Analysis and modelling of traffic flow under variable speed limits

We develop the relationship between speed and density to analyse the flow of traffic under the operation of variable speed limits. By statistical analysis of traffic data from the UK motorway network, we find that the functional form preferred for this does not have an explicit jam density that will induce zero speed in traffic. We deduce that it is zero speed that induces jam density in traffic rather than vice versa, so that the direction of causality between speed and density differs according to circumstances. We develop an approach to modelling traffic in light of this. We apply this to analyse speed control as a traffic management measure and show how it can be used to estimate the effect of speed management on road capacity.