as an exogenous phenomenon, overestimate the value of reliability for the rush hour. Application with two distributions, uniform and exponential, provides an appraisal of the extent of the overestimation.

This paper investigates the existence and uniqueness of equilibrium in the Vickrey bottleneck model when each user controls a positive fraction of total traffic. Users simultaneously choose departure schedules for their vehicle fleets. Each user internalizes the congestion cost that each of its vehicles imposes on other vehicles in its fleet. We establish three results. First, a pure strategy Nash equilibrium (PSNE) may not exist. Second, if a PSNE does exist, identical users may incur appreciably different equilibrium costs. Finally, a multiplicity of PSNE can exist in which no queuing occurs but departures begin earlier or later than in the system optimum. The order in which users depart can be suboptimal as well. Nevertheless, by internalizing self-imposed congestion costs individual users can realize much, and possibly all, of the potential cost savings from either centralized traffic control or time-varying congestion tolls.

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This paper analyzes efficient pricing at a congested airport dominated by a single firm. Unlike much of the previous literature, we combine a dynamic (bottleneck) model of congestion and a vertical structure model that explicitly considers the role of airlines and passengers. We show that when a Stackelberg leader interacts with a competitive fringe, charging the congestion toll that is derived for fully atomistic carriers to both leader and fringe yields the first-best outcome. This holds regardless of the leader's internalization of congestion in the unregulated equilibrium, and regardless of the assumed demand substitution pattern between firms. This result implies that the financial deficit under optimal pricing may be less severe than what earlier studies suggest. Finally, we show that there are various alternative toll regimes that also induce the welfare maximizing outcome, and therefore widen the set of choices for regulators.

This paper considers the problem of dynamic congestion pricing which determines an optimal toll schedule to be charged at the entrance of a bottleneck on a single-destination traffic network. A two-person nonzero-sum Stacke!berg differential game model is formulated when the underlying information structure is open loop. Characteristics of the Stackelberg equilibrium solution are analyzed. The Pontryagin minimum principle is applied to derive the necessary conditions from which the open-loop Stackelberg equilibrium strategy can be obtained. The heuristic algorithm which obviates an evaluation of the gradient vector of the Hamiltonian is also proposed. Copyright

We consider commuting in a congested urban area. While an efficient time-varying toll may eliminate queuing, a toll may not be politically feasible. We study the benefit of a substitute: a parking fee at the workplace. An optimal time-varying parking fee is charged at zero rate when there is queuing and eliminates queuing when the rate is non-zero. Within certain limits, inability to charge some drivers for parking does not reduce the potential welfare gain. Drivers who cannot be charged travel when there is queuing. In some cases, interaction between morning and evening commutes can be exploited to remove queueing completely.

When drivers opt for carpooling, road capacity will be freed up, and this will reduce congestion. Therefore, carpooling is interesting for policy makers as a possible solution to congestion. We investigate the effects of carpooling in a dynamic equilibrium model of congestion, which captures various dimensions of heterogeneity: heterogeneity in preference for carpooling, "ratio heterogeneity" between the values of time and the values of schedule delay, and "proportional heterogeneity" that scales all values equally. We investigate three policy scenarios: no-toll, first-best pricing, and subsidization of carpooling. The optimal second-best subsidy equals each type's heterogeneous marginal external benefit (MEB) of switching to carpooling. If such differentiation is impossible, the third-best subsidy is a weighted average of the MEBs, where the weights depend on the number of each type and their sensitivity to the subsidy. In our numerical example, we find that when increasing the degree of "ratio heterogeneity", the relative efficiency of the second-best subsidization first increases and then falls with the degree of heterogeneity and L type carpoolers benefit more than H type carpoolers. However, when increasing the degree of "proportional heterogeneity", H type users benefit more than L types for both solo drivers and carpoolers. Moreover, the relative efficiency of the second-best subsidization decreases throughout.

