A behavioural model of traffic congestion: Endogenizing speed choice, traffic safety and time losses

Conventional economic models of traffic congestion assume that the relation between traffic flow and speed is a technical one. This paper develops a behavioural model of traffic congestion, in which drivers optimize their speeds by trading off time costs, expected accident costs and fuel costs. Since the presence of other drivers affects the latter two cost components and hence the Nash equilibrium speed, a ‘behavioural’ speed-flow relationship results for which external congestion costs include expected accident costs and fuel costs, in addition to the time costs considered in the conventional model. It is demonstrated that the latter in fact even cancel in the calculation of optimal congestion tolls. The overall welfare optimum in our model is found to be off the speed-flow function, and off the average and marginal cost functions derived from it in the conventional approach. This full optimum requires tolls to be either accompanied by speed policies, or to be set as a function of speed. Using an empirically calibrated numerical simulation model, we illustrate these qualitative findings, and attempt to assess their potential empirical relevance.     

Highway congestion and congestion tolls

Highway congestion is ubiquitous. We model the speed-flow relationship, identifying private and social costs, and the implied congestion toll for a number of proposed formulations. Using data for a limited access highway, we estimate these speed-flow relationships and find that flow as a quadratic function of speed fits best. The unit of observation is the individual vehicle and flow is measured in terms of the vehicles which passed a point shortly before or after the reference vehicle. Maximum possible flow occurs at 30–35 mph and the congestion toll is infinite for slower speeds. Rush-hour drivers have greater speeds for a given volume of traffic and thus congestion tolls must vary by time of day.     

Road congestion: A reconsideration of pricing theory

In this paper, the effect of congestion tolls upon the pattern of traffic flows is examined. Congestion tolls influence the individual commuter's decision of when to make a trip, inducing him to travel at less congested times. When all commuters are taken together, congestion tolls and the individual consumers' decisions lead to an efficient reorganization of traffic flows relative to a non-toll situation. In fact, for the same total number of commuters, per person costs of travel including the toll may decline with the imposition of tolls and efficient reorganization of traffic flows.     

The incidence of congestion tolls on urban highways

The incidence of an optimal short-run congestion toll is investigated using an equilibrium model of modal choice and congestion on a highway corridor served by express bus transit. It is argued that for an externality tax the usual equi-revenue analysis of burdens is inappropriate; instead, welfare effects are computed under three alternative assumptions about redistribution of toll revenues. In almost all cases the net result is benefits for all income groups. It is concluded that congestion tolls should not be rejected on grounds of income distribution, but that an explicit package of tolls and revenue uses is probably a political prerequisite for adoption.     

Clubs in an urban setting

In this paper the properties of a congestable concentrated local public good (CCoLPG) are described, taking into account both locational aspects and congestion. This discussion, therefore, completes the analysis of congestable local public goods (LPG) which was started in our earlier paper (Congestable local public goods in an urban setting, J. Urban Econ., 290–310 (1982). It is here shown that the optimal provision of CCoLPG leads to the creation of clubs, where the government has to determine the location and provide the optimal quantity of LPG in each club and also levy congestion tolls on users according to their level of utilization of the club. Congestion tolls cover the αest part of the costs, where α is the level of congestability of the CCoLPG. The rest of the costs are covered by taxing land rents. Clubs will form, possibly more than one per city, even if the LPG is pure (i.e., α = 0) and they will contain a single household if the LPG is private (i.e., α = 1). The difference between these results and those of classical club theorists stem from the fact that here we also take into account the limited supply of land of given accessibility (i.e., locational aspects), which like congestion lead to the creation of clubs. When these two factors are considered together, it explains why congestion tolls alone are not sufficient to finance clubs' operations, or why pure LPGs also have to be provided locally, etc.     

Efficient Congestion Tolls in the Presence of Unpriced Congestion: A Peak and Off-Peak Simulation Model

This paper develops a congestion pricing model to examine efficient congestion tolls for an urban highway facility that resembles California State Route 91, the highway that has been subject to congestion tolls since December 27, 1995. Two lanes out of six (each way) are subject to congestion tolls, and the other four lanes are not. The simulation model combines the economic theories of second-best pricing of transportation facilities and peak-load pricing, and considers both welfare-maximizing and profit-maximizing cases. The simulation results show that the second-best peak period toll is quite low and that the welfare gains from the toll are modest compared to a regime in which all lanes are subject to tolls.     

