Delay at signal controlled junctions operating within but near to capacity

The strong effect of carry over or overflow from one cycle to the next on delay in a signal controlled traffic stream operating near to capacity is analysed. A model is given for a signal controlled junction and a corresponding procedure for calculating whether given arrival rates of traffic are within the capacity of the junction is outlined. It is shown in outline that if they are, then delay minimising timings can be found iteratively. The reasons why this is the case are illustrated geometrically for a simple junction (a).