In studying congestion tolling, it is important to account for heterogeneity in preferences of drivers, as ignoring it can bias the welfare gains. We analyse the effects of tolling, in the bottleneck model, with continuous heterogeneity in the value of time and schedule delay. The welfare gain of a time-variant toll increases with heterogeneity in the value of schedule delay. With heterogeneity, tolling makes the arrival ordering more efficient, and this lowers scheduling costs. If there is not much more heterogeneity in the value of time than in the value of schedule delay, then first-best tolling decreases the generalised price for most users. In our model, firstbest tolling is not most detrimental for the lowest values of time and schedule delay: it raises prices more for users with an average value of schedule delay and a slightly larger value of time. Further, the lowest values of time are among those who gain most from a public pay-lane. JEL codes: R41, R48, H23 Keywords: biases in calculated welfare effects, bottleneck model, distributional effects, heterogeneity in the value of schedule delay, heterogeneity in the value of time, second-best tolls This is a pre-print version of the article:

This paper studies whether a regulator needs to correct the route structure choice by carriers with market power in the presence of congestion externalities, in addition to correct their pricing. We account for passenger benefits from increased frequency, passenger connecting costs, airline endogenous hub location and route structure strategic competition. We find that, for some parameters, an instrument directly aimed at regulating route structure choice may be needed to maximize welfare, in addition to per-passenger and per-flight tolls designed to correct output inefficiencies. This holds true when the regulator is constrained to set non-negative tolls, but also for the case of unconstrained tolling.

We consider a monocentric city where a traffic bottleneck is located at the entrance of the central business district. The commuters' choices of the departure times from home, residential location, and lot size, are all endogenous. We show that elimination of queuing time under optimal road pricing induces individuals to spend more time at home and to have larger houses, causing urban sprawl. This is opposite to the typical results of urban models with static congestion, which predict cities to become denser with road pricing.

This paper investigates the existence and uniqueness of equilibrium in the Vickrey bottleneck model when each user controls a positive fraction of total traffic. Users simultaneously choose departure schedules for their vehicle fleets. Each user internalizes the congestion cost that each of its vehicles imposes on other vehicles in its fleet. We establish three results. First, a pure strategy Nash equilibrium (PSNE) may not exist. Second, if a PSNE does exist, identical users may incur appreciably different equilibrium costs. Finally, a multiplicity of PSNE can exist in which no queuing occurs but departures begin earlier or later than in the system optimum. The order in which users depart can be suboptimal as well. Nevertheless, by internalizing self-imposed congestion costs individual users can realize much, and possibly all, of the potential cost savings from either centralized traffic control or time-varying congestion tolls.

Due to the uncertain and dynamic environment around scheduling systems, timely revisions or reschedules of the master plans are essential for achieving optimal utilization. With the recent development of Industry 4.0 technologies, many researchers perceive the creation of cyber-physical systems as a solution for managing systems under uncertainty. This article focuses on a loading facility under uncertain truck arrivals due to road congestion and proposes utilizing real-time truck location information to improve performance. We do this by developing an integrated system consisting of a predictive model using machine learning (MC) classifiers and a mathematical model for real-time slot rescheduling. The ML classifier is used to predict the presence probabilities of all the incoming trucks at a particular slot based on the historical traffic data and the real-time truck location. Subsequently, a Mixed-Integer Quadratic Programming (MIQP) model is developed to solve a Probabilistic Slo...

This paper studies whether a regulator needs to correct the route structure choice by carriers with market power in the presence of congestion externalities, in addition to correct their pricing. We account for passenger benefits from increased frequency, passenger connecting costs, airline endogenous hub location and route structure strategic competition. We find that, for some parameters, an instrument directly aimed at regulating route structure choice may be needed to maximize welfare, in addition to per-passenger and per-flight tolls designed to correct output inefficiencies. This holds true when the regulator is constrained to set non-negative tolls, but also for the case of unconstrained tolling.

