As a means to obtain a more accurate description of traffic flows than that provided by the basic model of traffic assignment, there have been suggestions to impose upper bounds on the link flows. This can be done either by introducing explicit link capacities or by employing travel time functions with asymptotes at the upper bounds. Although the latter alternative has the disadvantage of inherent numerical ill-conditioning, the capacitated assignment model has been studied and applied to a limited extent, the main reason being that the solutions can not be characterized by the classical Wardrop equilibrium conditions; they may, however, be characterized as Wardrop equilibria in terms of a welldefined, natural generalized travel cost. The introduction of link capacity side constraints makes the problem computationally more demanding. The availability of efficient algorithms for the basic model of traffic assignment motivates the use of dualization approaches for handling the capacity c...

In this paper we present a version of the (static) traffic equilibrium problem in which the cost incurred on each path is not simply the sum of the costs on the arcs that constitute that path. We motivate this nonadditive version of the problem by describing several situations in which the classic additivity assumption fails. We describe existence and uniqueness conditions for this problem and we also present convergence theory for a generic algorithm for solving nonadditive problems. INTRODUCTION Paraphrasing Wardrop [33], the (static) traffic equilibrium problem is to find a set of path flows that satisfy certain demand constraints and have the property that the costs on all used paths connecting an origin-destination pair are equal and less than or equal to the cost on all unused paths connecting that pair. In order to prove existence/uniqueness results and develop convergent algorithms, this problem has been formulated as a nonlinear program (NLP) [4], a nonlinear complementarity...

The purpose of this paper is to provide a unified description of iterative algorithms for the solution of traffic equilibrium problems. We demonstrate that a large number of well known solution techniques can be described in a unified manner through the concept of partial linearization, and establish close relationships with other algorithmic classes for nonlinear programming and variational inequalities. In the case of nonseparable travel costs, the class of partial linearization algorithms are shown to yield new results in the theory of finite-dimensional variational inequalities. The possibility of applying truncated algorithms within the framework is also discussed.

. In this paper we develop an algorithm for solving a version of the (static) traffic equilibrium problem in which the cost incurred on each path is not simply the sum of the costs on the arcs that constitute that path. The method we describe is based on the recent NE/SQP algorithm, a fast and robust technique for solving nonlinear complementarity problems. Finally, we present an example that illustrates both the importance of using nonadditive costs and the effectiveness of the NE/SQP method. 1 Introduction In modeling (static) traffic equilibria, researchers have generally made use of what is known as the additive model. In this approach, the path costs faced by users of the traffic network are simply the sum of the arc costs for all the arcs on the path in question. While this modeling assumption is computationally attractive, it is not appropriate in a variety of realistic and important situations. Gabriel and Bernstein [8] provide several examples in which nonadditivity is more a...

The inclusion of explicit bounds on the link flows in traffic assignment models has been proposed as a means to obtain a more accurate description of the traffic behaviour than that given by the basic, uncapacitated, model. Although the capacitated problem has the advantage of being numerically more tractable than models involving travel cost functions which tend to infinity as flows approach the link capacities, it has received very limited attention in the past. The main reason for this is that the explicit capacities make the problem computationally more demanding, since they destroy the Cartesian product structure of the feasible set of the uncapacitated model, which enables the development of highly efficient solution procedures for that problem. The availability of efficient procedures for the basic model motivates the use of dualization approaches for handling the capacity constraints of the more complex model; we propose and evaluate an augmented Lagrangean method in which unca...

This paper considers a mass transit system in a regional area. The problem of improving the quality of the service in terms of costs perceived by the passenger is studied. A model to improve the effectiveness of the system maintaining the feasibility of the traffic assignment is proposed, along with new definitions of passenger assignment to support the proposed model. 1. Introduction In this paper we will consider a mass transit system in a regional area where both road and rail transportation may be used by commuters. Unlike the urban case [10], in a regional mass transit system, line frequencies are relatively low and trips can be considered as singular entities. We will assume that all the trips run on time according to a given time-table which is known by users; in addition, the vehicles have a fixed capacity (number of seats) which cannot be exceeded. Often transit companies have to cope with the problem of improving the level of service perceived by the users without increasing...

This paper describes the impact and influence of the book, Studies in the Economics of Transportation, by M. J. Beckmann, C. B. McGuire, and C. B. Winsten, published in 1956 by Yale University Press. The focus of this paper is on the book’s impacts on innovations in modeling, methodological developments, and applications in transportation science and in other disciplines as well.

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