On kinematic waves II. A theory of traffic flow on long crowded roads

DOI10.1098/rspa.1955.0089zbMath0064.20906OpenAlexW2095797625WikidataQ55953996 ScholiaQ55953996MaRDI QIDQ5847948

Publication date: 1955

Published in: Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1098/rspa.1955.0089

zbMATH Keywords

fluid mechanics

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pattern formation in highway traffic models, Flow on Sweeping Networks, STABILITY AND KINK–ANTIKINK SOLITON SOLUTION FOR TOTAL GENERALIZED OPTIMAL VELOCITY MODEL, A non-local macroscopic model for traffic flow, Attainable profiles for conservation laws with flux function spatially discontinuous at a single point, Fold-over Regions in Nonlinear First Order PDEs, Second-Order Traffic Flow Models on Networks, A Diffusion-Based Analysis of a Multiclass Road Traffic Network, Optimal Boundary Control of Nonlinear Hyperbolic Conservation Laws with Switched Boundary Data, ON THE DIRICHLET-NEUMANN BOUNDARY PROBLEM FOR SCALAR CONSERVATION LAWS, On the Global Controllability of Scalar Conservation Laws with Boundary and Source Controls, A mixed ODE–PDE model for vehicular traffic, A Heterogeneous Multiclass Traffic Flow Model with Creeping, Stability of a Nonlocal Traffic Flow Model for Connected Vehicles, Solitary wave solution to a class of higher-order viscous traffic flow model, Hybrid Stochastic Galerkin Finite Volumes for the Diffusively Corrected Lighthill-Whitham-Richards Traffic Model, Entropy Dissipation at the Junction for Macroscopic Traffic Flow Models, A complete system of conditions for uncongested traffic of vehicles in front of a traffic light at a symmetrical two-lane intersection, Traveling solutions for a multi-anticipative car-following traffic model, Unnamed Item, Homogenization of a microscopic pedestrians model on a convergent junction, Nonlinear adaptive cruise control of vehicular platoons, A nonlinear heat equation arising from automated-vehicle traffic flow models, Lyapunov Stabilization for Nonlocal Traffic Flow Models, Reconstruction of density and cost potential field of eikonal equation: applications to discrete pedestrian flow models, Traffic flow control on cascaded roads by event‐triggered output feedback, Differential games for crowd dynamics and applications, Optimal observer‐based output feedback controller for traffic congestion with bottleneck, Convergence, bounded variation properties and Kruzhkov solution of a fully discrete Lagrangian–Eulerian scheme via weak asymptotic analysis for <scp>1D</scp> hyperbolic problems, Derivation and Stability Analysis of a Macroscopic Multilane Model for Traffic Flow, On the coupling of well posed differential models, Limits of solutions to the Aw-Rascle traffic flow model with generalized Chaplygin gas by flux approximation, Macroscopic traffic flow modelling: from kinematic waves to autonomous vehicles, Density Fluctuations in Stochastic Kinematic Flows, Analysis of the generalized Aw-Rascle model, Macroscopic limits of non-local kinetic descriptions of vehicular traffic, The initial boundary value problem for second order traffic flow models with vacuum: existence of entropy weak solutions, Fifth-Order A-WENO Path-Conservative Central-Upwind Scheme for Behavioral Non-Equilibrium Traffic Models, Existence of entropy weak solutions for 1D non-local traffic models with space-discontinuous flux, Discontinuous nonlocal conservation laws and related discontinuous ODEs -- existence, uniqueness, stability and regularity, Unnamed Item, The discontinuous finite element method for red-and-green light models for the traffic flow, Modelling of freeway merging and diverging flow dynamics, Phase plane analysis method of nonlinear traffic phenomena, Optimal Boundary Control of Hyperbolic Balance Laws with State Constraints, Second-order delay ordinary differential equations, their symmetries and application to a traffic problem, Global solutions of nonconcave hyperbolic conservation laws with relaxation arising from traffic flow, Using deep learning to extend the range of air pollution monitoring and forecasting, Spatio-temporal modelling and prediction of bus travel time using a higher-order traffic flow model, Computing dynamic user equilibrium on large-scale networks without knowing global parameters, Hyperbolic balance laws: modeling, analysis, and numerics. Abstracts from the workshop held February 28 -- March 6, 2021 (hybrid meeting), An exit-flow model used in dynamic traffic assignment, Well-posedness theory for nonlinear scalar conservation laws on networks, Bifurcation analysis of a class of `car following' traffic models, Stochastic perturbation of the Lighthill-Whitham-Richards model via the method of stochastic characteristics, Uncertainty quantification in hierarchical vehicular flow models, A new higher-order viscous continuum traffic flow model considering driver memory in the era of autonomous and connected vehicles, A unified view of transport equations, Impacts of energy consumption and emissions on the trip cost without late arrival at the equilibrium state, A cellular automata traffic flow model for three-phase theory, Analysis of the trip costs of a traffic corridor with two entrances and one exit under car-following model, KdV-Burgers equation in a new continuum model based on full velocity difference model considering anticipation effect, Social optimum for evening commute in a single-entry traffic corridor with no early departures, KdV-Burgers equation in the modified continuum model considering the effect of friction and radius on a curved road, Impacts of moving bottlenecks on traffic flow, Nonlinear analysis for a modified continuum model considering driver's memory and backward looking effect, An extended continuum traffic model with the consideration of the optimal velocity difference, A two-lane lattice hydrodynamic model with heterogeneous lane changing rates, Modeling vehicular traffic networks. I., Analysis of trip cost allowing late arrival in a traffic corridor with one entry and one exit under car-following model, A route-based traffic flow model accounting for interruption factors, Analysis of trip cost in a two-lane traffic corridor with one entry and one exit, Travel times, rational queueing and the