A generalised stability criterion for motorway traffic

A common scenario on the motorway is that traffic that appears to be moving smoothly can suddenly spontaneously break down. This paper develops a new general criterion that determines whether these catastrophic events will occur. Primarily this is done in the context of the many car-following models described in the literature. The general criterion is shown to agree with the specific stability conditions of these models, including those in which drivers take into account vehicles more than one ahead. As described in the literature, when the flow is stable, columns of vehicles are seen to smooth any perturbations to the flow. This enables the general criterion to be extended to include non-identical drivers. The stability criterion is also seen to agree with those established from continuum theory. Finally, the stability condition is considered with respect to data obtained from the M25 in the UK.