Traffic Flow on a Road Network

By Giuseppe Maria Coclite, Mauro Garavello, Benedetto Piccoli. SIAM Journal on Mathematical Analysis, 2002

381 citations recorded by the source corpus.

This paper is concerned with a fluidodynamic model for traffic flow. More precisely, we consider a single conservation law, deduced from the conservation of the number of cars, defined on a road network that is a collection of roads with junctions. The evolution problem is underdetermined at junctions; hence we choose to have some fixed rules for the distribution of traffic plus optimization criteria for the flux. We prove existence of solutions to the Cauchy problem and we show that the Lipschitz continuous dependence by initial data does not hold in general, but it does hold under special assumptions.Our method is based on a wave front tracking approach [A. Bressan, Hyperbolic Systems of Conservation Laws. The One-dimensional Cauchy Problem, Oxford University Press, Oxford, UK, 2000] and works also for boundary data and time-dependent coefficients of traffic distribution at junctions, including traffic lights.

Subfields: Computational Mechanics, Control and Systems Engineering, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/3cc46aecc8362f369f065eddcd0db6f4e8033402

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Citations in the corpus

Analysis of a conservation law modeling a highly re-entrant manufacturing system (2009, neutral): “[12].”
On the Modeling of Traffic and Crowds: A Survey of Models, Speculations, and Perspectives (2011, background): “They are also useful for dealing with modeling traffic on networks [44], [59], [79].”
Traffic Flow on a Road Network Using the Aw–Rascle Model (2006, methodology): “Appendix: Total Variation of the Flux In the case of a road network where the Lighthill–Whitham–Richards scalar model is considered in each road, if every junction has exactly 2 incoming and 2 outgoing roads, then an increment of the total variation of the flux can happen only when a wave on an outg”
Conservation laws on complex networks (2009, methodology): “More precisely in [12,24] there is a counterexample to the Lipschitz continuous dependence property in the case of a node with two incoming and two outgoing arcs.”
A robust optimization approach for dynamic traffic signal control with emission considerations (2012, neutral): “Other studies of the network extension of the LWR model or the CTM include Bretti et al. (2006); Coclite et al (2005); Herty and Klar (2003); Holden and Risebro (1995); Jin (2010); Jin and Zhang (2003); Lebacque and Khoshyaran (1999) and Lebacque and Khoshyaran (2002).”
Analysis and control of a scalar conservation law modeling a highly re-entrant manufacturing system (2010, background): “In many aspects these models are quite similar to those of traffic flows [7] and pedestrian flows [8,9,15].”
Source-Destination Flow on a Road Network (2005, methodology): “Basic definitions We introduce some basic notations and recall some results from [7, 8].”
A kinematic wave theory of multi-commodity network traffic flow (2012, methodology): “In this sense, the multicommodity kinematic wave theory is not complete for network traffic flow.4 In (Holden and Risebro, 1995; Coclite et al., 2005), junction models have been presented in density-flux space.”