The class of simplicial decomposition (SD) schemes have shown to provide efficient tools for nonlinear network flows. When applied to the traffic assignment problem, shortest route subproblems are solved in order to generate extreme points of the polyhedron of feasible flows, and, alternately, master problems are solved over the convex hull of the generated extreme points. We review the development of simplicial decomposition and the closely related column generation methods for the traffic assignment problem; we then present a modified, disaggregated, representation of feasible solutions in SD algorithms for convex problems over Cartesian product sets, with application to the symmetric traffic assignment problem. The new algorithm, which is referred to as disaggregate simplicial decomposition (DSD), is given along with a specialized solution method for the disaggregate master problem. Numerical results for several well known test problems and a new one are presented. These experimenta...

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...

This research develops and applies a new structure for the transportation planning model that includes feedback between demand, assignment, and traffic control. New methods, combined with a renewed interest in transportation planning models prompted by the Clean Air Act of 1990 and the Intermodal Surface Transportation Efficiency Act of 1991, warrant a reconsideration of the traditional "four-step " transportation planning model. This paper presents an algorithm for feedback which results in consistent travel times as input to travel demand and output from route assignment. The model, including six stages of Trip

. 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...

This paper addresses the general time-route assignment problem : One considers an air transportation network in a 2 dimensional space with asymmetric non-separable link cost and a fleet of aircraft with their associated route and slot of departure. For each flight a set of alternative routes and a set of possible slots of departure are defined. One must find "optimal" route and slot allocation for each aircraft in a way that significaly reduces the peak of workload in the most congested sectors and in the most congested airports, during one day of traffic. A state of the art of

Major disruption to a transportation network can disturb traffic flow patterns significantly. To deploy effective and efficient traffic restoration projects, a good prediction of the traffic flow pattern under network disruption is vital. Although traffic flow evolution processes have been modeled in various ways in the literature, very limited attention has been paid to the traffic flow evolution process after an unexpected network disruption. In fact, due to the lack of data, none of the existing day-to-day traffic assignment models have been compared against reality, and thus their quality has not yet been verified. There clearly exists a gap between day-to-day traffic flow evolution modeling and their practical applications, especially under network disruption scenarios that are of great interest to traffic management authorities. This doctoral research is dedicated to bridging that gap by developing and validating innovative new models for deterministic day-to-day traffic assignment problem. The first innovation is the development of a link-based traffic dynamic model for studying traffic evolution. Existing deterministic day-to-day traffic assignment models were all built upon path flow variables. Most path-based models, however, suffer two

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This work offers a simulation-based approximation algorithm for dynamic marginal cost pricing (MCP) that is a direct extension of static MCP. The algorithm approximates the time-dependent marginal costs, and is incorporated into the inner approximation dynamic user equilibrium algorithm to evaluate the results of dynamic MCP, which are then compared to static assignment results with MCP from previous study. The status quo and dynamic MCP-on-freeways scenarios are simulated (and then compared) on Dallas-Fort Worth 35,732-link network. Due to computational requirements for such large-scale DTA application, the dynamic MCP scenario is simulated without feedback, and only route choices are permitted to vary. When prices are imposed, some minor system benefits are observed, including a delay in the onset of congestion. Dynamic prices vary substantially over the analysis period, reflecting changes in congestion. Reasons for any inconsistencies between dynamic and static results are discussed, along with important enhancements to future implementation.