AN EXTENDED TRAFFIC MODEL FOR FREEWAY CONTROL

This report presents a basic nonlinear invariant model for simulating motorway traffic flow, and extends it to show more realistic behaviour at bottlenecks. Section i lists seven different reasons for developing mathematical models of road traffic flow, and briefly discusses some earlier models. Section II formulates the basic model, presenting and interpreting its equations in terms of their physical meaning; the model is given in a discrete form, to adapt it for running on digital computers. The model covers the whole range of traffic conditions from free flow to heavy congestion. Section III analyses the defects of the basic model, and develops an extended model able to cope with traffic bottlenecks caused by changes in the number of lanes in a highway and by merging of on-ramp flows. Section IV shows how to calibrate the parameters of the extended model to achieve optimal agreement with observed traffic flows. It then uses the calibrated model for a quantitative comparison between the model's performance and the real road traffic flow phenomena, and for evaluating its accuracy. Section v presents some conclusions: there was good agreement between theory and observations, and the bottleneck phenomena were modelled fairly realistically. Future work should include tests of the extended model with more data sets from different traffic situations and different sections of intercity motorways. Appendix a gives a sample of motorway measurement data, and appendix b gives a FORTRAN program listing of the simulation model.