The Stability Analysis of a Macroscopic Traffic Flow Model with Two-Classes of Drivers

One of the most important objectives in the development of traffic theories is the improvement of traffic conditions. To achieve this goal, it is important a good understanding of multistyle and/or multilane traffic. In this work, we summarize the traffic model presented in Mendez and Velasco (FTC J Phys A Math Theor 46(46):462001, 2013) and additionally include the stability analysis of the same. The presented traffic model considers different driving styles, different vehicle types or both, for a two-classes of vehicles in which a model for the average desired speed is introduced (the aggressive drivers model) (Mendez and Velasco, Transp Res Part B 42:782–797, 2008; Velasco and Marques, Phys Rev E 72:046102, 2005). The kinetic model was solved for the steady and homogeneous state and also we obtained the local distribution function from an information entropy maximization procedure. The macroscopic traffic model is constructed by the usual methods in kinetic theory and a method akin with the Maxwellian iterative procedure is accomplished in order to close the macroscopic model for the mixture, where only the densities are present as relevant quantities. The linear stability analysis is carried out in order to have an insight of the unstable traffic regions of the model, which is very helpful in the numerical solution.