Clas Rydergren

On Traffic Equilibrium Models with a Nonlinear Time/Money Relation

We consider a traffic equilibrium problem in which each route has two attributes, time delay and monetary outlay, which are combined into a generalized time through a nonlinear relation. It is shown that this problem can be stated as a convex optimization model. Two simplicial decomposition type methods are proposed for its solution. The subproblem of these methods, which is a two-attribute shortest route problem, can be efficiently solved by the multi-labelling technique which has previously been applied to resource-constrained shortest path problems. Our numerical experiments show that both methods are feasible approaches to the equilibrium problem.

Most Likely Traffic Equilibrium Route Flows Analysis and Computation

When analyzing equilibrium traffic flows it is usually the link flows and link travel demands that are of interest, but in some certain cases analyses require the knowledge of route flows. It is well known that the route flows are non-unique in the static and deterministic cases of traffic equilibrium. Furthermore, different assignment methods can generate different route flow output. We show how this non-uniqueness can affect the results in applications such as in the O-D estimation/adjustment problem, in the construction of induced O-D matrices, exhaust fume emission analyses and in link toll usage analyses. We state a model for finding, uniquely, the most likely route flows given the equilibrium link flows, and propose a solution algorithm for the problem based on partial dualization. We present computational results for the proposed algorithm and results from an application to exhaust fume emissions.

A column generation procedure for the side constrained traffic equilibrium problem

We present a column generation procedure for the side constrained traffic equilibrium problem. A dual stabilization scheme is introduced to improve the computational performance. Computational experiments for the case of linear side constraints are presented. The test problems are well known traffic equilibrium instances where side constraints of link flow capacity type and general linear side constraints are added. The computational results are promising especially for instances with a relatively small number of side constraints.

Applications of Simplicial Decomposition with Nonlinear Column Generation to Nonlinear Network Flows

The simplicial decomposition method for linearly constrained nonlinear programs has been proven to be efficient for certain classes of structured large-scale problems. This method alternates between a multi-dimensional search over a restriction of the feasible set and an augmentation of the restriction through the solution of a linear column generation problem. The quality of the columns generated may however be very poor, since the first-order approximation of the objective function is used globally.

Solving a mixed integer linear program approximation of the toll design problem using constraint generation within a branch-and-cut algorithm

This paper addresses the global optimality of the toll design problem (TDP) by formulating a mixed integer linear program (MILP) approximation. In the TDP, the objective is to maximise the social surplus by adjusting toll locations and levels in a road traffic network. The resulting optimisation problem can be formulated as a mathematical program with equilibrium constraints. An MILP is obtained by piecewise linear approximation of the nonlinear functions in the TDP, and we present a domain reduction scheme to reduce the error introduced by these approximations. Previous approaches for solving the MILP approximation have been relying on a large number of MILPs to be solved iteratively within a cutting constraint algorithm (CCA). This paper instead focuses on the development of a solution algorithm for solving the MILP approximation in which the CCA is integrated within a branch-and-cut algorithm, which only requires one MILP to be solved.

Optimal toll locations and toll levels in congestion pricing schemes: a case study of Stockholm

As congestion pricing has moved from theoretical ideas in the literature to real-world implementation, the need for decision support when designing pricing schemes has become evident. This paper deals with the problem of finding optimal toll levels and locations in a road traffic network and presents a case study of Stockholm. The optimisation problem of finding optimal toll levels, given a predetermined cordon, and the problem of finding both optimal toll locations and levels are presented, and previously developed heuristics are used for solving these problems. For the Stockholm case study, the possible welfare gains of optimising toll levels in the current cordon and optimising both toll locations and their corresponding toll levels are evaluated. It is shown that by tuning the toll levels in the current congestion pricing cordon used in Stockholm, the welfare gain can be increased significantly, and furthermore improved by allowing a toll on a major bypass highway. It is also shown that, by optimising both toll locations and levels, a congestion pricing scheme with welfare gain close to what can be achieved by marginal social cost pricing can be designed with tolls being located on only a quarter of the tollable links.

A comparison of feasible direction methods for the stochastic transportation problem

The feasible direction method of Frank and Wolfe has been claimed to be efficient for solving the stochastic transportation problem. While this is true for very moderate accuracy requirements, substantially more efficient algorithms are otherwise diagonalized Newton and conjugate Frank–Wolfe algorithms, which we describe and evaluate. Like the Frank–Wolfe algorithm, these two algorithms take advantage of the structure of the stochastic transportation problem. We also introduce a Frank–Wolfe type algorithm with multi-dimensional search; this search procedure exploits the Cartesian product structure of the problem. Numerical results for two classic test problem sets are given. The three new methods that are considered are shown to be superior to the Frank–Wolfe method, and also to an earlier suggested heuristic acceleration of the Frank–Wolfe method.

Hybrid Approach for Short-Term Traffic State and Travel Time Prediction on Highways

Traffic management and traffic information are essential in urban areas and require reliable knowledge about the current and future traffic state. Parametric and nonparametric traffic state prediction techniques have previously been developed with different advantages and shortcomings. While nonparametric prediction has shown good results for predicting the traffic state during recurrent traffic conditions, parametric traffic state prediction can be used during nonrecurring traffic conditions, such as incidents and events. Hybrid approaches have previously been proposed; these approaches combine the two prediction paradigms by using nonparametric methods for predicting boundary conditions used in a parametric method. In this paper, parametric and nonparametric traffic state prediction techniques are instead combined through assimilation in an ensemble Kalman filter. For nonparametric prediction, a neural network method is adopted; the parametric prediction is carried out with a cell transmission model with velocity as state. The results show that the hybrid approach can improve travel time prediction of journeys planned to commence 15 to 30 min into the future, with a prediction horizon of up to 50 min ahead in time to allow the journey to be completed.

Evaluation of travel time estimation based on LWR-v and CTM-v: A case study in Stockholm

Real-time estimations of current and future traffic states are an essential part of traffic management and traffic information systems. Within the Mobile Millennium project considerable effort has been invested in the research and development of a real-time estimation system that can fuse several sources of data collected in California. During the past year this system has been adapted to also handle traffic data collected in Stockholm. This paper provides an overview of the model used for highways and presents results from an initial evaluation of the system. As part of the evaluation process, GPS data collected in an earlier field-test and estimations generated by the existing system used by the TMC in Stockholm, are compared with the estimations generated by the Mobile Millennium system. Given that the Mobile Millennium Stockholm system has not undergone any calibration, the results from the evaluation are considered promising. The estimated travel times correspond well to those measured in the field test. Furthermore, the estimations generated by the Mobile Millennium system can be regarded as superior to those of existing traffic management system in Stockholm. The highway model was found to perform well even with a reduction in the number of sensors providing data. The findings of this study indicate the robustness of the Mobile Millennium system and demonstrate how the system can be migrated to other geographical areas with similar sources of available data.

A decision support methodology for strategic traffic management

We propose a methodology for decision support in strategic traffic management. The methodology is based on an integrated model of traffic assignment and management decisions and its core is a traffic equilibrium model which assumes that the travellers choose their routes in accordance with Wardrop’s principle. The management goals, regarding traffic flows and travel times in the network, are presumed to be described by constraints. It is also possible to specify a set of admissible actions in the network for achieving the goals; examples of such actions are changes in link capacities and the introduction of monetary tolls. The proposed approach constitutes a systematic methodology for finding appropriate changes in the traffic network in order to fulfill the management goals. We present a two-stage procedure for finding approximate solutions to the model.