31.7. 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.

Fundamental diagrams are graphical representations that show the relationships between key traffic parameters: flow (the number of vehicles passing a point), density (the number of vehicles per unit distance), and speed (how fast vehicles are moving). These diagrams are essential tools in transportation engineering for analyzing traffic flow characteristics and behavior.

Think of a water flow system, where you can visualize how many liters of water flow through a pipe (flow) depending on how full the pipe is (density) and how fast the water is moving (speed). Just like different relationships in the water system, traffic parameters are interrelated and can be represented graphically.

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 diagrams of traffic flow. Some characteristics of an ideal flow-density relationship is listed below:

1. When the density is zero, flow will also be zero, since there are no vehicles on the road.
2. When the number of vehicles gradually increases, the density as well as flow increases.
3. 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.
4. 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.

The flow-density curve illustrates how vehicle flow changes with varying densities. Initially, as density increases with more vehicles on the road, flow also increases. However, beyond a certain point, additional vehicles lead to congestion, resulting in decreased flow. The maximum flow occurs at a specific density, which is where the road operates most efficiently before reaching jam condition.

Imagine a busy restaurant. When it is empty (zero density), no one is seated (zero flow). As more diners arrive, the restaurant becomes busy (increasing density), and more tables are filled (increasing flow). Eventually, if too many people arrive, diners must wait for tables (jam density) and no new guests can be seated (zero flow). This represents how traffic behaves on the road.

Similar to the flow-density relationship, speed will be maximum, referred to as the free flow speed, and when the density is maximum, the speed will be zero. The most simple assumption is that this variation of speed with density is linear. Corresponding to the zero density, vehicles will be flowing with their desired speed, or free flow speed. When the density is jam density, the speed of the vehicles becomes zero.

The speed-density diagram depicts how vehicle speed changes with varying densities on the road. At low density (few cars), vehicles can travel at their maximum speed, known as free flow speed. As density increases, speed decreases until it reaches zero at jam density (when the road is fully congested). This relationship helps us understand how traffic conditions directly affect vehicle speeds.

Think of a crowded amusement park ride. When the line is short (low density), thrill-seekers enjoy the full speed of the ride (free flow speed). As more people come, it slows down due to loading and safety checks. At maximum capacity (jam density), no one is moving; everyone is just waiting their turn.

The relationship between the speed and flow can be postulated as follows. The flow is zero either because there are no vehicles or there are too many vehicles so that they cannot move. At maximum flow, the speed will be in between zero and free flow speed.

The speed-flow relationship highlights how vehicle speed varies with the flow of traffic. When the flow is zero, indicating that there are no vehicles or all vehicles are in a jam, the speed naturally is also zero. As flow increases to its maximum (the capacity of the road), the speed will be neither too fast nor too slow, settling somewhere between zero and the maximum speed.

Imagine a traffic signal that allows cars to move freely. When the light is red, no cars move (zero flow, zero speed). When the light turns green, cars start flowing through at various speeds, eventually reaching a point where the road is optimally filled (maximum flow). Ideally, cars can move at a steady speed that's neither too fast nor too slow – it's just right for the road's capacity.

The diagrams shown in the relationship between speed-flow, speed-density, and flow-density are called the fundamental diagrams of traffic flow.

Combined diagrams synthesize the relationships represented in the speed-flow, speed-density, and flow-density diagrams into a single visual representation. This integration helps traffic engineers analyze and predict traffic flow behaviors more holistically, enabling better traffic management and design.

Consider a traffic management system that uses a dashboard to show various metrics. Each metric (speed, density, flow) is represented in a separate graph. A comprehensive dashboard that combines all these graphs into one provides a clearer understanding of overall traffic behavior, just like how combined diagrams help recognize patterns in traffic flow.

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