macroscopic fundamental diagram of traffic flow, Research on preceding vehicle's taillight effect and energy consumption in an extended macro traffic model, An improved anisotropic continuum model considering the driver's desire for steady driving, Research on critical characteristics of highway traffic flow based on three phase traffic theory, A new queue shock wave theory based on platoon dispersion modeling, A quasi-contagion process modeling and characteristic analysis for real-world urban traffic network congestion patterns, Nonlinear analysis for a modified continuum model considering electronic throttle (ET) and backward looking effect, Research on the influence of multiple historical speed information with different weight distribution on traffic flow stability, Constructing artificial traffic fluids by designing cruise controllers, An iterative learning identification strategy for nonlinear macroscopic traffic flow model, Controllability of the one-dimensional fractional heat equation under positivity constraints, Lagrangian-antidiffusive remap schemes for non-local multi-class traffic flow models, The BGK approximation of kinetic models for traffic, Implementation of the vehicular occupancy-emission relation using a cubic B-splines collocation method, A new car-following model with consideration of roadside memorial, A multiscale model for traffic regulation via autonomous vehicles, On traffic flow with nonlocal flux: a relaxation representation, Travelling wave solutions of the perturbed mKdV equation that represent traffic congestion, Asymptotic methods for solitary solutions and compactons, Continuous approximation of \(M_t/M_t/ 1\) distributions with application to production, Burgers type equations, Gelfand's problem and Schumpeterian dynamics, Comparative study of macroscopic traffic flow models at road junctions, Two-lane lattice hydrodynamic model considering the empirical lane-changing rate, Traffic congestion evaluation and signal control optimization based on wireless sensor networks: model and algorithms, Formation and propagation of local traffic jam, Spatial distribution complexities of traffic congestion and bottlenecks in different network topologies, Thresholds for shock formation in traffic flow models with nonlocal-concave-convex flux, The follow-the-leader model without a leader: an infinite-dimensional Cauchy problem, Interpolated variational iteration method for solving the jamming transition problem, Estimation of travel time through a composite ring road by a viscoelastic traffic flow model, Modulation theory, dispersive shock waves and Gerald Beresford Whitham, Modeling crowd dynamics through coarse-grained data analysis, Assimilating Eulerian and Lagrangian data in traffic-flow models, Shock waves of viscoelastic Burgers equations, A combinatorial dynamic network trajectory reservation algorithm for connected autonomous vehicles, Computing dynamic user equilibria on large-scale networks with software implementation, Numerical homogenization of a second order discrete model for traffic flow, Numerical simulation of air pollution due to traffic flow in urban networks, Multilane analysis of a viscous second-order macroscopic traffic flow model, Smoothing effect of degenerate diffusion, A game-theoretic framework for autonomous vehicles velocity control: bridging microscopic differential games and macroscopic mean field games, Entropy solutions for a two-phase transition model for vehicular traffic with metastable phase and time depending point constraint on the density flow, A hierarchical MPC and sliding mode based two-level control for freeway traffic systems with partial demand information, Robust variable speed limit control with respect to uncertainties, Modeling the asymmetry in traffic flow. II: Macroscopic approach, Exact boundary controllability for free traffic flow with Lipschitz continuous state, An optimization model of multi-intersection signal control for trunk road under collaborative information, A multiclass Lighthill-Whitham-Richards traffic model with a discontinuous velocity function, Properties of the LWR model with time delay, Rule 184 fuzzy cellular automaton as a mathematical model for traffic flow, Modeling random traffic accidents by conservation laws, Homogenization of a stochastic viscous transport equation, Simultaneous downstream and upstream output-feedback stabilization of cascaded freeway traffic, Impacts of bounded rationality on trip cost in a two-route traffic network, Kinetic derivation of Aw-Rascle-Zhang-type traffic models with driver-assist vehicles, Studying perturbations and wave propagations by lane closures on traffic characteristics based on a dynamic approach, Vanishing viscosity for a \(2 \times 2\) system modeling congested vehicular traffic, Multi-class traffic flow model based on three dimensional flow-concentration surface, A double velocity control method for a discrete-time cooperative driving system with varying time-delay, Stabilized finite element computations with a two-dimensional continuum model for disorderly traffic flow, A PDE model for unidirectional flows: stationary profiles and asymptotic behaviour, On a class of new nonlocal traffic flow models with look-ahead rules, Estimate of traffic emissions through multiscale second order models with heterogeneous data, A streaming-data-driven method for freeway traffic state estimation using probe vehicle trajectory data, Estimating fundamental diagram for multi-modal signalized urban links with limited probe data, Model of vehicle interactions with autonomous cars and its properties, On a nonclassical problem for some quasilinear hyperbolic equation, Optimal neural networks architectures for the flow-density relationships of traffic models, Data-driven uncertainty quantification in macroscopic traffic flow models, Burgers' equation revisited: extension of mono-dimensional case on a network, Analyses of lattice hydrodynamic area occupancy model for heterogeneous disorder traffic, High order numerical methods for flows with hysteretic fluxes, Towards numerical procedures for those technical phenomena whose mathematical models lead to non-standard conservation laws, On the distribution of calls in a wireless network driven by fluid traffic