Greenshields model was developed to aid our understanding of uninterrupted flow. Unfortunately, Greenshields model is unable to cope with the added complexities that are generated under interrupted flow conditions. Interrupted flow requires an understanding of Queuing Theory, which is an entirely separate model of traffic flow.
Queuing Theory can be used to analyze the flow of traffic on the approach to and through an intersection controlled by a traffic signal. This is accomplished by analyzing the cumulative passage of vehicles as a function of time. The queuing diagram for interrupted flow shows the flow on one intersection approach. Traffic is stopped from time t1 to t2 during the red signal interval. At the start of the green interval (t2), traffic begins to leave the intersection at the saturation flow rate (qG), and continues until the queue is exhausted. Thereafter, the departure rate D(t), equals the arrival rate, A(t), until t3, which is the beginning of the next red signal. At this point, the process starts over.
For further information on Queing Theory, consult the chapter entitled "Signal
Queuing Diagram for Interrupted Flow1.) Papacostas , C.S. and Prevedouros, P.D., Transportation Engineering and Planning, 2 nd Edition, Prentice Hall, Englewood Cliffs, New Jersey, 1993