Discontinuous periodic behaviour in a looped macroscopic model of traffic dynamics

A whole link model of traffic flow in which the link trip time varies linearly with link volume is investigated in the case where a fraction of the flow exiting the link is ‘re-injected’ as inflow, thus forming the link into a loop. The scenario where the fraction of flow re-injected linearly decreases as the volume of traffic on the link increases is considered. It is found that for certain parameter choices a continuous periodic inflow can lead to sharp post-transient discontinuities in periodic outflow. The conditions under which this type of behaviour can occur are considered.