Individual users often control a significant share of total traffic flows. Examples include airlines, rail and maritime freight shippers, urban goods delivery companies and passenger transportation network companies. These users have an incentive to internalize the congestion delays their own vehicles impose on each other by adjusting the timing of their trips. We investigate simultaneous trip-timing decisions by large users and small users in a dynamic model of congestion. Unlike previous work, we allow for heterogeneity of trip-timing preferences and for the presence of small users such as individual commuters and fringe airlines. We derive the optimal fleet departure schedule for a large user as a best-response to the aggregate departure rate of other users. We show that when the vehicles in a large user's fleet have a sufficiently dispersed distribution of desired arrival times, there may exist a pure-strategy Nash-equilibrium (PSNE) in which the large user schedules vehicles when there is a queue. This resolves the problem of non-existence of a PSNE identified in Silva et al. (2017) for the case of symmetric large users. We also develop some examples to identify under what conditions a PSNE exists. The examples illustrate how self-internalization of congestion by a large user can affect the nature of equilibrium and the travel costs that it and other users incur.

This paper investigates the existence and uniqueness of equilibrium in the Vickrey bottleneck model when each user controls a positive fraction of total traffic. Users simultaneously choose departure schedules for their vehicle fleets. Each user internalizes the congestion cost that each of its vehicles imposes on other vehicles in its fleet. We establish three results. First, a pure strategy Nash equilibrium (PSNE) may not exist. Second, if a PSNE does exist, identical users may incur appreciably different equilibrium costs. Finally, a multiplicity of PSNE can exist in which no queuing occurs but departures begin earlier or later than in the social optimum. The order in which users depart can be suboptimal as well. Nevertheless, by internalizing self-imposed congestion costs individual users can realize much, and possibly all, of the potential cost savings from either centralized traffic control or time-varying congestion tolls.

Private-sector involvement in the construction and operation of roads is growing around the world and private toll roads are seen as a useful tool in the battle against congestion. Yet serious concerns remain about exercise of monopoly power if private operators can set tolls freely. A number of theoretical studies have investigated private toll-road pricing strategies, and compared them with first-best and second-best public tolls. But most of the analyses have employed simple road networks and/or used static models that do not capture the temporal dimension of congestion or describe the impacts of tolling schemes that vary by time of day. This paper takes a fresh look at private toll road pricing using METROPOLIS: a dynamic traffic simulator that treats endogenously choices of transport mode, departure time and route at the level of individual travellers. Simulations are performed for the peak-period morning commute on a stylized urban road network with jobs concentrated towards t...

This paper focuses on the interaction between two aspects of road transportation previously considered only separately-user heterogeneity and route choice. The model, which treats two groups and two parallel routes, is static, though it includes as a special case the reduced form of Vickrey's dynamic bottleneck model. In equilibrium groups may travel together or separately, depending on the relative magnitude of own-and cross-group congestion costs. Optimal tolls are solved for both integrated and separated usage. In the bottleneck case, separated usage may be optimal if one group has both higher travel time and schedule delay costs. 1. Introduction This paper focuses on the interaction between two aspects of road transportation that have previously been considered only separately-user heterogeneity and route choice. Urban and rural roads serve diverse vehicle types-cars, delivery vehicles, and trucks of various size. Furthermore, within a given vehicle class drivers may differ significantly in driving behavior, wages, scheduling constraints, and so on. For example, scheduling constraints vary with trip purpose, such as commuting, shopping, and recreation.

We analyze the market for autonomous vehicles (AVs). We show how di↵erent market structures and di↵erent rules for the available capacity utilization a↵ect the internalization of congestion externality in a setting in which there is instant information on congestion and vehicles are part of fleets, therefore displaying a non-atomistic behavior. We also show how taxation should be implemented in such a setting in order to restore e ciency.

Many airports around the world suffer from peak-load demand problems. To meet demand at the peak periods, airports need to over-invest in capacity. However, the costs associated with the peak-load problem are not only those related to the new investment but much more extensive affecting other economic agents. We use data from the airport in Gran Canaria where the peaks in capacity are associated with tourist arrivals and departures. We estimate the costs that demand peaks impose not only on agents located inside the airport, but also to the society in general. The aim of this paper is to provide a methodology for analyzing the costs imposed on those agents and to explore alternative airport policies.

