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

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

The marginal social cost of headway for a scheduled service

This brief paper derives the marginal social cost of headway for a scheduled service, i.e. the cost for users of marginal increases to the time interval between departures. In brief we may call it the value of headway in analogy with the value of travel time and the value of reliability. Users have waiting time costs as well as schedule delay costs measured relative to their desired time of arrival at the destination. They may either arrive at the station to choose just the next departure or they may plan for a specific departure in which case they incur also a planning cost. Then planning for a specific departure is costly but becomes more attractive at longer headways. Simple expressions for the user cost result. In particular, the marginal cost of headway is large at short headways and smaller at long headways. The difference in marginal costs is the value of time multiplied by half the headway.     

The stability of stochastic equilibrium in a two-link transportation network

Most research and applications of network equilibrium models are based on the assumption that traffic volumes on roadways are virtually certain to be at or near their equilibrium values if the equilibrium volumes exist and are unique. However, it has long been known that this assumption can be violated in deterministic models. This paper presents an investigation of the stability of stochastic equilibrium in a two-link network. The stability of deterministic equilibrium also is discussed briefly. Equilibrium is defined to be stable if it is unique and the link volumes converge over time to their equilibrium values regardless of the initial conditions. Three models of route choice decision-making over time are formulated, and the stability of equilibrium is investigated for each. It is shown that even when equilibrium is unique, link volumes may converge to their equilibrium values, oscillate about equilibrium perpetually, or converge to values that may be considerably different from the equilibrium ones, depending on the details of the route choice decision-making process. Moreover, even when convergence of link volumes to equilibrium is assured, the convergence may be too slow to justify the standard assumption that these volumes are usually at or near their equilibrium values. When link volumes converge to non-equilibrium values, the levels at which the volumes stabilize typically depend on the initial link volumes or perceptions of travel costs. Conditions sufficient to assure convergence to equilibrium in two of the three models of route choice decision-making are presented, and these conditions are interpreted in terms of the route choice decision-making process.     

Solutions to the optimal network design problem with shipments related to transportation cost

Two versions of an optimal network design problem with shipments proportional to transportation costs are formulated. Extensions of an algorithm developed in prior research for solving these problems are proposed and tested. The performance of the algorithms is found to improve substantially as the dependence of shipments on costs is increased. Moreover, the optimal solutions obtained are unexpectedly robust with respect to a wide range of transportation cost assumptions. These findings could have important computational and policy implications if applicable to larger networks.     

Three-player game-theoretic model over a freight transportation network

With recent development in freight transportation industry, its network structure has become more complicated, as many decision-makers competing for profits with each other are involved. While most recent research in this area is focused on the perfectly competitive market and the prices are given as a constant tariff rate, little attention has been paid to the system optimization problem in the absence of regulatory authority. In this paper, we investigate the competitive equilibrium in an oligopolistic market on a freight network. A partially non-cooperative game among shippers, carriers and infrastructure companies (IC) is examined. All three kinds of players act as profit maximizing agents, except that the carriers and ICs are assumed to behave cooperatively in their own coalitions. We consider the vertically efficient nonlinear tariff schedules which are commonly used in the transportation industry. By introducing a three-stage game-theoretic model, we show that the equilibrium flows can also maximize total system profits if the IC and the carrier both use vertically efficient nonlinear pricing schedules. The division of the surplus associated with each shipment is obtained by solving a linear programming problem. We provide a few examples under different situations to show the existence of the resulting equilibrium.     

Solving a discrete multimodal transportation network design problem

This paper investigates the multimodal network design problem (MMNDP) that optimizes the auto network expansion scheme and bus network design scheme in an integrated manner. The problem is formulated as a single-level mathematical program with complementarity constraints (MPCC). The decision variables, including the expanded capacity of auto links, the layout of bus routes, the fare levels and the route frequencies, are transformed into multiple sets of binary variables. The layout of transit routes is explicitly modeled using an alternative approach by introducing a set of complementarity constraints. The congestion interaction among different travel modes is captured by an asymmetric multimodal user equilibrium problem (MUE). An active-set algorithm is employed to deal with the MPCC, by sequentially solving a relaxed MMNDP and a scheme updating problem. Numerical tests on nine-node and Sioux Falls networks are performed to demonstrate the proposed model and algorithm.     

Locating new passenger facilities on a transportation network

This paper examines the problem of locating additional passenger facilities on a transportation network to supplement ones that already exist. A distinction is made between “supporting” facilities which operate only in concert with already existing ones and “new” facilities which are self-sufficient and operate independently. It is shown that, when the objective is to maximize the utility of travel times to all users, at least one set of optimal locations for the new facilities exist on the nodes of the network if the utility function for travel times is convex. This result is proven under very general conditions including the assumption of a probabilistic transportation network, i.e. a network where travel times on network branches are random variables. A straightforward algorithm for solving a specific simple case is also provided and the results are illustrated by examples.     