A generalized congestion function for highway travel

Urban planners designing the optimal scale and pricing of highway services must pay close attention to the choice of the functional form used to describe the relationship between highway speed and the volume of roadway traffic. This congestion relationship is a crucial empirical fact for planning. While past work have posited a variety of speed-volume models, no successful efforts have been made to statistically compare the different specifications. This paper presents a generalized congestion function (GCF) which allows us to select the preferred (by a maximum likelihood criterion) speed-volume specification. The most prominent previous speed-volume models are all shown to be special cases of GCF. Failure to use the GCF approach may be very costly. For example, in the design of highway tolls the switch from the optimal GCF specification to a statistically “second-best” model may lead to a consumer surplus loss of $1 million annually for a typical urban area.     

The incidence of congestion and congestion tolls

In contrast with the enormous literature on efficiency aspects of congestion tolls, very little has appeared on their equity implications. Simulation is applied to a standard urban model to learn about the distributional aspects of an optimal toll, or the absence of one. Tolls are found to produce distributional changes which may overshadow their effects on allocative efficiency. In passing, the model is used to demonstrate that lagged supply adjustments to increases in the demand for suburban housing may be an effective, if second-best, alternative to congestion tolls.     

Alternative congestion pricing schedules

It is important that alternative congestion pricing schedules are compared with respect to a broad spectrum of their effects. This paper uses an equilibrium simulation model of peak-period commuting along an urban highway to compare quantitatively both positive and normative effects of six congestion pricing schedules. Three of these schedules have been investigated qualitatively in the literature; the others are new. The results indicate that flat tolls are favored over smoothly varying tolls for revenue generation or increase in vehicle occupancy, but are disfavored for efficiency maximization, increase in consumer surplus, or reduction in congestion delays.     

Congestable local public goods in an urban setting

In this paper, we recognize two types of unpure local public goods (LPGs): congestable and pollutable. This paper and the forthcoming one (Clubs in an urban setting, mimeo, 1980) are devoted to congestable LPGs (CLPG). In Part I we define, classify, and characterize CLPGs. CLPGs may vary in their degree of congestability between zero, in the case of a pure LPG, and one, in the case of a private good. Spatially, we recognize two types of LPGs: the dispersed LPG (DiLPG) and the concentrated LPG (CoLPG). The first is distributed throughout the residential ring and the second is provided in specific locations to which households must travel. The second part of this paper is devoted to the investigation of the properties of a CDiLPG in an urban setting. The properties of CoLPG are investigated in (Clubs in an urban setting, mimeo, 1980). A version of Samuelson's rule as to the optimal allocation of pure public goods is extended on one hand to local dispersed public goods and on the other hand to CLPGs. Two corrective Pigouvian taxes are identified: congestion tolls levied on households, and a residential land tax. These two taxes cover total government expenditure on the LPG. The fraction of the expenses on the LPG covered by congestion tolls is α, and that covered by land taxes is (1 − α), where α is the degree of congestability. Efficiency can also be achieved by zoning the residential ring and regulating the housing density in it. This procedure may replace taxation and its advantage is that we can control a large number of externalities by a single set of zoning rules and regulations. An a posteriori rule to guide the local government as to the desirability of its actions is provided.     

Congestion, Land Use, and Job Dispersion: A General Equilibrium Model

In dispersed cities, congestion tolls would drive up central wages and rents and would induce centrally located producers to want to disperse closer to their workers and their customers, paying lower rents and realizing productivity gains from land to labor substitution. But the tolls would also induce residents to want to locate more centrally in order to economize on commuting and shopping travel. In a computable general equilibrium model, we find that the centralizing effect of tolls on residences dominates on the decentralizing effect of tolls on firms, causing the dispersed city to have more centralized job and population densities. Under stylized parameters, we find that efficiency gains from levying congestion tolls on work and shopping travel are 3.0% of average income. About 80% of such gains come from road planning and 20% from tolls.     

Inside the queue:: hypercongestion and road pricing in a continuous time–continuous place model of traffic congestion

This paper develops a continuous-time–continuous-place dynamic economic model of traffic congestion, based on car-following theory. The model integrates two archetype congestion technologies used in the economics literature: ‘static flow congestion’ and ‘dynamic bottleneck congestion.’ With endogenous departure times and a bottleneck along the route, ‘hypercongestion’ arises as a dynamic equilibrium phenomenon on the upstream road segment. Congestion tolls based on an intuitive dynamic and space-varying generalization of the standard Pigouvian tax rule can hardly be improved upon. A naïve application of a toll schedule based on Vickrey's bottleneck model performs much worse and reduces welfare in the numerical model.     

Second-Best Congestion Pricing: The Case of an Untolled Alternative

This paper deals with second-best one-route congestion pricing in case of an untolled alternative. Using a two-link network simulation model, the effects of various demand and cost parameters on the relative efficiency of one-route tolling are analyzed. It is investigated whether the existence of costs of congestion charging may be a reason for one-route tolling to be more “overall efficient” than two-route tolling. Finally, the efficiency of revenue-maximizing one-route and two-route tolling is discussed.     

