A Hybrid Lagrangian Model Based on the Aw–Rascle Traffic Flow Model
S. Moutari, M. Rascle
Source abstract
In this paper, we propose a simple fully discrete hybrid model for vehicular traffic flow, for which both the macroscopic and the microscopic models are based on a Lagrangian discretization of the Aw–Rascle (AR) model [A. Aw and M. Rascle, SIAM J. Appl. Math., 60 (2000), pp. 916–938]. This hybridization makes use of the relation between the AR macroscopic model and a follow-the-leader-type model [D. C. Gazis, R. Herman, and R. W. Rothery, Oper. Res., 9 (1961), pp. 545–567; R. Herman and I. Prigogine, Kinetic Theory of Vehicular Traffic, American Elsevier, New York, 1971], established in [A. Aw, A. Klar, M. Materne, and M. Rascle, SIAM J. Appl. Math., 63 (2002), pp. 259–278]. Moreover, in the hybrid model, the total variation in space of the velocity v is nonincreasing, the total variation in space of the specific volume is bounded, and the total variations in time of v and are bounded. Finally, we present some numerical simulations which confirm that the models' synchronization processes do not affect the waves propagation.
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