Finite Difference Formulation of Lighthill Whitham Richards Macroscopic Model for Traffic Flow Prediction

Abstract

Mathematical modelling of traffic flow for accurate prediction of future traffic conditions plays a vital role in real time traffic control systems. Modelling of traffic at macroscopic level using Lighthill Whitham Richards (LWR) model is computationally less intensive than microscopic car following models. With advanced computing facilities, numerical solution of the LWR model is preferred than traditional analytical approaches. In the present study, an attempt has been made to solve numerically the LWR model using "Forward-Time Backward-Space (FTBS)" finite difference scheme. Actual traffic flow data collected from a roadway in Vellore were used to frame the initial and boundary conditions and for corroboration of the results. The results were promising as the predicted flow values by the FTBS scheme were matched closely with the actuals with mean absolute percentage error (MAPE) of 12.854. This showed the suitability of the proposed numerical scheme for traffic flow prediction.