Capacities, especially at bottlenecks

An important concept is capacity. The capacity of a link is its maximum flow. As we see from our fundamental diagrams, this looks like a fairly well-defined quantity. For field measurements, a question is which time averages one wants to use. Another question comes up when traffic can ``break down'', something that we have not discussed in this course.

However, in city traffic, the main obstruction to flow is not the dynamics along the link, but the dynamics at intersections. As an approximate number, an unobstructed link has a capacity of 2000 vehs/hour/lane. If at the end of the link we have a traffic light which is green half of the time, then the result will be a link capacity of approximately 1000 vehs/hour/lane. This is a time-averaged number; we have already learned how to describe queue dynamics at traffic lights more realistically via kinematic waves. Here, we will however use the time-averaged description.

If, via the link, there are more cars flowing towards the node than the node can process, then a queue will form. The density inside that queue can be found via the fundamental diagram by going to the high density branch for the given node capacity (point ``A'' in Fig. 27.13). In consequence, in a situation where the node capacity is smaller than the link capacity, certain density ranges of the fundamental diagram do not occur under steady state conditions.

Figure 27.13: Fundamental diagrams when node capacity is smaller than link capacity.