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A Second Order Traffic Flow Model with Lane Changing

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Abstract

This paper concerns modeling and computation of traffic flow for a single in-lane flow as well as multilane flow with lane changing. We consider macroscopic partial differential equation models of two types: (i) First Order Models: equilibrium models, scalar models expressing car mass conservation; and (ii) Second Order Models: dynamic models, \(2 \times 2\) hyperbolic systems expressing mass conservation as well as vehicle acceleration rules. A new second order model is proposed in which the acceleration terms take lead from microscopic car-following models, and yield a nonlinear hyperbolic system with viscous and relaxation terms. Lane changing conditions are formulated and mass/momentum inter-lane exchange terms are derived. Numerical results are shown, illustrating the merit of the models in describing a rich array of realistic traffic scenarios including varying road conditions, lane closure, and stop-and-go flow patterns.

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Notes

  1. The term Fundamental Diagram is often used to denote the flux–density relation, here we use it equivalently to refer to the velocity–density relation.

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Acknowledgements

S. Karni has benefitted from stimulating and insightful conversations during a couple of visits to the University of Zurich, Switzerland. The generous hospitality of Rémi Abgrall is gratefully acknowledged. S. Karni wishes to extend her sincere gratitude to Jack Haddad of the Technion, Israel, for stimulating discussions. The authors are also grateful to Romesh Saigal and Philip Roe for productive discussions.

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  1. Department of Mathematics, University of Michigan, Ann Arbor, USA

    Jiah Song & Smadar Karni

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  1. Jiah Song
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  2. Smadar Karni
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Correspondence to Smadar Karni.

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In fond memory of Saul Abarbanel, an appreciated teacher, a generous colleague and a warm-hearted mensch.

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This work was supported in part by NSF Grant DMS 1417053 and by a University of Michigan Crosby Award.

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Song, J., Karni, S. A Second Order Traffic Flow Model with Lane Changing. J Sci Comput 81, 1429–1445 (2019). https://doi.org/10.1007/s10915-019-01023-z

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