The Aw-Rascle traffic flow model with phase transitions
نویسنده
چکیده
We introduce a new model of traffic flow with phase transitions. The model is obtained by coupling together the classical Lighthill-Whitham-Richards (LWR) equation with the 2 × 2 system described in [A. Aw and M. Rascle, Resurrection of “second order” models of traffic flow, SIAM J. Appl. Math., 60 (2000), pp. 916–938]. We describe the solutions of the Riemann problem, and we compare the results with the ones obtained using the LWR model and the biphasic model described in [R.M. Colombo, Hyperbolic phase transitions in traffic flow, SIAM J. Appl. Math., 63 (2002), pp. 708–721]
منابع مشابه
Moving bottlenecks for the Aw-Rascle-Zhang traffic flow model
We introduce a second order model for traffic flow with moving bottlenecks. The model consists of the 2×2 Aw-Rascle-Zhang system with a point-wise flow constraint whose trajectory is governed by an ordinary differential equation. We define two Riemann solvers, characterize the corresponding invariant domains and propose numerical strategies, which are effective in capturing the non-classical sh...
متن کاملExistence of Solutions for the Aw–rascle Traffic Flow Model with Vacuum
We consider the macroscopic model for traffic flow proposed by Aw and Rascle in 2000. The model is a 2×2 system of hyperbolic conservation laws, or, when the model includes a relaxation term, a 2 × 2 system of hyperbolic balance laws. The main difficulty is the presence of vacuum, which makes us unable to control the total variation of the conservative variables. We allow vacuum to appear and p...
متن کاملCar-following and the Macroscopic Aw–rascle Traffic Flow Model
We consider a semi-discrete car-following model and the macroscopic Aw–Rascle model for traffic flow given in Lagrangian form. The solution of the car-following model converges to a weak entropy solution of the system of hyperbolic balance laws with Cauchy initial data. For the homogeneous system, we allow vacuum in the initial data. By using properties of the semi-discrete model, we show that ...
متن کاملA Hybrid Lagrangian Model Based on the Aw--Rascle Traffic Flow Model
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 [3]. This hybridization makes use of the relation between the AR macroscopic model and a Follow-the-Leader type model [15, 22], established in [2]. Moreover, in the hybrid model...
متن کاملOn the Controversy around Daganzo’s Requiem for and Aw-Rascle’s Resurrection of Second-Order Traffic Flow Models
Daganzo’s criticisms of second-order fluid approximations of traffic flow [C. Daganzo, Transpn. Res. B. 29, 277-286 (1995)] and Aw and Rascle’s proposal how to overcome them [A. Aw and M. Rascle, SIAM J. Appl. Math. 60, 916-938 (2000)] have stimulated an intensive scientific activity in the field of traffic modeling. Here, we will revisit their arguments and the interpretations behind them. We ...
متن کامل