1,408 research outputs found

    A diffusion-based analysis of a multi-class road traffic network

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    This paper studies a stochastic model that describes the evolution of vehicle densities in a road network. It is consistent with the class of (deterministic) kinematic wave models, which describe traffic flows on the basis of conservation laws that incorporate the macroscopic fundamental diagram (a functional relationship between vehicle density and flow). Our setup is capable of handling multiple types of vehicle densities, with general macroscopic fundamental diagrams, on a network with arbitrary topology. Interpreting our system as a spatial population process, we derive, under a natural scaling, fluid and diffusion limits. More specifically, the vehicle density process can be approximated with a suitable Gaussian process, which yield accurate normal approximations to the joint (in the spatial and temporal sense) vehicle density process. The corresponding means and variances can be computed efficiently. Along the same lines, we develop an approximation to the vehicles' travel-time distribution between any given origin and destination pair. Finally, we present a series of numerical experiments that demonstrate the accuracy of the approximations and illustrate the usefulness of the results

    Genealogy of traffic flow models

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    Cellular Automata Models of Road Traffic

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    In this paper, we give an elaborate and understandable review of traffic cellular automata (TCA) models, which are a class of computationally efficient microscopic traffic flow models. TCA models arise from the physics discipline of statistical mechanics, having the goal of reproducing the correct macroscopic behaviour based on a minimal description of microscopic interactions. After giving an overview of cellular automata (CA) models, their background and physical setup, we introduce the mathematical notations, show how to perform measurements on a TCA model's lattice of cells, as well as how to convert these quantities into real-world units and vice versa. The majority of this paper then relays an extensive account of the behavioural aspects of several TCA models encountered in literature. Already, several reviews of TCA models exist, but none of them consider all the models exclusively from the behavioural point of view. In this respect, our overview fills this void, as it focusses on the behaviour of the TCA models, by means of time-space and phase-space diagrams, and histograms showing the distributions of vehicles' speeds, space, and time gaps. In the report, we subsequently give a concise overview of TCA models that are employed in a multi-lane setting, and some of the TCA models used to describe city traffic as a two-dimensional grid of cells, or as a road network with explicitly modelled intersections. The final part of the paper illustrates some of the more common analytical approximations to single-cell TCA models.Comment: Accepted for publication in "Physics Reports". A version of this paper with high-quality images can be found at: http://phdsven.dyns.cx (go to "Papers written"

    Dynamic network loading: a stochastic differentiable model that derives link state distributions

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    We present a dynamic network loading model that yields queue length distributions, accounts for spillbacks, and maintains a differentiable mapping from the dynamic demand on the dynamic queue lengths. The model also captures the spatial correlation of all queues adjacent to a node, and derives their joint distribution. The approach builds upon an existing stationary queueing network model that is based on finite capacity queueing theory. The original model is specified in terms of a set of differentiable equations, which in the new model are carried over to a set of equally smooth difference equations. The physical correctness of the new model is experimentally confirmed in several congestion regimes. A comparison with results predicted by the kinematic wave model (KWM) shows that the new model correctly represents the dynamic build-up, spillback, and dissipation of queues. It goes beyond the KWM in that it captures queue lengths and spillbacks probabilistically, which allows for a richer analysis than the deterministic predictions of the KWM. The new model also generates a plausible fundamental diagram, which demonstrates that it captures well the stationary flow/density relationships in both congested and uncongested conditions

    A kinematic wave theory of capacity drop

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    Capacity drop at active bottlenecks is one of the most puzzling traffic phenomena, but a thorough understanding is practically important for designing variable speed limit and ramp metering strategies. In this study, we attempt to develop a simple model of capacity drop within the framework of kinematic wave theory based on the observation that capacity drop occurs when an upstream queue forms at an active bottleneck. In addition, we assume that the fundamental diagrams are continuous in steady states. This assumption is consistent with observations and can avoid unrealistic infinite characteristic wave speeds in discontinuous fundamental diagrams. A core component of the new model is an entropy condition defined by a discontinuous boundary flux function. For a lane-drop area, we demonstrate that the model is well-defined, and its Riemann problem can be uniquely solved. We theoretically discuss traffic stability with this model subject to perturbations in density, upstream demand, and downstream supply. We clarify that discontinuous flow-density relations, or so-called "discontinuous" fundamental diagrams, are caused by incomplete observations of traffic states. Theoretical results are consistent with observations in the literature and are verified by numerical simulations and empirical observations. We finally discuss potential applications and future studies.Comment: 29 pages, 10 figure
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