Private-sector involvement in the construction and operation of roads is growing around the world and private toll roads are seen as a useful tool in the battle against congestion. Yet serious concerns remain about exercise of monopoly power if private operators can set tolls freely. A number of theoretical studies have investigated private toll-road pricing strategies, and compared them with first-best and second-best public tolls. But most of the analyses have employed simple road networks and/or used static models that do not capture the temporal dimension of congestion or describe the impacts of tolling schemes that vary by time of day. This paper takes a fresh look at private toll road pricing using METROPOLIS: a dynamic traffic simulator that treats endogenously choices of transport mode, departure time and route at the level of individual travellers. Simulations are performed for the peak-period morning commute on a stylized urban road network with jobs concentrated towards the centre of the city. Tolling scenarios are defined in terms of what is tolled (traffic lanes, whole links, or toll rings) and how tolls are varied over time. Three administration regimes are compared. The first two are the standard polar cases: social surplus maximization by a public-sector operator, and unconstrained profit maximization by a private-sector operator. The third regime entails varying tolls in steps to eliminate queuing on the tolled links. It is a form of third-best tolling that could be implemented either by a public operator or by the private sector under quality-of-service regulation. Amongst the results it is found that the no-queue tolling regime performs favourably compared to public step tolling, and invariably better than private tolling. Another provisional finding is that a private operator has less incentive than does a public operator to implement time-of-day congestion pricing.

Delay is a prominent event mostly experienced at the airport by both airline and passengers. Globally delay is permitted at 15mins later than the scheduled time. Assessing the level of delay in the airport is a major criterion for measuring airport performance. Aircraft not adhering to schedule flight results in increased airport congestion, cancellation flight and flight delay. This study made use of primary data through well-structured questionnaires to obtain information from selected NAMA Staff at the Murtala Muhammed International Airport (MMIA). Operational delay report for a month and Airlines flight were examined for two months under the MMA2 to know the deviation of scheduled flight time from actual flight time. Descriptive Analysis, Wilcoxon Rank test, Factor Analysis and Step Wise Regression were the statistical tools deployed for this research. Findings showed that on a monthly base, 63% of the domestic traffic flows are delayed. Some factors responsible for delay were considered: aircraft damage, bad weather, aircraft maintenance, VIP movement and fueling are the major factor responsible for delay of aircraft Movement.

Daily mobility patterns in highly populated urban environments rely on a well-functioning effective road network. Nevertheless, traffic bottlenecks are typical for urban environments with periodic traffic congestion. In this paper, we focus on the investigation of how traffic congestion is related with complicated crossings. First, we select an approach for the classification of the complexity of road partitions and the derivation of complicated crossings based on geodata from Open-StreetMap (OSM). Second, we calculate traffic congestions using Floating Taxi Data (FTD) from Shanghai in 2007. Then, we develop a matching technique to link the congestion and complicated crossings, and subsequently define the concept of traffic bottlenecks represented by polygons. The bottlenecks indicate locations where the transportation infrastructure is complex and traffic congestion appears periodically. Finally, we select suitable cartographic representations of traffic bottlenecks in potential thematic vehicle traffic maps.

Executive Summary Flight delay is a serious and widespread problem in the United States. Increasing flight delays place a significant strain on the US air travel system and cost airlines, passengers, and society at many billions of dollars each year. While a number of previous studies have attempted to estimate the total economic impact of delays, scientific knowledge about the cost of delay is still limited. The Federal Aviation Administration sponsored the five NEXTOR universities and the Brattle Group to conduct a ...

This paper research provides a better insight of the subject of internalization of congestion on airports. To be able to establish the hypothesis of internalization of congestion, the relationship between three measures for delay, and the level of concentration of airports, measured using the Hirschman-Herfindahl Index (HHI). The findings suggest that carriers do not account for the congestion costs when scheduling a new flight when operating on an airport. In this context, since there are no sighs that airlines internalize the congestion imposed, congestion pricing on airport is useful and could be welfare-improving. The research results reverse the findings of Brueckner (2001) and Ater (2012), which corroborate that the assumption of internalization of congestion holds, and fills in the gap in the literature by using new measures of delays.