Alternative methods for estimating full marginal costs of highway transportation

This paper presents various methods of estimating the full marginal cost (FMC) of highway passenger transportation. First, the computation of FMC is performed using the marginal cost functions, most of which were developed by Ozbay et al. [Ozbay, K., Bartin, B., Berechman, J., 2001. Estimation and evaluation of full marginal costs of highway transportation in New Jersey. Journal of Transportation and Statistics 4 (1)]. FMC is defined and calculated as “total cost per trip” as explained in this paper. However, in multiple origin-destination and multiple route highway networks, the practical application of the network-wide FMC concept is complicated. These issues are addressed in detail in this paper. Therefore, in the second method, a multiple route based FMC approach is proposed for a given origin-destination pair in the network. It is observed that the marginal values of different paths vary as much as 28%. Third, a comparison of FMC estimation results of two distinct measurement tools is presented. The FMC estimation is performed between a selected OD pair using the static transportation planning software output (TransCAD). The same analysis is repeated using the stochastic traffic simulation software output (PARAMICS). The differences in FMC values estimated by static transportation planning software and microscopic traffic simulation software are discussed.     

A theory and implications on dynamic marginal cost

This paper extends the conventional static marginal cost analysis to the dynamic one based on the time-dependent queueing analysis at a bottleneck. First, the supply function is reformulated so as to incorporate dynamically congestion phenomena. And, the marginal cost is shown to be more closely related to the duration of congestion rather than the personal cost, since a slight change of demand at one time affects an entire traffic condition thereafter. Next, the analysis is extended so as to include the departure time choice using previous departure time choice theory. Several implications such as road pricing schemes and ramp control strategies are also discussed.     

Measuring marginal congestion costs of urban transportation: Do networks matter?

In determining the marginal cost of congestion, economists have traditionally relied upon directly measuring traffic congestion on network links, disregarding any “network effects,” since the latter are difficult to estimate. While for simple networks the comparison of the network-based congestion costs with the link-based ones can be done within a theoretical framework, it is important to know whether such network effects in real large-scale networks are quantitatively significant.In this paper we use a strategic transportation planning model (START) to compare marginal congestion costs computed link-by-link with measures taking into account network effects. We find that while in aggregate network effects are not significant, congestion measured on a single link is a poor predictor of total congestion costs imposed by travel on that link. Also, we analyze the congestion proliferation effect on the network to see how congestion is distributed within an urban area.     

An artificial neural network approach for evaluating transportation network improvements

As demand increases over time, new links or improvements in existing links may be considered for increasing a network's capacity. The selection and timing of improvement projects is an especially challenging problem when the benefits or costs of those projects are interdependent. Most existing models neglect the interdependence of projects and their impacts during intermediate periods of a planning horizon, thus failing to identify the optimal improvement program. A multiperiod network design model is proposed to select the best combination of improvement projects and schedules. This model requires the evaluation of numerous network improvement alternatives in several time periods. To facilitate efficient solution methods for the network design model, an artificial neural network approach is proposed for estimating total travel times corresponding to various project selection and scheduling decisions. Efficient procedures for preparing an appropriate training data set and an artificial neural network for this application are discussed. The Calvert County highway system in southern Maryland is used to illustrate these procedures and the resulting performance.     

Towards marginal cost pricing: A comparison of alternative pricing systems

European urban areas are marred by the problems of congestion and environmental degradation due to the prevailing levels of car use. Strong arguments have thus been put forward in support of a policy based on marginal cost pricing (European Commission 1996). Such policy measures – which would force private consumers to pay for a public service that was previously provided "for free" – are, however, notoriously unpopular with the general public and hence also with their elected representatives – the politicians. There is thus an obvious tension between economic theory, which suggests that marginal cost pricing is the welfare maximising solution to urban transport problems, and practical experience, which suggests that such pricing measures are unwanted by the affected population and hence hard to implement through democratic processes. The AFFORD Project for the European Commission has aimed to investigate this paradox and its possible solutions, through a combination of economic analysis, predictive modelling, attitudinal surveys, and an assessment of fiscal and financial measures within a number of case study cities in Europe. In this paper the methodology and results obtained for the Edinburgh case study are reported in detail. The study analyses alternative road pricing instruments and compares their performance against the theoretical first best situation. It discusses the effect of coverage, location, charging mechanism and interaction with other instruments. The paper shows that limited coverage in one mode may lead to a deviation from the user pays principle in other modes, that location is as important as charge levels and that assumptions about the use of revenues are critical in determining the effect on equity and acceptability. Finally the results show that a relatively simple smart card system can come close to providing the economic first best solution, but that this result should be viewed in the context of the model assumptions.     

