A Finite Difference Formulation for a Traffic Flow Model

Abstract

A simple continuum model for traffic flow, based on the law of mass conservation, is discussed. A finite difference formulation for the model is obtained and real traffic data are used for further numerical investigations. The numerical scheme is implemented and solved using the spreadsheet features and Visual Basic capabilities (VBA) of Microsoft Excel. Results from the numerical tests show that predictions about traffic behaviour and conditions agree well with collected data provided initial and boundary conditions are carefully treated. The modelling exercise discussed in this paper provides an excellent example of applying relevant mathematics to a relatively complex real life problem. In addition, by using a simple computer tool (namely, a spreadsheet) in the numerical solution of the model, this paper has demonstrated the value of technology in making mathematical investigations more accessible.