Modeling of Traffic Flow on Freeways in Fundamental Diagrams

The traffic flow on freeways is described traditionally with help of three parameters: space-mean speed v, time-mean traffic flow rate q, and space-mean traffic density k. The functional relationship between these three parameters is called Fundamental Diagram. The three parameters can in general be determined by measurements. These three parameters are associated by the fundamental relationship q = v · k with each other. Accordingly, the Fundamental Diagram is then defined clearly, if a function is defined between two of the three parameters. The Fundamental Diagram is featured by the following parameters: desire speed V₀, maximum jam density k_max, maximum traffic flow rate q_max (=capacity C), and optimal density k_opt that is corresponding to q_max. The relationship between traffic density k, traffic flow rate q, and speed v — represented in the q-v Diagram — forms the elementary Knowledge for dimensioning of freeways and rural highways. The traffic flow rate q(k) attainable at a given traffic density k serves as a measure of quality of the traffic. However, one in general employs during the analysis of the traffic quality the k-v relationship since this functional relationship is monotonously falling here. The speed v decreases continuously with the increase in traffic density k. As an example, a measured k-v relationship (on German freeway A43) is represented at the left side in Figure 1.