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A kinematic wave theory of multi-commodity network traffic flow
Transportation Research Part B: Methodological, 2012Abstract A systematic understanding of traffic dynamics on road networks is crucial for many transportation studies and can help to develop more efficient ramp metering, evacuation, signal control, and other management and control strategies. In this study, we present a theory of multi-commodity network traffic flow based on the Lighthill–Whitham ...
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A simplified theory of kinematic waves in highway traffic, part I: General theory
Transportation Research Part B: Methodological, 1993Abstract In the theory of “kinematic waves,” as described originally by Lighthill and Whitham in 1955, the evaluation of the shock path is typically rather tedious. Instead of using this theory to evaluate flows or densities, one can use it to evaluate the cumulative flow A ( x , t ) past any point x by time t .
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Macroscopic Modeling Framework Unifying Kinematic Wave Modeling and Three-Phase Traffic Theory
Transportation Research Record: Journal of the Transportation Research Board, 2008Modeling breakdown probabilities or phase-transition probabilities is an important issue when assessing and predicting the reliability of traffic flow operations. Looking at empirical spatiotemporal patterns, these probabilities clearly are a function not only of the local prevailing traffic conditions (density, speed) but also of time and space.
Serge P. Hoogendoorn +2 more
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The application of kinematic wave theory to wave trains and packets with small dissipation
The Physics of Fluids, 1982The validity of kinematic wave theory for linear waves with small dissipation propagating through a homogeneous medium is examined with the aid of the higher-order theory of Chin. It is shown that both for nondissipative and weakly-dissipative waves the kinematic theory holds with errors of order ε2 for times of order ε−1 times the wave period, where ε
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A variational formulation of kinematic waves: basic theory and complex boundary conditions
Transportation Research Part B: Methodological, 2005Abstract This paper proves that the solution of every well-posed kinematic wave (KW) traffic problem with a concave flow-density relation is a set of least-cost (shortest) paths in space-time with a special metric. The equi-cost contours are the vehicle trajectories. If the flow-density relation is strictly concave the set of shortest paths is unique
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Singularities in kinematic wave theory: Solution properties, extended methods and duality revisited
Transportation Research Part B: Methodological, 2014Abstract According to Euler–Lagrange duality principle of kinematic wave (KW) theory any well-posed initial value traffic flow problem can be solved with the same methods either on the time–space (Euler) plane or the time vs vehicle number (Lagrange) plane.
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On Driver Anticipation, Two-Regime Flow, Fundamental Diagrams, and Kinematic-Wave Theory
Transportation Science, 2006The Cellular Automata (CA) Model CA-184a is introduced as a simplified traffic model that incorporates a rudimentary representation of driver anticipation. Simulations of single-loop and dual-loop acquisition of density-flow data upstream of a bottleneck are shown to display either a considerable similarity to density-flow data commonly so observed in
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Infectious disease in an era of global change
Nature Reviews Microbiology, 2021Rachel E Baker +2 more
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