An Integrated Dynamic Model of Road Traffic Congestion Based on Simple Car-Following Theory: Exploring Hypercongestion

This paper presents a dynamic version of the standard static economic model of road traffic congestion, based on car-following theory. It is proven formally and illustrated numerically that the “hypercongested” equilibria found in the standard model are dynamically unstable. For arrival rates of users below the road's maximum capacity, the model reproduces the non-hypercongested stationary state outcomes found in the standard model. When the arrival rate exceeds this maximum capacity, however, the model produces outcomes consistent with Vickrey's model of bottleneck congestion. The model thus offers an integration and a generalization of these two archetype models.     

Bottleneck Congestion and Modal Split

This paper analyzes commuting congestion when there is mass transit parallel to a road with a bottleneck between a residential area and a workplace. We investigate the optimality and efficiency of several railroad fare and road toll regimes and provide practical rules for attaining the social optimum. A welfare comparison is also made between these regimes, and it is shown that the road tolls are effective especially in the case of heavy road congestion.     

Optimum,market and second-best land use patterns in a von Thünen city with congestion

This paper constructs a von Thünen type model with traffic congestion and two production inputs. A comparison between optimum and market land use patterns is presented. The second-best problem in which congestion tolls are not allowed is also considered. The policy variable in the analysis is the allocation of land between production and transportation. The result is examined in a cost-benefit analysis based on market rent.     

Developing breakthrough products: challenges and options for market assessment

Competitive pressures and market forces are augmenting the importance of product innovation as a source of competitive advantage. Key drivers underpinning market success have the capacity to develop the “right” products for the “right” customers, using the “right” channels, with a shorter development cycle than competitors. But when breakthrough products (BTPs) are involved, how do we sort out what is “right”? How do we identify customers' future requirements when the technology platforms are still unfolding, products are still in development and customers lack experience with the product? Traditional product development market research techniques are problematic since they assume the customer has historical experience with products similar to those being created. The objective of this paper is to raise the awareness of the OM community with the strengths and weaknesses of existing methodologies for developing and introducing innovative products to market. Further, it suggests promising future directions for both practice and research when BTPs are involved. This is important because of the central role OM plays in managing the success of the BTP development process.     

Traffic externalities in cities: The economics of speed bumps,low emission zones and city bypasses

This paper considers various policy measures that governments can use to reduce traffic externalities in cities. Unlike much of the available literature that emphasized congestion, we focus on measures that reduce pollution, noise and some accident risks. These measures include noise barriers, speed bumps, traffic lights, tolls, emission standards, low emission zones, and bypass capacity to guide traffic around the city center. Using a simple model that distinguishes local and through traffic, we study the optimal use of these instruments by an urban government that cares for the welfare of its residents, and we compare the results with those preferred by a federal authority that also takes into account the welfare of road users from outside the city. Our results include the following. First, compared to the federal social optimum, we show that the city government will over-invest in externality-reducing infrastructure whenever this infrastructure increases the generalized cost of through traffic. We can therefore expect an excessive number of speed bumps and traffic lights, but the right investment in noise barriers. Second, when implementing low emission zones, the urban government will set both the fee for non-compliance and the emission standard at a more stringent level than the federal government. Moreover, at sufficiently high levels of through traffic the urban government will prefer imposing a toll instead of implementing a low emission zone. Third, whatever the tolling instruments in place, the city will always underinvest in bypass capacity. Finally, if it can toll all roads but is forced to invest all bypass toll revenue in the bypass, it will never invest in bypass capacity. Although the paper focuses on non-congestion externalities, most insights also hold in the presence of congestion.     

Financing Capacity in the Bottleneck Model

It is well known that, for a congestible facility with constant long-run average cost, the revenue from the unconstrained optimal congestion charge (set so that each individual faces the marginal (social) cost of a use) exactly covers the cost of optimal capacity. In the context of Vickrey′s bottleneck model of morning rush-hour auto congestion, this paper investigates under what circumstances the first-best pricing and investment rules apply when both the time variation of the congestion charge is constrained and users differ in unobservable characteristics so that the same congestion charge must be applied to heterogeneous users.     

Asymptotic behaviour of regression pre-test estimators with minimal Bayes risk

Pre-test estimators (PTE) are considered which are optimal under a Bayes risk among PTE with general measurable sets as “regions of significance” for the test statistic t associated with the estimate of a given regression coefficient. Asymptotic and some finite sample results are stated and numerical experiments are commented on.