Applications of sensitivity analysis for probit stochastic network equilibrium

Network equilibrium models are widely used by traffic practitioners to aid them in making decisions concerning the operation and management of traffic networks. The common practice is to test a prescribed range of hypothetical changes or policy measures through adjustments to the input data, namely the trip demands, the arc performance (travel time) functions, and policy variables such as tolls or signal timings. Relatively little use is, however, made of the full implicit relationship between model inputs and outputs inherent in these models. By exploiting the representation of such models as an equivalent optimisation problem, classical results on the sensitivity analysis of non-linear programs may be applied, to produce linear relationships between input data perturbations and model outputs. We specifically focus on recent results relating to the probit Stochastic User Equilibrium (PSUE) model, which has the advantage of greater behavioural realism and flexibility relative to the conventional Wardrop user equilibrium and logit SUE models. The paper goes on to explore four applications of these sensitivity expressions in gaining insight into the operation of road traffic networks. These applications are namely: identification of sensitive, ‘critical’ parameters; computation of approximate, re-equilibrated solutions following a change (post-optimisation); robustness analysis of model forecasts to input data errors, in the form of confidence interval estimation; and the solution of problems of the bi-level, optimal network design variety. Finally, numerical experiments applying these methods are reported

Private operators and time-of-day tolling on a congested road network

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.

Dynamic Congestion and Tolls with Mobile Source Emission

This paper proposes a dynamic congestion pricing model that takes into account mobile source emissions. We consider a tollable vehicular network where the users selfishly minimize their own travel costs, including travel time, early/late arrival penalties and tolls. On top of that, we assume that part of the network can be tolled by a central authority, whose objective is to minimize both total travel costs of road users and total emission on a network-wide level. The model is formulated as a mathematical program with equilibrium constraints (MPEC) problem and then reformulated as a mathematical program with complementarity constraints (MPCC). The MPCC is solved using a quadratic penalty-based gradient projection algorithm. A numerical study on a toy network illustrates the effectiveness of the tolling strategy and reveals a Braess-type paradox in the context of traffic-derived emission.Comment: 23 pages, 9 figures, 5 tables. Current version to appear in the Proceedings of the 20th International Symposium on Transportation and Traffic Theory, 2013, the Netherland

A Coevolutionary Particle Swarm Algorithm for Bi-Level Variational Inequalities: Applications to Competition in Highway Transportation Networks

A climate of increasing deregulation in traditional highway transportation, where the private sector has an expanded role in the provision of traditional transportation services, provides a background for practical policy issues to be investigated. One of the key issues of interest, and the focus of this chapter, would be the equilibrium decision variables offered by participants in this market. By assuming that the private sector participants play a Nash game, the above problem can be described as a Bi-Level Variational Inequality (BLVI). Our problem differs from the classical Cournot-Nash game because each and every player’s actions is constrained by another variational inequality describing the equilibrium route choice of users on the network. In this chapter, we discuss this BLVI and suggest a heuristic coevolutionary particle swarm algorithm for its resolution. Our proposed algorithm is subsequently tested on example problems drawn from the literature. The numerical experiments suggest that the proposed algorithm is a viable solution method for this problem

Second best toll and capacity optimisation in network: solution algorithm and policy implications

This paper looks at the first and second-best jointly optimal toll and road capacity investment problems from both policy and technical oriented perspectives. On the technical side, the paper investigates the applicability of the constraint cutting algorithm for solving the second-best problem under elastic demand which is formulated as a bilevel programming problem. The approach is shown to perform well despite several problems encountered by our previous work in Shepherd and Sumalee (2004). The paper then applies the algorithm to a small sized network to investigate the policy implications of the first and second-best cases. This policy analysis demonstrates that the joint first best structure is to invest in the most direct routes while reducing capacities elsewhere. Whilst unrealistic this acts as a useful benchmark. The results also show that certain second best policies can achieve a high proportion of the first best benefits while in general generating a revenue surplus. We also show that unless costs of capacity are known to be low then second best tolls will be affected and so should be analysed in conjunction with investments in the network

