Fundamental diagrams of traffic flow

The relation between flow and density, density and speed, speed and flow, can be represented with the help of some curves. They are referred to as the fundamental diagrams of traffic flow. They will be explained in detail one by one below.

Flow-density curve

The flow and density varies with time and location. The relation between the density and the corresponding flow on a given stretch of road is referred to as one of the fundamental diagram of traffic flow. Some characteristics of an ideal flow-density relationship is listed below:

When the density is zero, flow will also be zero,since there is no vehicles on the road.
When the number of vehicles gradually increases the density as well as flow increases.
When more and more vehicles are added, it reaches a situation where vehicles can't move. This is referred to as the jam density or the maximum density. At jam density, flow will be zero because the vehicles are not moving.
There will be some density between zero density and jam density, when the flow is maximum. The relationship is normally represented by a parabolic curve as shown in figure 1

**Figure 1:** Flow density curve
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The point O refers to the case with zero density and zero flow. The point B refers to the maximum flow and the corresponding density is $k_{max}$ . The point C refers to the maximum density $k_{jam}$ and the corresponding flow is zero. OA is the tangent drawn to the parabola at O, and the slope of the line OA gives the mean free flow speed, ie the speed with which a vehicle can travel when there is no flow. It can also be noted that points D and E correspond to same flow but has two different densities. Further, the slope of the line OD gives the mean speed at density

and slope of the line OE will give mean speed at density

. Clearly the speed at density

will be higher since there are less number of vehicles on the road.