Density Calculation from Detector Data

In traffic data analysis, there are three related types of data: speed, flow and density. Speed (miles per hour), is the best understood of these types, and some sensing systems can directly measure it. Flow is the rate in which vehicles arrive at a particular point on a roadway, described in terms of vehicles per hour. Traffic sensing systems usually record the traffic volume, which is the actual number of vehicles to arrive during a sampling period (e.g.. 30 seconds). Volume can be easily converted to a flow rate by multiplying the recorded volume by the number of sampling periods in an hour. Density is a measurement of how close vehicles are together, in vehicles per mile. With flow and speed measurements, density is easily calculated by dividing the flow rate by the speed:

Density (vehicles per mile)  = Flow (vehicles per hour) / Speed (miles per hour)

Unfortunately, older traffic sensing systems do not directly measure speed. In many cases, sensors provide only volume and occupancy, which is a percentage of time which the sensor is "occupied," by a vehicle. This presents some difficulties in determining both density and speed. Occupancy has a direct relationship to density, but that relationship is also affected by the average vehicle length and the sensitivity of the sensor. These two factors, taken together, are referred to as the average field length of the traffic sensor (usually described in feet).

Once the average field length of a sensor is known, it is trivial to convert occupancy data into density. Multiply the occupancy by the number of feet in a mile (5280), to determine the number of occupied feet per mile. Then divide the number of occupied feet per mile by the average field length to determine the number of vehicles per mile (density).

To compute the average field length for a sensor, it is necessary to take accurate speed and flow measurements, which can then be converted to density. Then multiply the recorded occupancy from the same sampling period by 5280 feet, to get the number of occupied feet per mile. After that, divide the number of occupied feet per mile by the measured density to determine the average field length for a sensor.

 

Last modified: 21 Apr 2000