Statistical metamodeling of dynamic network loading

Dynamic traffic assignment models rely on a network performance module known as dynamic network loading (DNL), which expresses flow propagation, flow conservation, and travel delay at a network level. The DNL defines the so-called network delay operator, which maps a set of path departure rates to a set of path travel times (or costs). It is widely known that the delay operator is not available in closed form, and has undesirable properties that severely complicate DTA analysis and computation, such as discontinuity, non-differentiability, non-monotonicity, and computational inefficiency. This paper proposes a fresh take on this important and difficult issue, by providing a class of surrogate DNL models based on a statistical learning method known as Kriging. We present a metamodeling framework that systematically approximates DNL models and is flexible in the sense of allowing the modeler to make trade-offs among model granularity, complexity, and accuracy. It is shown that such surrogate DNL models yield highly accurate approximations (with errors below 8%) and superior computational efficiency (9 to 455 times faster than conventional DNL procedures such as those based on the link transmission model). Moreover, these approximate DNL models admit closed-form and analytical delay operators, which are Lipschitz continuous and infinitely differentiable, with closed-form Jacobians. We provide in-depth discussions on the implications of these properties to DTA research and model applications

Mesoscopic simulator data to perform dynamic origin- destination matrices estimation in urban context

The aim of this paper is to explore a new approach to obtain better traffic demand (Origin-Destination, OD matrices) for dense urban networks using traffic simulation data. From reviewing existing methods, from static to dynamic OD matrix evaluation, possible deficiencies in the approach could be identified. To improve the global process of traffic demand estimation, this paper is focusing on a new methodology to determine dynamic OD matrices for urban areas characterized by complex route choice situation and high level of traffic controls. An iterative bi- level approach will be used to perform the OD estimation. The Lower Level (traffic assignment) problem will determine, dynamically, the utilization of the network by vehicles using heuristic data from mesoscopic traffic simulator particularly adapted for urban context. The Upper Level (matrix adjustment) problem will proceed to an OD estimation using optimization least square techniques. In this way, a full dynamic and continuous estimation of the final OD matrix could be obtained. First evaluation of the proposed approach and conclusions are presented

Formulation, existence, and computation of boundedly rational dynamic user equilibrium with fixed or endogenous user tolerance

This paper analyzes dynamic user equilibrium (DUE) that incorporates the notion of boundedly rational (BR) user behavior in the selection of departure times and routes. Intrinsically, the boundedly rational dynamic user equilibrium (BR-DUE) model we present assumes that travelers do not always seek the least costly route-and-departure-time choice. Rather, their perception of travel cost is affected by an indifference band describing travelers’ tolerance of the difference between their experienced travel costs and the minimum travel cost. An extension of the BR-DUE problem is the so-called variable tolerance dynamic user equilibrium (VT-BR-DUE) wherein endogenously determined tolerances may depend not only on paths, but also on the established path departure rates. This paper presents a unified approach for modeling both BR-DUE and VT-BR-DUE, which makes significant contributions to the model formulation, analysis of existence, solution characterization, and numerical computation of such problems. The VT-BR-DUE problem, together with the BR-DUE problem as a special case, is formulated as a variational inequality. We provide a very general existence result for VT-BR-DUE and BR-DUE that relies on assumptions weaker than those required for normal DUE models. Moreover, a characterization of the solution set is provided based on rigorous topological analysis. Finally, three computational algorithms with convergence results are proposed based on the VI and DVI formulations. Numerical studies are conducted to assess the proposed algorithms in terms of solution quality, convergence, and computational efficiency

Elastic demand dynamic network user equilibrium: Formulation, existence and computation

This paper is concerned with dynamic user equilibrium with elastic travel demand (E-DUE) when the trip demand matrix is determined endogenously. We present an infinite-dimensional variational inequality (VI) formulation that is equivalent to the conditions defining a continuous-time E-DUE problem. An existence result for this VI is established by applying a fixed-point existence theorem (Browder, 1968) in an extended Hilbert space. We present three computational algorithms based on the aforementioned VI and its re-expression as a differential variational inequality (DVI): a projection method, a self-adaptive projection method, and a proximal point method. Rigorous convergence results are provided for these methods, which rely on increasingly relaxed notions of generalized monotonicity, namely mixed strongly-weakly monotonicity for the projection method; pseudomonotonicity for the self-adaptive projection method, and quasimonotonicity for the proximal point method. These three algorithms are tested and their solution quality, convergence, and computational efficiency are compared. Our convergence results, which transcend the transportation applications studied here, apply to a broad family of VIs and DVIs, and are the weakest reported to date

Continuous-time link-based kinematic wave model: formulation, solution existence, and well-posedness

We present a continuous-time link-based kinematic wave model (LKWM) for dynamic traffic networks based on the scalar conservation law model. Derivation of the LKWM involves the variational principle for the Hamilton-Jacobi equation and junction models defined via the notions of demand and supply. We show that the proposed LKWM can be formulated as a system of differential algebraic equations (DAEs), which captures shock formation and propagation, as well as queue spillback. The DAE system, as we show in this paper, is the continuous-time counterpart of the link transmission model. In addition, we present a solution existence theory for the continuous-time network model and investigate continuous dependence of the solution on the initial data, a property known as well-posedness. We test the DAE system extensively on several small and large networks and demonstrate its numerical efficiency.Comment: 39 pages, 14 figures, 2 tables, Transportmetrica B: Transport Dynamics 201

Application of robust and inverse optimization in transportation

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 79-82).We study the use of inverse and robust optimization to address two problems in transportation: finding the travel times and designing a transportation network. We assume that users choose the route selfishly and the flow will eventually reach an equilibrium state (User Equilibrium). The first part of the thesis demonstrates how inverse and robust optimization can be used to find the actual travel times given a stable flow on the network and some noisy information on travel times from different users. We model the users' perception of travel times using three different sets and solve the robust inverse problem for all of them. We also extend the idea to find parametric functional forms for travel times given historical data. Our numerical results illustrate the significant improvement obtained by our models over a simple fitting model. The second part of the thesis considers the network design problem under demand uncertainty. We show that for affine travel time functions, the deterministic problem can be formulated as a mixed integer programming problem with quadratic objective and linear constraints. For the robust network design problem, we propose a decomposition scheme: breaking a tri-level programming problem into two smaller problems and re-iterating until a good solution is obtained. To deal with the expensive computation required by large networks, we also propose a heuristic robust simulated annealing approach. The heuristic algorithm is computationally tractable and provides some encouragingly results in our simulations.by Thai Dung Nguyen.S.M

The nonlinear equation system approach to solving dynamic user optimal simultaneous route and departure time choice problems

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