A cost-benefit analysis of tunnel investment and tolling alternatives in Antwerp

This paper presents and illustrates a comprehensive and operational model for assessing transport pricing and investment policies and regulatory regimes. The approach encompasses intra-modal as well as inter-modal competition, and could be used either by private operators or by the legislator for the purpose of evaluating market conduct. The model combines elements of contract theory, public economics, political economy, transportation economics and game theory. It incorporates a CES-based discrete-choice framework in which user charges and infrastructure investments are endogenously determined for two competing alternatives (air, rail or two parallel roads) that may be used for transportation of passengers and/or freight. The model includes separate modules for demand, supply, equilibrium and the regulatory framework. The demand module for passenger transport features a CES decision tree with three levels: choice between transport and consumption of a composite commodity, choice between peak and off-peak periods, and choice between the two transport alternatives. Elasticities of substitution at each level are parametrically given. Passengers can be segmented into classes that differ with respect to their travel preferences, incomes and costs of travel time. The demand module for freight transport also features three levels. The first level encompasses choice between transport and other production inputs, and the second and third levels are the same as for passenger transport. Freight transport can be segmented into local and transit traffic. The supply module specifies for each transport alternative travel time as a function of traffic volume and a rule for infrastructure maintenance. Operating, maintenance and investment costs are allowed to depend on the contractual form. Given the demand and supply functions, the equilibrium module computes a fixed-point solution in terms of prices and levels of congestion. Finally, the exogenous regulatory framework stipulates for each alternative the objective functions of the operators and infrastructure managers (public or private objectives), the nature of competition, procurement policies, the cost of capital, and the source and use of transport tax revenues. Possible market structures include: no tolls (free access), exogenous tolls, marginal social cost pricing, private duopoly and mixed oligopoly. Public decisions can be made either by local or central governments that may attach different welfare-distributional weights to agents (e.g. low-income vs. high-income passengers, or local vs. transit freight traffic) as well as different weights to air pollution and other (non-congestion) external transport costs. Primary outputs from the model are equilibrium prices, transport volumes, travel times, cost efficiency of operations, toll revenues and financial balances, travellers’ surplus and social welfare. In the final section of the paper the methodology is illustrated with an example of competition in the market for long-distance passenger travel between high-speed rail and air. A simple procedure allows the calibration of the parameters when aggregate data are available. The model is used to evaluate policies (pricing, investment, taxes, inter alia).

The Network Improvement Problem for Equilibrium Routing

In routing games, agents pick their routes through a network to minimize their own delay. A primary concern for the network designer in routing games is the average agent delay at equilibrium. A number of methods to control this average delay have received substantial attention, including network tolls, Stackelberg routing, and edge removal. A related approach with arguably greater practical relevance is that of making investments in improvements to the edges of the network, so that, for a given investment budget, the average delay at equilibrium in the improved network is minimized. This problem has received considerable attention in the literature on transportation research and a number of different algorithms have been studied. To our knowledge, none of this work gives guarantees on the output quality of any polynomial-time algorithm. We study a model for this problem introduced in transportation research literature, and present both hardness results and algorithms that obtain nearly optimal performance guarantees. - We first show that a simple algorithm obtains good approximation guarantees for the problem. Despite its simplicity, we show that for affine delays the approximation ratio of 4/3 obtained by the algorithm cannot be improved. - To obtain better results, we then consider restricted topologies. For graphs consisting of parallel paths with affine delay functions we give an optimal algorithm. However, for graphs that consist of a series of parallel links, we show the problem is weakly NP-hard. - Finally, we consider the problem in series-parallel graphs, and give an FPTAS for this case. Our work thus formalizes the intuition held by transportation researchers that the network improvement problem is hard, and presents topology-dependent algorithms that have provably tight approximation guarantees.Comment: 27 pages (including abstract), 3 figure

A cost-benefit analysis of tunnel investment and tolling alternatives in Antwerp

A proposal has been made to build a new tunnel under the Scheldt river near the centre of Antwerp in order to relieve traffic congestion on the ring road and in an existing tunnel. The new tunnel is expected to cost more than €1 billion, and tolls have been suggested to help finance construction and to manage demand. This paper conducts a preliminary cost-benefit analysis of a new tunnel and three alternative tolling schemes, and compares them with a do-nothing scenario and an option to toll the existing tunnel without building a new one. The analysis is performed using a model that was recently developed as part of the European-Union funded REVENUE project. The two tunnels are treated as imperfect substitutes, and a multi-year accounting framework is adopted that accounts for emissions, accidents and noise externalities, road damage, revenues accruing to the national and regional governments from existing transport user charges, and the salvage value of the new tunnel. With the base-case parameter values it is found that building the tunnel is worthwhile with all three tolling regimes and yields a higher benefit than not building the tunnel and tolling the old one. Nevertheless, the net benefit from building the tunnel differs appreciably between tolling regimes, and it is sensitive to the value assumed for the marginal cost of public funds.infrastructure investment, route choice, congestion, tolls