engineering

Fundamental diagram of traffic flow

Fundamental diagram of traffic flow is a engineering topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Fundamental diagram of traffic flow rather than just read about it. In short: The fundamental diagram of traffic flow is a diagram that gives a relation between road traffic flux (vehicles/hour) and the traffic density (vehicles/km). A macroscopic traffic model involving traffic flux, traffic density and velocity forms the basis of the fundamental diagram.

Key takeaways

Fundamental diagram of traffic flow belongs to engineering; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Fundamental diagram of traffic flow to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Fundamental diagram of traffic flow from memory before moving on to harder problems.

Reference excerpt

The fundamental diagram of traffic flow is a diagram that gives a relation between road traffic flux (vehicles/hour) and the traffic density (vehicles/km). A macroscopic traffic model involving traffic flux, traffic density and velocity forms the basis of the fundamental diagram. It can be used to predict the capability of a road system, or its behaviour when applying inflow regulation or speed limits.

Basic statements There is a connection between traffic density and vehicle velocity: The more vehicles are on a road, the slower their velocity will be. To prevent congestion and to keep traffic flow stable, the number of vehicles entering the control zone has to be smaller or equal to the number of vehicles leaving the zone in the same time. At a critical traffic density and a corresponding critical velocity the state of flow will change from stable to unstable. If one of the vehicles brakes in unstable flow regime the flow will collapse. The primary tool for graphically displaying information in the study of traffic flow is the fundamental diagram. Fundamental diagrams consist of three different graphs: flow-density, speed-flow, and speed-density. The graphs are two dimensional graphs. All the graphs are related by the equation “flow = speed * density”; this equation is the essential equation in traffic flow. The fundamental diagrams were derived by the plotting of field data points and giving these data points a best fit curve. With the fundamental diagrams researchers can explore the relationship between speed, flow, and density of traffic.

Speed-density The speed-density relationship is linear with a negative slope; therefore, as the density increases the speed of the roadway decreases. The line crosses the speed axis, y, at the free flow speed, and the line crosses the density axis, x, at the jam density. Here the speed approaches free flow speed as the density approaches zero. As the density increases, the speed of the vehicles on the roadway decreases. The speed reaches approximately zero when the density equals the jam density.

Flow-density In the study of traffic flow theory, the flow-density diagram is used to determine the traffic state of a roadway. Currently, there are two types of flow density graphs: parabolic and triangular. Academia views the triangular flow-density curve as more the accurate representation of real world events. The triangular curve consists of two vectors. The first vector is the freeflow side of the curve. This vector is created by placing the freeflow velocity vector of a roadway at the origin of the flow-density graph. The second vector is the congested branch, which is created by placing the vector of the shock wave speed at zero flow and jam density. The congested branch has a negative slope, which implies that the higher the density on the congested branch the lower the flow; therefore, even though there are more cars on the road, the number of cars passing a single point is less than if there were fewer cars on the road. The intersection of freeflow and congested vectors is the apex of the curve and is considered the capacity of the roadway, which is the traffic condition at which the maximum number of vehicles can pass by a point in a given time period. The flow and capacity at which this point occurs is the optimum flow and optimum density, respectively. The flow density diagram is used to give the traffic condition of a roadway. With the traffic conditions, time-space diagrams can be created to give travel time, delay, and queue lengths of a road segment.

Speed-flow

Speed – flow diagrams are used to determine the speed at which the optimum flow occurs. There are currently two shapes of the speed-flow curve. The speed-flow curve also consists of two branches, the free flow and congested branches. The diagram is not a function, allowing the flow variable to exist at two different speeds. The flow variable existing at two different speeds occurs when the speed is higher and the density is lower or when the speed is lower and the density is higher, which allows for the same flow rate. In the first speed-flow diagram, the free flow branch is a horizontal line, which shows that the roadway is at free flow speed until the optimum flow is reached. Once the optimum flow is reached, the diagram switches to the congested branch, which is a parabolic shape. The second speed flow diagram is a parabola. The parabola suggests that the only time there is free flow speed is when the density approaches zero; it also suggests that as the flow increases the speed decreases. This parabolic graph also contains an optimum flow. The optimum flow also divides the free flow and congested branches on the parabolic graph.

Macroscopic fundamental diagram A macroscopic fundamental diagram (MFD) is type of traffic flow fundamental diagram that relates space-mean flow, density and speed of an entire network with n number of links as shown in Figure 1. The MFD thus represents the capacity, μ ( n ) {\displaystyle \mu (n)} , of the network in terms of vehicle density with μ 1 {\displaystyle \mu _{1}} being the maximum capacity of the network and η {\displaystyle \eta } being the jam density of the network. The maximum capacity or “sweet spot” of the network is the region at the peak of the MFD function.

Flow The space-mean flow, q ¯ {\displaystyle {\bar {q}}} , across all the links of a given network can be expressed by:

… excerpt ends here. Continue reading the full article.

Illustrations

Worked examples

Example 1 — a first encounter with Fundamental diagram of traffic flow

Start with the simplest possible case. Write down what Fundamental diagram of traffic flow claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In engineering, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Fundamental diagram of traffic flow before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Fundamental diagram of traffic flow ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Fundamental diagram of traffic flow

In research: Fundamental diagram of traffic flow appears in engineering research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Fundamental diagram of traffic flow in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Fundamental diagram of traffic flow is common in secondary-school and first-year university syllabi. It links to neighbouring topics Road transport, Transportation engineering, so understanding it makes those chapters shorter.
In everyday life: Look for Fundamental diagram of traffic flow outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Fundamental diagram of traffic flow” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Fundamental diagram of traffic flow in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Fundamental diagram of traffic flow means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Fundamental diagram of traffic flow out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Fundamental diagram of traffic flow in simple terms?

Why does Fundamental diagram of traffic flow matter?

Because it connects several engineering ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Fundamental diagram of traffic flow?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Fundamental diagram of traffic flow.