This research shows that certain time-dependent congestion reduction schemes involving tolls have the potential for benefiting every driver even if the collected revenues are not returned to the payers. The paper considers a population of commuters who use a single bottleneck during the morning rush hour and try to arrive at work on time. It is assumed that the number of commuters is fixed (independent of the control strategy) and that each commuter wishes to pass through the bottleneck at a given time, which may differ across commuters. Commuters are otherwise identical. Each of them chooses his/her arrival time at the bottleneck so as to minimize a linear combination of monetary cost (tolls), queuing time, and deviation from the desired passage time. A time-dependent toll is applied during a time window, but some commuters are exempted from paying it. Every day, each commuter is classified as either "free" or "paying." The classification method is such that, in the long-run, the fraction of days, f, that a commuter is free is the same for all commuters, and the fraction of free commuters is f every day. Free commuters are allowed to use the bottleneck without paying the toll, whereas paying commuters can avoid the toll only if they pass through the bottleneck outside the time window. It is shown that, if commuters wish to pass through the bottleneck close together, then the toll, the window, and the fraction of free commuters can be chosen in a way that will benefit everyone by inducing an equilibrium where the "peak is smoothed out" in a particular way. Up to 25% of the total user cost can be eliminated in this way.

This research shows that certain time-dependent congestion reduction schemes involving tolls have the potential for benefiting every driver even if the collected revenues are not returned to the payers. The paper considers a population of commuters who use a single bottleneck during the morning rush hour and try to arrive at work on time. It is assumed that the number of commuters is fixed (independent of the control strategy) and that each commuter wishes to pass through the bottleneck at a given time, which may differ across commuters. Commuters are otherwise identical. Each of them chooses his/her arrival time at the bottleneck so as to minimize a linear combination of monetary cost (tolls), queuing time, and deviation from the desired passage time. A time-dependent toll is applied during a time window, but some commuters are exempted from paying it. Every day, each commuter is classified as either "free" or "paying." The classification method is such that, in the long-run, the fraction of days, f, that a commuter is free is the same for all commuters, and the fraction of free commuters is f every day. Free commuters are allowed to use the bottleneck without paying the toll, whereas paying commuters can avoid the toll only if they pass through the bottleneck outside the time window. It is shown that, if commuters wish to pass through the bottleneck close together, then the toll, the window, and the fraction of free commuters can be chosen in a way that will benefit everyone by inducing an equilibrium where the "peak is smoothed out" in a particular way. Up to 25% of the total user cost can be eliminated in this way.

Noncooperative network-formation games in oligopolies analyze optimal connection structures that emerge when linking represent the appropriation of cost-reducing one-way externalities. These models reflect situations where one firm access to another firm's (public or private) information and this last cannot refuse it. What would happen if decisions are sequential? A model of exogenous Stackelberg leadership is developed and first-mover advantages are observed and commented.

This paper considers coarse tolling of congestion under heterogeneous preferences, and especially the distributional effects of such tolls. With coarse tolling, the toll equals a fixed value during the centre of the peak; outside this period, it is zero. This paper investigates three dimensions of heterogeneity. With the first, all values of time and schedule delay vary in fixed proportions, and this heterogeneity may stem from income differences. The second has differences in flexibility of users when to arrive. The third captures differences in willingness to arrive before or after the preferred arrival time. The paper uses three models of coarse tolling: the Laih, ADL, and Braking model.
All three dimensions affect the welfare gain of coarse tolling. In the Laih model, the generalised price with coarse tolling is in between the no-toll and first-best one. In the other models this is not so, and distributional effects may be non-monotonic and very different from the first-best toll’s effects. In the Braking model, the capacity goes unused for some time during the tolled period. Compared with in the Laih model, this raises total cost, and it is most harmful for users with low values and difficulty to arrive late: e.g. low-income users with a strict work start time or a trip to the doctor.

Specification tests using stochastic bottleneck models of airport congestion investigate whether dominant airlines internalize or ignore self-imposed delays at twenty-seven major US airports. Data on flight times determine the airport's landing and takeoff delays for every minute of operation during peak travel days. Dynamic congestion functions based on stochastic-queuing theory separately identify delays that aircraft experience directly, impose internally on their airline's other aircraft, or impose externally on other airlines. Specification tests largely reject internalization and fail to reject non-internalization by dominant airlines. Optimal pricing should value all time using non-dominant aircraft time values and treat all delays as external.

