# Speed and flow relationship

### Model of Traffic Speed-Flow Relationship at Signal Intersections

Download scientific diagram | Speed -flow relationship (The Highway Capacity Manual) from publication: Towards reducing traffic congestion using cooperative . The speed-density relationship is linear with a negative slope; therefore, as the density increases the speed of the roadway. The fundamental traffic flow characteristics are flow, speed, and density. Analysts can easily obtain the relationship between traffic density and average.

Two of them were approximate. Thus, the model of time-headway is reasonable. Regressive analysis between position of queued vehicles and start-up time. Comparison to the Tr reaction time. Fitted model for the Ht-V relationship. Speed-Flow Relationship The final power exponential function of Ht-V is fitted by the combined data intersection A and intersection Bwhich is showed in Figure 5.

The relationship between traffic flow rate Q and time-headway Ht is as follows: In the speed-flow relationship, the Q increases gradually with the speed increases after vehicle starting-up.

The constant parameters a and c are greater than zero, and b is smaller than zero but greater than negative one. The value c represents the reaction time of drivers.

The traditional quadratic polynomial model Greenshields model, Equation 1 is compared with the S-shaped curve model. The blue dotted line is quadratic polynomial model and the red line is S-shaped curve model in Figure 6.

### FLOW, SPEED, and DENSITY

There is no significant difference for two models when speed is in a low level. However, when the flow reaches to saturation flow, the flow rate tends to decrease for Greenshields model. This does not comply with the actual situation.

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- Fundamental diagram of traffic flow

At this time, there are some errors for the Greenshields model when speed is zero. 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.

### Fundamental diagram of traffic flow - Wikipedia

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[ edit ] 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.

## FLOW, SPEED, and DENSITY

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[ edit ] 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.