Discrete Models of Traffic Flow (2-2)

Fundametal Diagram and Flow Diagram 2

Flow Diagram

Despite its central role in the analysis of traffic flow, the fundamental diagram has its limitations. After all, a given traffic flow is represented in fundamental diagram as a single value of F. Naturally, different types of flow pattern with different mode of congestion can still result in the same value of F, and they cry for a way to express their difference. A convenient way to depict the spatial and temporal patterns is the flow diagram.

To obtain a flow diagram, we fix a time step and represent the location of the cars on a road as a symbol on otherwise blank horizontal line that represents empty road. Just below this line, we place another line with symbols representig the cars at next time step, and repeat this process. The perpendicular line then represents the time evolution from top to bottom. We show an example of a flow diagram constructed in this way.

Here on the horizontal line, "." stands for an empty cell, and "C" stands for a cell with a car. The block with many "C"s next to each other represents the traffic jam. To make the movement of the car visible, one car which is at the left-most position at the start is maked in blue, and the second preceding car is marked red. The way those car get sucked into the jamming block, inside of which they stop moving, is clearly seen in this flow diagram. It is also visible that the jamming block moves backward one cell at each step.