Numerical simulation of multilane traffic flow model based on exponential velocity-density function

In this paper, we study a multilane traffic flow model incorporating the exponential velocity-density relationship, which yields a nonlinear first-order system of hyperbolic partial differential (PDEs) equations formulated as an initial-boundary value problem (IBVP). This study seeks to construct a physically consistent and computationally efficient model for a multilane traffic flow model, which captures nonlinear vehicular interactions and lane-changing dynamics. Numerical solutions of the multilane traffic flow model, under the specified initial and boundary conditions, are obtained using the finite difference method. The numerical simulations are performed by employing the well-known first-order Explicit Upwind Scheme, the Lax-Friedrichs Scheme, and the second-order Lax-Wendroff Scheme. We evaluate the convergence rate of the numerical solutions, along with detailed well-posedness and stability analysis. To assess the stability and accuracy of three numerical schemes, we compare the velocity and density profiles derived from different schemes. The outcomes of our study have significant applications in traffic management in the real world, including predicting the effect of congestion, optimizing the lane-change effects, and enhancing efficiency through intelligent transportation system intelligent transportation system (ITS) and safety on multilane highways.