# The relationship between traffic flow speed and density

### Fundamentals of Transportation/Traffic Flow - Wikibooks, open books for an open world

The speed-density relationship is linear with a negative slope; therefore, as the density increases the speed of the. The fundamental traffic flow characteristics are flow, speed, and density. Analysts can easily obtain the relationship between traffic density and average. and space mean speed and the relationship between them will be discussed in detail The relation- ship between the fundamental parameters of traffic flow . tion between flow(q), density(k) and mean speed vs is, q = k × vs.

### Speed-Flow-Density Relationship

Traffic phases in a the microscopic fundamental diagram truncated triangular Traffic phases in the queueing cumulative input-output Newell diagram Microscopic Models[ edit ] Microscopic models predict the following behavior of cars their change in speed and position as a function of the behavior of the leading vehicle. Macroscopic Models[ edit ] Macroscopic traffic flow theory relates traffic flow, running speed, and density. Analogizing traffic to a stream, it has principally been developed for limited access roadways Leutzbach Many empirical studies have quantified the component bivariate relationships q vs.

**Relationship between Speed, Density & Volume - Traffic Engineering**

The most widely used model is the Greenshields model, which posited that the relationships between speed and density is linear. These were most appropriate before the advent of high-powered computers enabled the use of microscopic models.

Macroscopic properties like flow and density are the product of individual microscopic decisions. Yet those microscopic decision-makers are affected by the environment around them, i. While traffic flow theorists represent traffic as if it were a fluid, queueing analysis essentially treats traffic as a set of discrete particles.

These two representations are not-necessarily inconsistent. 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.

### Fundamental relations of traffic flow

There will be some density between zero density and jam density, when the flow is maximum. Flow density curve The point O refers to the case with zero density and zero flow.

- Navigation menu

The point B refers to the maximum flow and the corresponding density is. The point C refers to the maximum density 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.