Heterogeneity in preferences of users affects both the aggregate efficiency effects as the distributional effects of congestion pricing. This thesis considers two dimensions of heterogeneity. Proportional heterogeneity scales the values of time and schedule delay proportionally. More proportional heterogeneity raises the welfare gain of road pricing, because the efficiency gain from the reordering of the arrival times increases. More heterogeneity in the ratio between the value of time and value of schedule delay lowers the gain from tolling, because congestion externalities decrease.

This thesis finds that, in the bottleneck model of congestion, the distributional effects of congestion pricing are non-monotonic in the value of time and value of schedule delay. It is not users with the lowest values who lose most—or gain the least—from tolling, but an intermediate type of user. This differs from the traditional view that is based on the static flow model of congestion, and states that the higher the value of time is, the less harmful tolling is.

Preference heterogeneity also affects empirical estimates. If two heterogeneous marginal utilities are correlated, it can even bias the willingness-to-pay estimates obtained by logit estimation. The empirical chapters find that travel-cost compensation lowers price elasticities and increases the value of time and the values of restricting the timings of the travel moments.

We consider price and service-quality setting in oligopolistic markets for congestible services, applied to the case of private roads. Previous studies show that parallel competitors set a volume/capacity ratio (and thereby a travel time or service quality) that is socially optimal if they take the actions of the others as given. We find that this result does not hold when capacity and toll setting are separate stages—as then firms aim to limit toll competition by setting lower capacities, and thus higher travel times—or when firms set capacities sequentially, as then firms aim to limit the capacities of later entrants by setting higher capacities. In our Stackelberg competition, the last firm to act has no capacity decisions to influence. Hence, it is only concerned with the toll-competition substage, and sets a travel time that is longer than socially optimal. The first firm cares mostly about the competitors’ capacities that it can influence: it sets a travel time that is shorter than socially optimal. The average travel time will be too short from a societal point of view.

When analysing the effects of transport policies it is important to adequately control for heterogeneity: previous studies note that ignoring heterogeneity biases the estimated welfare effects of tolling. This paper examines the effects of tolling, in a bottleneck model, with a continuously distributed value of time. With homogeneous users, first-best public tolling has no effect on prices. With heterogeneity it does: low values of time lose, and high values of time gain. The average congestion externality decreases with the heterogeneity in the value of time. Consequently, the welfare gain of first-best tolling also decreases. The more heterogeneous the value of time is, the lower the relative efficiency of a public pay-lane. This finding contrasts with the previous literature. Earlier studies, using static flow congestion, conclude that the relative efficiency increases with this type of heterogeneity. With more heterogeneity in the value of time, the relative efficiency of a private pay-lane is also lower, while that of a public time-invariant toll is higher. Our results suggest that the welfare gains of different tolling schemes are affected differently by heterogeneity. Further, the impact of heterogeneity on the effects of a policy also depends on the type of congestion considered.

Airport congestion pricing has often been advocated as a means of controlling demand for airport operations and for achieving efficient resource allocation. Competition between airlines affects the extent to which an airline would be willing to pay for airport slots. Accurate modeling of competition is critical in order to determine the effectiveness of a congestion pricing mechanism. We develop an equilibrium model of airline frequency competition in the presence of delay costs and congestion prices. Using a small hypothetical network, we evaluate the impacts of congestion prices on the various stakeholders and investigate the dependence of effectiveness of congestion pricing on the characteristics of frequency competition in individual markets. We find that the effectiveness of congestion pricing critically depends on three essential parameters of frequency competition. Our results show that variation in the number of passengers per flight plays a vital role in determining the degree of attractiveness of congestion pricing to the airlines. A significant part of the impact of congestion pricing cannot be accounted for using the models in prior literature, which are based on the assumptions of constant load factors and constant aircraft sizes. Further, we find that, in comparison to flat pricing, marginal cost pricing is more effective in reducing congestion without penalizing the airlines with exceedingly high congestion prices.