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

On the Invariants of Towers of Function Fields over Finite Fields

We consider a tower of function fields F=(F_n)_{n\geq 0} over a finite field F_q and a finite extension E/F_0 such that the sequence \mathcal{E):=(EF_n)_{n\goq 0} is a tower over the field F_q. Then we deal with the following: What can we say about the invariants of \mathcal{E}; i.e., the asymptotic number of places of degree r for any r\geq 1 in \mathcal{E}, if those of F are known? We give a method based on explicit extensions for constructing towers of function fields over F_q with finitely many prescribed invariants being positive, and towers of function fields over F_q, for q a square, with at least one positive invariant and certain prescribed invariants being zero. We show the existence of recursive towers attaining the Drinfeld-Vladut bound of order r, for any r\geq 1 with q^r a square. Moreover, we give some examples of recursive towers with all but one invariants equal to zero.Comment: 23 page

Reactive Dynamic Assignment for a Bi-dimensional Traffic Flow Model

International audience This paper develops a graph-theoretic framework for large scale bi-dimensional transport networks and provides new insight into the dynamic traffic assignment. Reactive dynamic assignment are deployed to handle the traffic contingencies, traffic uncertainties and traffic congestion. New shortest paths problem in large networks is defined and routes cost calculation is provided. Since mathematical modelling of traffic flow is a keystone in the theory of traffic flow management, and then in the traffic assignment, it is convenient to elaborate a good model of assignment for large scale networks relying on an appropriate model of flow related to very large networks. That is the zone-based optimization of traffic flow model on networks developed by [8], completed and improved by [9]. Document type: Part of book or chapter of boo

Intersection modeling using a convergent scheme based on Hamilton-Jacobi equation

AbstractThis paper presents a convergent scheme for Hamilton-Jacobi (HJ) equations posed on a junction. The general aim of the approach is to develop a framework using similar tools to the variational principle in traffic theory to model intersections taking in account many incoming and outgoing roads. Then a time-explicit numerical scheme is proposed. It is based on the very classical Godunov scheme. The proposed model could be characterized as a pointwise model of intersection without any internal state. Moreover, our model respects the invariance principle. This scheme is applied to the cases of diverge junctions. The goal is to know how to manage the fluxes in order to maximize the flow through the junction

A variational formulation for higher order macroscopic traffic flow models: numerical investigation

This paper deals with numerical methods providing semi-analytic solutions to a wide classofmacroscopictrafficflow modelsfor piecewiseaffine initial andboundaryconditions. In a very recent paper, a variational principle has been proved for models of the Generic Second Order Modeling (GSOM) family, yielding an adequate framework for effective numerical methods. Any model of the GSOM family can be recast into its Lagrangian form as a Hamilton-Jacobi equation (HJ) for which the solution is interpreted as the position of vehicles. This solution can be computed thanks to Lax-Hopf like formulas and a generalization of the inf-morphism property. The efficiency of this computational method is illustrated through a numerical example and finally a discussion about future developments is provided

INTRODUCING BUSES INTO FIRST-ORDER MACROSCOPIC TRAFFIC FLOW MODELS

The aim of this paper is to provide a simple model of the interaction between buses and the surrounding traffic flow. Traffic flow is assumed to be described by a first-order macroscopic model of the Lighthill-Whitman-Richards type. As a consequence of their kinematics, which in large measure can be considered to be independent of the flow of other vehicles, buses should be considered as a moving capacity restriction from the point of view of other drivers. This simple interaction model is analyzed, mainly by considering the moving frame associated with the bus in order to derive analytical computation rules for derivation of the effects of the presence of the bus in the traffic flow. After deriving traffic equations in the moving frame associated with a bus, the usual basic concepts of first-order models, including those of relative traffic supply and demand, are generalized to the moving frame. A simple model for the bus-traffic interaction, assuming that the dimension of the bus can be neglected, can be derived from analytical calculations in the moving frame. Finally, some tentative results for the inclusion of buses into first-order traffic flow models, discretized according to Godunov\u27s scheme, are given