Queue Length at a Traffic Light via Flow Theory

Let us consider the following design problem. Suppose we have a road which, under normal operation, has a traffic flow q of 1000 veh/h at a flow concentration k of 20 veh/mi. There are two intersections on this road, 0.2 mi miles apart. We wish to install a stoplight at one of these intersections. Our primary interest is whether the queue which forms at the downstream light backs up to the upstream intersection (see Figure 11.1). Clearly, if the downstream queue does interfere with the operation of the upstream intersection, then other considerations must be made, possibly installing a synchronized light at the upstream intersection.