A Second Order Traffic Flow Model with Lane Changing
- 92 Downloads
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.
KeywordsGas 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.
- 10.Greenshields, B.D., Bibbins, J.R., Channing, W.S., Miller, H.H.: A study of traffic capacity. In: Highway Research Board Proceedings (1935)Google Scholar
- 19.LeVeque, R.J.: Finite Volume Methods for Hyperbolic Problems. Cambridge University Press, Cambridge (2002)Google Scholar
- 22.Payne, Models of freeway traffic and control. In: Mathematical Models of Public Systems, Simulation Council Proceedings Series, vol. 1, no 1, pp. 51–61 (1971) Google Scholar
- 25.Roe, P.L.: Fluctuation and signals—a framework for numerical evolution problems. In: Morton, K.W., Baines, M.J. (eds.) Numerical Methods for Fluid Dynamics, pp. 219–257. Academic Press, New York (1982)Google Scholar
- 27.Song, J.: Mathematical modeling and simulations of traffic flow, Ph.D. Dissertation, University of Michigan (2019)Google Scholar
- 30.Wong, G.C.K., Wong, S.C.: A multi-class traffic flow model—an extension of LWR model with heterogeneous drivers. Transp. Res. Part A: Policy Pract. 36, 827–841 (2002)Google Scholar