Abstract The traffic shock-wave theory of Lighthill and Whitham is applied to a general incident, i.e. a moving incident with filtering (overtakings). It is shown that individual and total delays and the related costs can be determined simply by graphical means. A formulation, which is independent of any particular macroscopic theory of traffic flow, is obtained for the total delay upstream of the incident. It is shown to be identical to that obtained by using deterministic queuing theory. Simple incidents such as a red traffic signal light and a slow truck in a no passing zone are shown to be special cases.