Journal of Scientific Computing

, Volume 81, Issue 3, pp 1429–1445 | Cite as

A Second Order Traffic Flow Model with Lane Changing

  • Jiah Song
  • Smadar KarniEmail author


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.


Gas dynamics Conservation laws Hyperbolic systems Traffic flow 



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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Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA

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