An analysis of Gipps's car-following model of highway traffic

A mathematical analysis of Gipps's (1981) car-following model is performed. This model is of practical importance as it powers the UK Transport Research Laboratory highway simulation package SISTM. Uniform flow solutions and a speed-headway function are derived under simplifying conditions. A linear stability analysis of uniform flow is then performed, and stable and unstable regimes are identified. Finally, some numerical simulations for a variety of parameter regimes are presented.