Robin Lindsey

Economics of a bottleneck

This paper is the first in a series of papers which examine the economics of congestable facilities with peak-load demand, provides a thorough analysis of the simplest bottleneck model: A fixed number of individuals, one per car, must travel from home to work. Between home and work is a bottleneck of given capacity. The costs of travel include queuing time and schedule delay. Equilibrium with no toll, a coarse toll, and a fine toll are compared and optimal bottleneck capacity computed for each case.

Departure time and route choice for the morning commute

Most theoretical studies of traffic congestion during the morning commute have been limited to one origin, one destination, and one route. This paper is the first to analyze systematically user equilibrium, system optimum, and various pricing regimes for a simple network of routes in parallel. Departure time and route decisions of commuters are assumed to be governed by the tradeoff between travel time and schedule delay (the difference between actual and desired arrival time). In equilibrium without tolls wasteful queuing occurs, although the numbers of drivers on each route is the same as in the system optimum. An optimal time-varying toll eliminates queuing without affecting route usage. Uniform and step tolls alter route usage, but only slightly. Step tolls generally yield much greater efficiency gains than uniform tolls because they reduce queuing by altering departure times.

A temporal and spatial equilibrium analysis of commuter parking

In major cities parking costs typically exceed automobile running costs, while the time to find a parking spot and walk to work can be comparable to driving time. Yet models of urban commuting have ignored parking completely. The purpose of this paper is to examine the effects of parking on morning rush hour congestion and to assess the relative merits of road tolls and parking fees as tools for congestion relief. The paper extends Vickreys (1969) bottleneck road congestion model by assuming on-street parking is located along commuting routes radiating from the CBD. Absent pricing, drivers occupy parking spots in order of increasing distance from the CBD. Three pricing schemes are considered: 1) an optimal time-varying road toll, 2) competitively set parking fees, and 3) optimal location-dependent parking fees. The optimal road toll is shown to eliminate queueing, but does not affect the order in which parking spots are occupied. In contrast, competitive parking fees do nothing to reduce queueing , but induce drivers to park in order of decreasing distance from the CBD, so that in the aggregate commuters arrive at work closer to their preferred time. Optimal parking fees reduce queueing in addition to supporting the efficient order of parking. For reasonable parameter values competitively set parking fees are found to be relatively inefficient-indeed potentially welfare-reducing. Optimal parking fees, however, are generally superior to a road toll. In light of the logistical drawbacks of tolls and political opposition that road pricing has met, this suggests that parking fees deserve more attention than they have received in the literature.

Existence, Uniqueness, and Trip Cost Function Properties of User Equilibrium in the Bottleneck Model with Multiple User Classes

Under relatively general assumptions a unique deterministic departure-time user equilibrium with a finite departure rate exists in the bottleneck model with drivers who differ in their unit costs of travel time, preferred times of arrival, and schedule delay cost functions. Existence requires that schedule delay cost functions be upper semicontinuous with respect to arrival time, and that schedule delay costs decline at a rate smaller than the unit cost of travel time. Uniqueness requires, more restrictively, that schedule delay cost functions be continuous.Several properties of equilibrium trip cost functions are derived forn groups of users withN iin groupi. The trip cost of a user in groupi is a nondecreasing function of eachN j , but typically rises more quickly with respect toN ithanN j ,j?i. Thus, users experience lower trip costs when they travel with users unlike themselves than with an equal number of users like themselves.

Route choice with heterogeneous drivers and group-specific congestion costs☆

Abstract 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 Vickreys 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.

Reducing Urban Road Transportation Externalities: Road Pricing in Theory and in Practice

Urban road transportation creates several externalities, the most important of which are congestion (time delay and extra fuel consumption), accidents, pollution, and greenhouse gas emissions. Road pricing is widely promoted as a tool to reduce these externalities. Based on a review of theory as well as experience with existing schemes, this article draws four conclusions about urban road pricing: (1) the benefits of road pricing exceed the costs; (2) the benefits of congestion relief are larger than the benefits of improvements in environmental quality; (3) success depends in part, but only to a limited extent, on the presence of public transit and on how service is adjusted; and (4) the distributional effects and public acceptance of road pricing pose important challenges for policy design.

Properties of Dynamic Traffic Equilibrium Involving Bottlenecks, Including a Paradox and Metering

D. Braess and others have shown that creating a new link in a congested network, or adding capacity to an existing link, can raise total travel costs if drivers switch routes. Here we show that a paradox can also result when routes are fixed, but users choose when to travel. As is true of the Braess paradox, the paradox here arises when the inefficiency due to underpricing of congestion increases by more than the direct benefit of the new capacity. For a corridor with two groups of drivers, we show that expanding capacity of an upstream bottleneck raises travel costs when the reduction in congestion upstream is more than offset by increased congestion downstream. Metering can thus improve efficiency. Optimal capacity for an upstream bottleneck is equal to, or smaller than, optimal capacity downstream. Total construction costs equal total variable travel costs when capacities are optimal and construction costs are independent of scale.

Congestion Pricing with Heterogeneous Travelers: A General-Equilibrium Welfare Analysis

Traffic congestion pricing is studied using a general-equilibrium framework that incorporates public goods expenditures, an income tax, a government budget constraint, and preferences for equity. Individuals differ with respect to wages, values of travel time, and the congestion characteristics of their vehicles. Formulae for optimal tolls are derived and decomposed to reveal the separate influences of individual and vehicle heterogeneity, road network effects, fiscal effects and equity concerns. Using an example various tolling regimes are considered, defined by how much of the network is tolled, by whether and how tolls are differentiated by route, and by vehicle and individual characteristics.

Private roads, competition, and incentives to adopt time-based congestion tolling

Abstract This paper investigates whether time-based congestion tolling is profitable for a private toll road operator when competing for traffic with another road. Despite the fact that congestion tolling boosts revenue by reducing congestion delay it can be unprofitable if it induces a private or public toll road rival to reduce its toll severely. The size of the rivals response depends on the price elasticity of travel demand and on whether the rival also employs congestion tolling. In a private duopoly adoption may be unilaterally profitable, but parallel adoption unprofitable, so that a Prisoners Dilemma obtains.

COMPARISON OF MORNING AND EVENING COMMUTES IN THE VICKREY BOTTLENECK MODEL

Dynamic user equilibrium has received considerable theoretical attention for morning peak-period travel but very little for the evening peak. In an attempt to redress this imbalance, morning and evening travel are characterized and compared by using Vickrey’s bottleneck model. To focus ideas, it is assumed that morning and evening travel differ in just one respect: scheduling preferences for the morning are defined in terms of arrival time at work, whereas preferences for the evening are defined in terms of departure time from work. Sufficient conditions are identified for the existence and uniqueness of a deterministic dynamic user equilibrium in terms of departure times for the morning and evening peaks. These conditions, which go well beyond previous work, involve relatively general assumptions about the schedule delay cost functions for morning and evening and essentially no restrictions on the degree of heterogeneity in trip-timing preferences of travelers. Plausibility of the conditions is examined in light of the limited empirical evidence. A numerical example is developed at length to illustrate the importance of traveler heterogeneity and the extent of differences between morning and evening in the time pattern of departures and aggregate travel costs.