Transportation policy analysis with a geographic information system: The virtual network of freight transportation in Europe

This paper presents a multi-modal freight transportation model based on a digitized geographic network. A systematic analysis and decomposition of all the transport operations i.e. moving, loading and unloading, transshipping and transiting, leads to the development of a virtual network where each virtual link corresponds to a specific operation, and all transportation modes and means are inter-linked. Software, called NODUS, automatically generates the virtual network so that the model can be conveniently applied to large networks. The analytical structure of the links notation makes it easy to attach specific cost functions to each virtual link. The model is applied to the trans-European freight network of roads, railways and inland waterways for the transportation of wood. Cost functions are built up for each operation by each mode/means combination. A detailed point-to-point origin-destination matrix, calibrated on Eurostat statistics, is generated by a Monte-Carlo technique. Then, the total transportation cost is minimized with respect to the choices of routes, modes and means. This provides estimations of transportation services demands as well as modal splits, to the extent that the two hypotheses of demand based on generalized cost minimization and market contestability are accepted. A sensitivity analysis on the relative road cost is made, which provides measures of arc-elasticities.     

Integrating GIS concepts into transportation network data structures

Transportation network data structures must be designed to meet the requirements of the analyses being conducted and must be compatible with the selected graphical user interface. Increasing interest in geographic information systems (GIS) and intelligent transportation systems (ITS) have further burdened the network data structure. It is possible to implement object oriented programming (OOP) technology to satisfy these needs, without making the data structure excessively complicated.

This paper shows how a well‐developed network data structure can incorporate major capabilities normally associated with stand‐alone GIS's. The design of a network data structure derives from both theoretical and practical considerations. A design of a network data structure, composed entirely of objects, is presented. Examples of its implementation, limitations, advantages, and possible extensions are drawn from experience with the General Network Editor (GNE).     

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

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

Integrated modeling of urban hierarchy and transportation network planning

A major problem addressed during the preparation of spatial development plans relates to the accessibility to facilities where services of general interest such as education, health care, public safety, and justice are offered to the population. In this context, planners typically aim at redefining the level of hierarchy to assign to the urban centers of the region under study (with a class of facilities associated with each level of hierarchy) and redesigning the region’s transportation network. Traditionally, these two subjects – urban hierarchy and transportation network planning – have been addressed separately in the scientific literature. This paper presents an optimization model that simultaneously determines which urban centers and which network links should be promoted to a new level of hierarchy so as to maximize accessibility to all classes of facilities. The possible usefulness of the model for solving real-world problems of integrated urban hierarchy and transportation network planning is illustrated through an application to the Centro Region of Portugal.     

Estimating the marginal cost of railway track renewals using corner solution models

Economic theory advocates marginal cost pricing for efficient utilisation of transport infrastructure. A growing body of literature has emerged on the issue of rail marginal infrastructure wear and tear costs, but the majority of the work is focused on costs for infrastructure maintenance. Railway track renewals are a substantial part of an infrastructure manager’s budget, but in disaggregated statistical analyses they cause problems for traditional regression models since there is a piling up of values of the dependent variable at zero. Previous econometric work has sought to circumvent the problem by aggregation in some way. In this paper we instead apply corner solution models to disaggregate (track-section) data, including the zero observations. We derive track renewal cost elasticities with respect to traffic volumes and in turn marginal renewal costs using Swedish railway renewal data over the period 1999–2009. This paper is the first attempt in the literature to apply corner solution models, and in particular the two-part model, to disaggregate renewal cost data in railways. It is also the first paper that we are aware of to report usage elasticities specifically for renewal costs and therefore adds important new evidence to the previous literature where there is a paucity of studies on renewals and considerable uncertainty over the effects of rail traffic on renewal costs. In the Swedish context, we find that the inclusion of marginal track renewal costs in the track access pricing regime, which currently only reflects marginal maintenance costs, would add substantially to the existing track access charge. EU legislation requires that access charges reflect the ‘costs directly incurred as a result of operating the train service’, which should include a marginal renewal cost component. This change would also increase the cost recovery ratio of the Swedish infrastructure manager, thus meeting a policy objective of the national government.     

Evaluating marginal improvements to a transport network: An application to the Santiago underground

This paper describes a simplified methodology designed for quick investment appraisal of improvements to a transport network, and discusses its limitations and advantages particularly in the context of a developing country. The approach basically considers:

- a method to define the total population (relevant origin-destination pairs) affected by the project

- the selection of a low-cost background model to represent transport demand on a network at an aggregate level

- the choice of a suitable marginal demand model (in this case a discrete mode choice model) capable of providing the required sensitivity and accuracy to model the project

- the estimation of the marginal demand due to the project during all the years of the study horizon, and

- a sensitivity analysis to assess the robustness of the decision recommended using these two models.

Finally, the paper summarises the results of applying the methodology to the case of an extension to the Santiago underground; it was found that the project has a high social rate of return (almost 20 per cent). However, from the point of view of a private evaluation, it can cover its operating costs only.     

A regional railroad network optimization model for coal transportation

A regional railroad network is presented to evaluate the system's response to increased coal traffic. An optimal, multimodal, coal-shipping pattern is developed for the study region to minimize total costs and to efficiently use the existing network. A two-stage, general model allocates resources among demands and then assigns flows to the network according to efficiency criteria. The model is sufficiently general to permit modification for specific needs, assumptions and data. Government agencies and industries can apply the model in resource allocation decisions and transportation policy analysis.